Safety Research :

Safety, Risk, Reliability and Quality:

Statistic, Probability and Uncertainty :

IN MEMORY OF Yu. BELIAEV	35-37

Editorial

The Gnedenko Forum is deeply saddened to announce the death, at the age of 93 of one of the leading experts in probability theory, mathematical statistics and their applications, Doctor of Physical and Mathematical Sciences, Professor, Laureate of the State Prize of the USSR YURI KONSTANTINOVICH BELYAEV (31 August 1932, Moscow - 22 January 2025, Umeå, Sweden).

A NEW GENERALIZED EXPONENTIATED FAMILY OF CONTINUOUS DISTRIBUTIONS WITH APPLICATIONS TO ENVIRONMENTAL DATA SETS	38-52

Ibrahim, Sule, Olalekan Akanji, Bello, Ismail Adekunle, Kolawole

Different researchers in the field of distribution theory have derived new models for generalizing the classical ones to make them more flexible and to aid their application in various fields. This generalization and extension of the classical models is mostly done using families of distributions. This article presents a new family of distributions called the Exponentiated Pareto-G family of distributions with two positive shape parameters. Some statistical properties of the new family of distributions, such as explicit expressions for the quantile function, probability-weighted moments, moments, generating function, Reliability function, hazard function, and order statistics are discussed. A maximum likelihood estimation technique is employed to estimate the model parameters. Two submodels such as Weibull and Frechet distributions are employed to check the fit of the family of distributions with the aid of their pdf and hazard function plots. Also, a simulation study is presented to assess the performance of the maximum likelihood estimator. Furthermore, two real-life applications are carried out to assess the fit and flexibility of the new family using the Weibull model as the baseline. The results showed that the new distribution fits better in the two real data sets considered among the range of distributions considered.

Cite: Ibrahim, Sule, Olalekan Akanji, Bello, Ismail Adekunle, Kolawole A NEW GENERALIZED EXPONENTIATED FAMILY OF CONTINUOUS DISTRIBUTIONS WITH APPLICATIONS TO ENVIRONMENTAL DATA SETS. Reliability: Theory & Applications. 2025, March 1(82):38-52. DOI: https://doi.org/10.24412/1932-2321-2025-182-38-52

A WEIGHTED THREE-PARAMETER XGAMMA DISTRIBUTION WITH PROPRTIES AND ITS APPLICATION TO REAL LIFE DATA	53-66

P. Pandiyan, Athira D V

In this article, a weighted three-parameter Xgamma distribution has been proposed. It is an extension of two-parameter Xgamma distribution. The weighted three-parameter Xgamma distribution designed for modelling real-life data. The density function and cumulative distribution function, moments, hazard and survival function, moment-generating function and characteristic function, Bonferroni and Lorenz curve, renyi entropy of this distribution have all been derived. The parameter of this distribution is estimated by maximum likelihood estimation method. Finally, an application of the model to a real-life data set is presented and compared with some other existing distributions.

Cite: P. Pandiyan, Athira D V A WEIGHTED THREE-PARAMETER XGAMMA DISTRIBUTION WITH PROPRTIES AND ITS APPLICATION TO REAL LIFE DATA. Reliability: Theory & Applications. 2025, March 1(82):53-66. DOI: https://doi.org/10.24412/1932-2321-2025-182-53-66

STRESS-STRENGTH MODELLING: RANKED SET AND SIMPLE RANDOM SAMPLING IN GENERALIZED INVERSE WEIBULL ANALYSIS	67-79

Surinder Kumar, Bhupendra Meena, Rahul Shukla, Shivendra Pratap Singh

This study explores the stress-strength reliability model (P) for Generalized Inverse Weibull (GIW) distribution through transformation techniques. We compare two sampling methods: ranked set sampling (RSS) and simple random sampling (SRS), where stress and strength are two independent random variables from the GIW distribution respectively. RSS, is used for estimating stress-strength model, as this technique of sampling is more efficient alternative of SRS for obtaining the more informative sample. In this article, the maximum likelihood estimator (MLE) for stress-strength model is obtained through transforming technique. MLE estimates of stress-strength obtained through Ranked set sampling (RSS) methods are evaluated against corresponding estimates derived from simple random sampling (SRS) to understand their relative effectiveness and accuracy. The statistical estimators derived from Ranked Set Sampling (RSS) methodology exhibit superior efficiency relative to their Simple Random Sampling (SRS) counterparts. The empirical utility of RSS-based estimation procedures is subsequently validated through application to real datasets.

Cite: Surinder Kumar, Bhupendra Meena, Rahul Shukla, Shivendra Pratap Singh STRESS-STRENGTH MODELLING: RANKED SET AND SIMPLE RANDOM SAMPLING IN GENERALIZED INVERSE WEIBULL ANALYSIS. Reliability: Theory & Applications. 2025, March 1(82):67-79. DOI: https://doi.org/10.24412/1932-2321-2025-182-67-79

AGRICULTURAL PRODUCTION PATTERNS IN TAMIL NADU: INSIGHTS FROM VECTOR AUTOREGRESSIVE ANALYSIS USING PYTHON PROGRAMMING	80-91

R. Kamalanathan, A. Sheik Abdullah, A. Jawahar Farook

Understanding agricultural production patterns is crucial for enhancing productivity and ensuring food security. This study explores the dynamics of agricultural production in Tamil Nadu using the Vector Autoregressive (VAR) model to capture the interdependence among various crop yields and rainfall over time. Employing Python programming for data analysis and modeling, the study leverages historical time-series data to identify trends, forecast production, and analyze the impact of external shocks on agricultural outputs. The research incorporates preprocessing techniques to ensure stationarity, optimal lag selection using Akaike’s Information Criterion(AIC) and Bayesian Information Criterion(BIC), and diagnostic checks for model accuracy and stability. The findings provide insights into the temporal relationships among various crops and rainfall. Additionally, Impulse Response Functions(IRF) and variance decomposition analyses offer a deeper understanding of how shocks to one variable propagate through the system. The study demonstrates the utility of Python-based VAR models in agricultural forecasting and decision-making, offering policymakers and stakeholders a robust tool to improve resource allocation and agricultural planning in Tamil Nadu. This work highlights the potential of data-driven approaches to address challenges in the agricultural sector effectively.

Cite: R. Kamalanathan, A. Sheik Abdullah, A. Jawahar Farook AGRICULTURAL PRODUCTION PATTERNS IN TAMIL NADU: INSIGHTS FROM VECTOR AUTOREGRESSIVE ANALYSIS USING PYTHON PROGRAMMING . Reliability: Theory & Applications. 2025, March 1(82):80-91. DOI: https://doi.org/10.24412/1932-2321-2025-182-80-91

APPLICATION OF FUZZY DYNAMIC GROUP MULTI-CRITERIA DECISION MAKING BASED ON Z-NUMBERS	92-104

Kamala Aliyeva

Dynamic group multi-criteria decision making is essential for making informed, balanced, and adaptive decisions in complex and evolving environments. By integrating multiple methodologies and considering the dynamic nature of criteria and group interactions, dynamic group multi-criteria decision making provides a robust framework for decision-making across various fields and applications. Dynamic group fuzzy multi-criteria decision making under Z-information is a sophisticated approach that incorporates the dynamic aspects of decision making, the involvement of multiple stakeholders, and the use of fuzzy logic to handle uncertainties and imprecise information. Z-information refers to a type of uncertain information that combines fuzzy numbers and Z-numbers, where Z-numbers account for both the reliability of the information and its fuzziness. By integrating fuzzy logic and Z-numbers, it effectively handles dual uncertainties of fuzziness and reliability, while dynamically adapting to changes in criteria and stakeholder preferences. In this article, a dynamic multi-criteria decision-making model is proposed to solve strategic vendor selection problems that need to be evaluated in different time periods and involve uncertainty. Z-information is used to express uncertainty and in the proposed model, the decision-making group is asked to evaluate the alternatives in different time periods, and the evaluations made for these different periods are combined.

Cite: Kamala Aliyeva APPLICATION OF FUZZY DYNAMIC GROUP MULTI-CRITERIA DECISION MAKING BASED ON Z-NUMBERS . Reliability: Theory & Applications. 2025, March 1(82):92-104. DOI: https://doi.org/10.24412/1932-2321-2025-182-92-104

A NEW CLASS OF COS-G FAMILY OF DISTRIBUTIONS WITH APPLICATIONS	105-123

Pankaj Kumar, Laxmi Prasad Sapkota, Vijay Kumar

This paper introduces a novel family of probability distributions, termed the Cos-G family, which is derived from a trigonometric transformation approach. We present the general structural properties of this family and focus on one of its unique members. This newly proposed distribution, formulated from the inverse Weibull distribution, exhibits flexible hazard rate shapes, including reverse-J, increasing, and inverted bathtub forms. We investigate its fundamental statistical properties and employ the maximum likelihood estimation method to estimate its parameters. The performance of the estimation technique is assessed through a Monte Carlo simulation, revealing that biases and mean square errors decrease as sample size increases, ensuring reliable parameter estimation even for small samples. To illustrate its practical applicability, we fit the suggested model to three real-world datasets and compare its performance against existing models using various goodness-of-fit measures and model selection criteria. The results confirm the superiority of the proposed model in capturing complex data structures.

Cite: Pankaj Kumar, Laxmi Prasad Sapkota, Vijay Kumar A NEW CLASS OF COS-G FAMILY OF DISTRIBUTIONS WITH APPLICATIONS. Reliability: Theory & Applications. 2025, March 1(82):105-123. DOI: https://doi.org/10.24412/1932-2321-2025-182-105-123

SOME APPLICATIONS OF EXPONENTIATED LOG-UNIFORM DISTRIBUTION	124-134

Anu AV, Rani Sebastian

In this paper we introduced Exponentiated Log - Uniform distribution as a generalisation of the Log - Uniform distribution and its properties are studied. We provide graphical representations of its density function, cumulative distribution function, hazard rate function, and survival function. And derive various statistical properties such as moments, mean deviations, and quantile function of the new distribution. We also obtain the probability density functions of the order statistics of the Exponentiated Log-Uniform Distribution.To estimate the parameters of the distribution and the stress strength parameters, we use the maximum likelihood method, and validate the estimates of the model parameters through a simulation study. Our findings reveal that the Exponentiated Log-Uniform Distribution exhibits the least bias and that the values of the mean square error decrease as the sample size increases, indicating the effectiveness of this distribution in modeling real-world data. We applied the Exponentiated Log-Uniform distribution to a real data set and compared it with Exponentiated Quasi Akash Distribution and Exponentiated Weibull Distribution. It was found that the new distribution was a better fit than the other distributions based on the values of the AIC, CAIC, BIC, HQIC, the Kolmogorov-Smirnov (K-S) goodness-of-fit statistic and the p-values.

Cite: Anu AV, Rani Sebastian SOME APPLICATIONS OF EXPONENTIATED LOG-UNIFORM DISTRIBUTION. Reliability: Theory & Applications. 2025, March 1(82):124-134. DOI: https://doi.org/10.24412/1932-2321-2025-182-124-134

APPLICATIONS OF SIMULATIONS AND QUEUING THEORY IN SUPERMARKET	135-140

Shruti Gupta, Nishant Yadav, Khushwant Singh, Puneet Garg

This paper describes the role of queuing theory in supermarket or shopping complex. Generally, a supermarket is a place where people are gathered to purchase the daily requirement products and here, a queue represents the customers/items in ascending or descending order. An interesting aspect of queuing process resides in the measures of its system’s performance especially in terms of average service rate and system’s utilization. Simulation is a powerful and versatile tool for modeling facilities in supermarket. So, queuing process with simulation provide the average service rate and it helps in predicting queue lengths as well as waiting durations when multiple items are manufactured and distributed using first come first serve discipline. M/M/s model and poisson process are used to explore the supermarket with server arrival rate and service rate.

Cite: Shruti Gupta, Nishant Yadav, Khushwant Singh, Puneet Garg APPLICATIONS OF SIMULATIONS AND QUEUING THEORY IN SUPERMARKET. Reliability: Theory & Applications. 2025, March 1(82):135-140. DOI: https://doi.org/10.24412/1932-2321-2025-182-135-140

ALPHA POWER TRANSFORMED WEIBULL LOMAX DISTRIBUTION: PROPERTIES AND ITS APPLICATIONS	141-156

Fathima Thensi N, Nazeema Beevi.T

We proposed a new model called the Alpha Power Transformed Weibull-Lomax (APTWL) distribution which extends the Weibull Lomax distribution and have an increasing, decreasing and bathtub shapes for the hazard rate function. Various structural properties of the new distribution are derived including moments, probability weighted moments, generating and quantile function. The Renyi and q entropies are also obtained. Statistical inference is presented for the APTWL distribution using the method of maximum likelihood estimation to estimate the parameters of proposed distribution. The potentiality of the new model is illustrated by means of three real life datasets. The results of the analysis of the datasets show the superiority of APTWL distribution over some compared distributions.

Cite: Fathima Thensi N, Nazeema Beevi.T ALPHA POWER TRANSFORMED WEIBULL LOMAX DISTRIBUTION: PROPERTIES AND ITS APPLICATIONS. Reliability: Theory & Applications. 2025, March 1(82):141-156. DOI: https://doi.org/10.24412/1932-2321-2025-182-141-156

ALTERNATE QUADRA-SUBMERGING POLAR FUZZY GRAPH AND ITS DECISION MAKING ANALYSIS	157-171

Anthoni Amali A, J . Jesintha Rosline, Aruna G

In this article, the two extreme values [-1,1] is proposed with it’s uncertain submerging values [-0.5,0.5] as the Alternate Quadra Submerging Polar (AQSP) Fuzzy Graph. The AQSP Fuzzy graph COVID-19 vaccines survey model has been analyzed to find the highest and the lowest membership and the non-membership value of the five influencing factors effectively. The notion of the AQSP fuzziness has been considered from the various points of view, in the specification of variables with the multiple input of single output rule. The self-reporting nature of the collected survey data of the COVID - 19 Booster shots acceptance and the non-acceptance values between [-1,0] and [0,1] converges precisely with the level of fixation [-0.5.0] and [0,0.5] alternatively by using the uncertain values in decision making process of the human behaviours in mathematical Analysis.

Cite: Anthoni Amali A, J . Jesintha Rosline, Aruna G ALTERNATE QUADRA-SUBMERGING POLAR FUZZY GRAPH AND ITS DECISION MAKING ANALYSIS. Reliability: Theory & Applications. 2025, March 1(82):157-171. DOI: https://doi.org/10.24412/1932-2321-2025-182-157-171

A PRODUCTION INVENTORY MODEL FOR DETERIORATING ITEMS WITH TIME AND PRICE RELIANT DEMAND USING FLOWER POLLINATION OPTIMIZATION	172-188

Amit Kumar, Ajay Singh Yadav, Dharmendra Yadav

Effective management of production inventory for deteriorating items with dynamic demand patterns is crucial for businesses operating in today’s competitive markets. This paper proposes a comprehensive model that addresses the complexities arising from the dual storage locations, item deterioration, and demand dependencies on both time and selling price. To optimize the decision variables associated with production and inventory control, we employ the Flower Pollination Optimization (FPO) algorithm, a nature-inspired meta-heuristic known for its ability to efficiently navigate complex search spaces. The two-storage production inventory model integrates the dynamics of item deterioration over time, capturing the real-world challenges faced by supply chain managers. The demand for items is modeled to be sensitive to both temporal variations and changes in selling prices, reflecting the intricate nature of market dynamics. Our approach leverages the FPO algorithm to explore and exploit the solution space, allowing for the identification of optimal or near-optimal strategies for production quantities, order quantities, and inventory levels. The FPO algorithm mimics the pollination process in nature, striking a balance between exploration and exploitation to efficiently search for solutions in a highly dynamic and nonlinear environment. The proposed model and optimization approach are validated through extensive simulations and sensitivity analyses. The results demonstrate the effectiveness of the FPO algorithm in finding robust solutions that enhance inventory management, mitigate deterioration-related losses, and adapt to varying demand scenarios. This research contributes to the field of supply chain optimization by offering a novel perspective on tackling the challenges associated with dual storage, item deterioration, and demand dependencies. The findings provide valuable insights for practitioners seeking advanced strategies for optimizing their production inventory systems in the face of evolving market conditions.

Cite: Amit kumar, Ajay Singh Yadav, Dharmendra Yadav A PRODUCTION INVENTORY MODEL FOR DETERIORATING ITEMS WITH TIME AND PRICE RELIANT DEMAND USING FLOWER POLLINATION OPTIMIZATION. Reliability: Theory & Applications. 2025, March 1(82):172-188. DOI: https://doi.org/10.24412/1932-2321-2025-182-172-188

A FAILURE DISTRIBUTION FOR RELIABILITY PREDICTION OF MECHATRONIC COMPONENTS AND HUMAN-MACHINE SYSTEM	189-197

Iftikhar Chalabi

Modern machines and equipment’s have a complex mechatronic structure consisting of various components, and their reliability depends on a large number of random factors that arise during design, production and operation, which are often impossible to predict. Each element of the modern machines is characterized by different performance criteria and corresponding failures. Various statistical models of failure distribution are widely used to quantify the reliability of machines and devices. The choice of a statistical model and its parameters is important for a proper assessment of reliability. The chosen statistical model should reflect the actual distribution of failures fairly correctly. In presented article is proposed a new failure distribution for reliability prediction of mechatronic components of modern machines and human-machine systems. A large number of sudden failures of modern complex technical facilities containing electronic and mechatronic structural elements seriously affect its λ-characteristic. Various studies have already shown that the failure behavior of complex systems cannot always be characterized by the "bathtub curve". This is especially true for modern complex machines, which, among other things, consist of numerous electronic components for which no wear and fatigue failures are assumed. For this reason, an alternative service life distribution for the description failure behavior of modern mechatronic components and human-machine systems is proposed. This is about the failure curves, which are initially characterized by a low or high failure rate and then tend to a constant failure rate. To determine the reliability indexes are provided analytical formulas. Methods for estimating the parameters of this distribution are presented based on failure statistic. To determine distribution parameters, statistical data on failures of the technical system are sufficient only in the first period of its operation. This is one of the main advantages of the presented distribution. On the example of practical cases, the hypothesis of compliance of the proposed theoretical distribution to the actual statistical data on failures of various mechatronic systems and human-machine system was tested.

Cite: Iftikhar Chalabi A FAILURE DISTRIBUTION FOR RELIABILITY PREDICTION OF MECHATRONIC COMPONENTS AND HUMAN-MACHINE SYSTEM . Reliability: Theory & Applications. 2025, March 1(82):189-197. DOI: https://doi.org/10.24412/1932-2321-2025-182-189-197

MODERN APPROACHES TO MODELING RELIABLE AND EFFICIENT WATER SUPPLY SYSTEMS	198-205

M.T. Babayev, N.V. Budagova

The reliability of water supply systems plays a crucial role in ensuring sustainable water use, minimizing economic losses, and preventing failures in critical infrastructure. This paper proposes a mathematical approach to modeling the reliability of water systems based on probability theory and Markov processes. The main types of failures, their impact on operational characteristics, and economic consequences are examined. A simulation of the water supply network is conducted, considering the probabilistic characteristics of failures and recovery processes. The analysis of results demonstrates that the implementation of predictive monitoring methods and the optimization of maintenance strategies significantly enhance the resilience of water supply systems. The developed model can be applied in the planning of modernization and management of water supply infrastructure to improve its efficiency and economic feasibility.

Cite: M.T. Babayev, N.V. Budagova MODERN APPROACHES TO MODELING RELIABLE AND EFFICIENT WATER SUPPLY SYSTEMS . Reliability: Theory & Applications. 2025, March 1(82):198-205. DOI: https://doi.org/10.24412/1932-2321-2025-182-198-205

COMPARATIVE BAYESIAN ANALYSIS OF THE INVERSE TOPP-LEONE DISTRIBUTION	206-218

Aijaz Ahmad, Fathima Bi, Mahfooz Alam, Aafaq A. Rather, Danish Qayoom, Asgar Ali

This paper focuses on the Bayesian estimation of the shape parameter for the Inverse Topp-Leone (ITL) distribution. To achieve this, we employ both the extended Jeffrey’s prior and the gamma prior, facilitating the derivation of posterior distributions for the shape parameter. The Bayesian estimators are calculated under various loss functions, including the squared error loss function (SELF), entropy loss function (ELF), precautionary loss function (PLF), and Linex loss function (LLF), each chosen to address different practical scenarios and estimator biases. In addition to the Bayesian approach, we also explore maximum likelihood estimation (MLE) to provide a comparative benchmark. The performance of these estimators is assessed and compared based on mean squared error (MSE) across multiple sample sizes, allowing for a detailed evaluation of estimator robustness and accuracy. A real-world dataset is then analyzed to further demonstrate the relative efficiency of each estimator under the different loss functions, providing practical insights into the applicability of each estimation approach for the ITL distribution. This analysis offers a comprehensive perspective on the versatility and precision of Bayesian and classical estimation methods for the ITL model.

Cite: Aijaz Ahmad, Fathima Bi, Mahfooz Alam, Aafaq A. Rather, Danish Qayoom, Asgar Ali COMPARATIVE BAYESIAN ANALYSIS OF THE INVERSE TOPP-LEONE DISTRIBUTION . Reliability: Theory & Applications. 2025, March 1(82):206-218. DOI: https://doi.org/10.24412/1932-2321-2025-182-206-218

BAYESIAN SPATIAL TEMPORAL TREND ANALYSIS FOR DECISION MAKING AND RISK ASSESSMENT IN DENGUE INCIDENCE STUDIES: A CASE OF TAMILNADU	219-226

Jaisankar Ramasamy, Ranjani Murugesan

This study presents a Bayesian spatial-temporal analysis for studying Dengue incidence in Tamil Nadu, aiming to provide insights into decision-making and risk assessment strategies. Statistical models that allow a more accurate depiction of true disease rates by borrowing information from neighboring regions will help mitigate the effects of sparsely populated regions and deliver better inference. Perhaps the most conspicuous manner of modeling spatial dependence is to introduce spatially associated random effects within a Bayesian hierarchical setting. The Bayesian modeling and inferential framework are flexible and extremely rich in its capabilities to accumulate various scientific hypotheses and assumptions. The spatial and spatial temporal epidemiology is concerned with the description and analysis of spatial and spatial temporal variations in disease risk with respect to risk factors. As the primary aim of this work is to quantify the spatial disease pattern of dengue incidences apart from the mapping of disease modelling the disease and finding spatial clusters/hotpots is one important aspect in epidemiology is to find the temporal trends in or outside of clusters. In this study, a spatial-temporal trends model is fitted using the Leroux CAR prior’s set up for studying the spatial-temporal disease patterns with the estimation of the temporal trends with reference to dengue incidences in Tamil Nadu, India.

Cite: Jaisankar Ramasamy, Ranjani Murugesan BAYESIAN SPATIAL TEMPORAL TREND ANALYSIS FOR DECISION MAKING AND RISK ASSESSMENT IN DENGUE INCIDENCE STUDIES: A CASE OF TAMILNADU . Reliability: Theory & Applications. 2025, March 1(82):219-226. DOI: https://doi.org/10.24412/1932-2321-2025-182-219-226

OPTIMIZATION OF RESOURCE ALLOCATION USING INTEGER PROGRAMMING OF IMPROVED RATIO ESTIMATOR UNDER STRATIFIED RANDOM SAMPLING	227-241

Bhatt Ravi Jitendrakumar, Monika Saini, Ashish Kuma, Yashpal Singh Raghav

This paper provides a case study that illustrates how integer programming may be used to optimize resource allocation. With the known population median of the study variable acting as auxiliary data, an exponential ratio estimator is shown for estimating the finite population mean under stratified random sampling. The objective is to minimize a cost function within specific bounds. Using integer programming techniques and the Lagrange multiplier approach, we transform the proposed problem into an optimization problem with a linear cost function. This allows us to propose an optimal way for minimizing total costs while maintaining desired accuracy levels. We found that the suggested estimator performed better than methods involving stratified random sampling. Additionally, a numerical example is given to verify the theoretical conclusions for real-world applications. We go over how the problem was formulated, how to use LINGO software to solve it, and the results. It is advised to choose the estimator with the lowest MSE in real-world stratified random sampling situations. The strategy shows significant cost savings and efficient use of resources. The effectiveness of the recommended approach is demonstrated by testing the methodology on both simulated and real-world datasets.

Cite: Bhatt Ravi Jitendrakumar, Monika Saini, Ashish Kuma, Yashpal Singh Raghav OPTIMIZATION OF RESOURCE ALLOCATION USING INTEGER PROGRAMMING OF IMPROVED RATIO ESTIMATOR UNDER STRATIFIED RANDOM SAMPLING. Reliability: Theory & Applications. 2025, March 1(82):227-241. DOI: https://doi.org/10.24412/1932-2321-2025-182-227-241

RELIABILITY ANALYSIS OF C-SECTION WHERE STRENGTH AND HEAR STRESS ARE NORMALLY DISTRIBUTED	242-252

T. Raja jithendar, M. TirumalaDevi, K. Sandhya

The failure of a component depends on many parameters, such as complexity, time, design, reliability of components, and operating conditions. If failure depends on the stress of a component, such reliability models are called stress dependent models. There are many types of stresses that occur in the body, like tensile, compressive, shear, and bending. Shear stress develops in a body when a pair of opposite forces act across the section tangentially. In structural design, the choice of section shapes for different components is crucial for efficiency, strength, and stability. That’s why C –sections are used as purlins. C-sections have a shape that allows for effective load distribution. In this paper, reliability analysis has been conducted over the C-section by applying load and finding the shear stress in the flange and web of C-section. It is observed from the computations that reliability decreases as the load and overall depth of the section increase. Reliability increases as the thickness and width of the web increase.

Cite: T. Raja jithendar, M. TirumalaDevi, K. Sandhya RELIABILITY ANALYSIS OF C-SECTION WHERE STRENGTH AND HEAR STRESS ARE NORMALLY DISTRIBUTED . Reliability: Theory & Applications. 2025, March 1(82):242-252. DOI: https://doi.org/10.24412/1932-2321-2025-182-242-252

AN ALGORITHM FOR CONDITIONAL EXTREME VALUE THEORY GARCH-EVT TECHNIQUE FOR ESTIMATING VALUE AT RISK	253-276

K.M. Sakthivel, V. Nandhini

Extreme events in financial time series are characterized by their low probability yet high impact and they pose significant challenges in financial risk management. This study aims to model and forecast extreme events, with a particular emphasis on Value at Risk (VaR) estimation. It explores the concept of conditional Extreme Value Theory (EVT) for modeling volatility series to estimate VaR by integrating Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models with EVT, forming the GARCH-EVT approach. An automated algorithm was developed to optimize both model selection and threshold determination, ensuring accurate estimation of VaR. This automated procedure enhances the model selection process by identifying the optimal GARCH model and the most appropriate EVT threshold, addressing the complexities inherent in modeling extreme events. The comprehensive backtesting procedures are used to assess the effectiveness and precision of the algorithm in forecasting VaR, along with a simulation that evaluates both in-sample and out-of-sample performance of the model and candidate thresholds across various methods. The automated GARCH-EVT approach demonstrates effectiveness in accurately estimating VaR, providing a reliable and efficient method for extreme risk assessment in financial markets. This method streamlines the process of model selection and threshold optimization, contributing to improved risk management in financial markets.

Cite: K.M. Sakthivel, V. Nandhini AN ALGORITHM FOR CONDITIONAL EXTREME VALUE THEORY GARCH-EVT TECHNIQUE FOR ESTIMATING VALUE AT RISK . Reliability: Theory & Applications. 2025, March 1(82):253-276. DOI: https://doi.org/10.24412/1932-2321-2025-182-253-276

STRATIFIED RANDOM SAMPLING WITH RISK APPROACH	277-289

Astha Jain, Diwakar Shukla

In stratified random sampling, the sample size allocation is a problem which is tackled by many scientists and survey practitioners. Generally the proportional allocation, Neyman allocation and cost based allocation, are used to conduct sample surveys for gathering information from each strata. One can think of risk imposed on the life of investigators which is yet not considered while sample size allocation to risky strata. In this paper, the risk indicators stratum-wise are defined using police station records and hospital records. Such indicators are used for the determination of sample size allocation. For optimization, the Lagrange multiplier technique is used with two constants whose values need to be determined. An algorithm is proposed and analysed for such using simulation. The outcome of analysis provides that sample size allocation is directly proportional to the strata size and variability but inversely proportional to the square root of risk indicators of the stratum (with varying values of constants). This paper opens a new approach for the consideration of risk based sample size allocation and estimation in the setup of stratified sampling.

Cite: Astha Jain, Diwakar Shukla STRATIFIED RANDOM SAMPLING WITH RISK APPROACH. Reliability: Theory & Applications. 2025, March 1(82):277-289. DOI: https://doi.org/10.24412/1932-2321-2025-182-277-289

DIGITAL INVENTORY: REFORMAT RISK OPTIMIZATION MODEL FOR A LAPTOP	290-300

Diwakar Shukla, Deepti Sahu

In recent times, due to advancements in technologies specially in the computer world, people face problem related to limited digital capacity of a digital devices. Many reasons exist such as unwanted or unnecessary files stored in (a) System digital space (b) ROM space (c) Working space for users and (d) Hard disk space. By the regular use of a laptop, user space and hard disk digital space get occupied because of the creation of new files and new folders at every moment. Such a situation motivates for development of a digital inventory model for digital space. This paper presents a digital inventory model which is a useful tool for laptop reformat risk minimization. Users Categories are defined as per their intensive professional involvements. Several graphs are drawn showing the output analysis and importance of the study. Theoretical findings are supported by the numerical computations. It is found that reformat risk is directly proportional to the growth of file/folder creation in either of categories.

Cite: Diwakar Shukla, Deepti Sahu DIGITAL INVENTORY: REFORMAT RISK OPTIMIZATION MODEL FOR A LAPTOP. Reliability: Theory & Applications. 2025, March 1(82):290-300. DOI: https://doi.org/10.24412/1932-2321-2025-182-290-300

ENHANCING PATTERN SEQUENCE-BASED FORECASTS: A MODIFIED STRATEGY RELATIVE TO ELECTRICAL LOAD	301-311

Suseelatha Annamareddi, Sudheer Gopinathan

A precise forecast of the one-day-ahead load is essential for the efficient management of modern power system operations. This paper proposes a univariate model for short term load forecasting (STLF) that improves the precision of the Pattern sequence forecasting (PSF) algorithm. An analysis was conducted to identify the underlying patterns in the electrical load data using Kmeans clustering and hierarchical clustering algorithms. The results demonstrate the efficacy of hierarchical clustering. The limitations of the original PSF algorithm, particularly in its clustering and prediction phases are addressed using hierarchical clustering and a new weighted average formula. The proposed method was validated using real-time series datasets and its performance was compared with those of three pattern sequence-based forecasting models. The performance is further evaluated on two electricity demand data sets and compared with bench mark models. The uncertainty and reliability of the forecast model was assessed using an error variance metric. The results show the superior forecast accuracy of the model.

Cite: Suseelatha Annamareddi, Sudheer Gopinathan ENHANCING PATTERN SEQUENCE-BASED FORECASTS: A MODIFIED STRATEGY RELATIVE TO ELECTRICAL LOAD. Reliability: Theory & Applications. 2025, March 1(82):301-311. DOI: https://doi.org/10.24412/1932-2321-2025-182-301-311

EXPONENTIATED POISSON-G FAMILY OF DISTRIBUTION: SUB-MODELS, PROPERTIES, ESTIMATION WITH REAL-LIFE APPLICATION	312-323

Habibah Rahman, Tanusree Deb Roy

This study proposes a new family of distributions. A study is done on some of its basic characteristics, such as quantile, skewness, kurtosis, hazard rate function, moments, mean deviations, availability and reliability function of successive linear and circular systems, mean time to failure, mean time between failure, and availability, Bonferroni and Lorenz curves, and entropies. Two unique models of the new family are studied in depth once the general class is introduced. The special basis models have been taken from the exponential and Fréchet distributions. The parameters of the model are estimated using maximum likelihood techniques. There is a thorough analysis of percentage points. Three unique real data sets are used to demonstrate the significance of the new family. A comparison is drawn between the suggested distribution family and well-known two-, three-, and four-parameter components. To model actual data, it can be used as an alternative model to various lifetime distributions found in the statistical literature.

Cite: Habibah Rahman, Tanusree Deb Roy EXPONENTIATED POISSON-G FAMILY OF DISTRIBUTION: SUB-MODELS, PROPERTIES, ESTIMATION WITH REAL-LIFE APPLICATION . Reliability: Theory & Applications. 2025, March 1(82):312-323. DOI: https://doi.org/10.24412/1932-2321-2025-182-312-323

IMPROVED ADAPTIVE THRESHOLDING LASSO CHART FOR MONITORING DISPERSION OF HIGH-DIMENSIONAL PROCESSES USING GENERALIZED MULTIPLE DEPENDENT STATE SAMPLING	324-338

Mehrdad Hajiesmaeili, Mohammad Reza Maleki, Ali Salmasnia

In many applications of multivariate statistical quality control, it is commonly observed that the number of quality characteristics exceeds the sample size. This poses significant challenges in monitoring high-dimensional data. In such conditions, it is challenging to detect sparse changes where an assignable cause leads to the deviation of only a few elements in the covariance matrix. On the other hand, the utilization of the multiple dependent state (MDS) sampling technique to enhance the sensitivity of control charts has recently attracted the attention of researchers. However, to the best of the authors' knowledge, no previous research has been conducted on equipping multivariate dispersion control charting methods with the MDS technique under high dimensionality. Therefore, this article integrates the adaptive thresholding Lasso statistic with the MDS and generalized MDS techniques to track all types of disturbances in the covariance matrix of high-dimensional processes, including diagonal, off-diagonal, and joint diagonal/off-diagonal deviations. The performance of the proposed control charts will be compared through a numerical example under seven out-of-control patterns in terms of three metrics: average, standard deviation, and median of run length. The results clearly indicate that the use of both sampling techniques significantly improves the run length properties of the adaptive thresholding Lasso chart.

Cite: Mehrdad Hajiesmaeili, Mohammad Reza Maleki, Ali Salmasnia IMPROVED ADAPTIVE THRESHOLDING LASSO CHART FOR MONITORING DISPERSION OF HIGH-DIMENSIONAL PROCESSES USING GENERALIZED MULTIPLE DEPENDENT STATE SAMPLING . Reliability: Theory & Applications. 2025, March 1(82):324-338. DOI: https://doi.org/10.24412/1932-2321-2025-182-324-338

A NEUTROSOPHIC FUZZY ACCEPTANCE SAMPLING PLAN BASED ON NEGATIVE BINOMIAL DISTRIBUTION	339-349

Jayalakshmi S, Gopinath M

This paper suggests a novel method for acceptance sampling that integrates neutrosophical fuzzy logic with the negative binomial distribution. The complexity and ambiguity that characterize real-world circumstances are typically overlooked by traditional acceptance sampling methodologies. The neutrosophic Fuzzy Acceptance Sampling Plan (NFASP) incorporates the negative binomial distribution, which is particularly well-suited for count data, to account for circumstances where defect occurrences are important. The efficacy of the methodology is demonstrated by theoretical study and simulations. This innovative method lifts acceptance sampling to a more accurate and sophisticated procedure by dealing with ambiguity and indeterminacy.

Cite: Jayalakshmi S, Gopinath M A NEUTROSOPHIC FUZZY ACCEPTANCE SAMPLING PLAN BASED ON NEGATIVE BINOMIAL DISTRIBUTION . Reliability: Theory & Applications. 2025, March 1(82):339-349. DOI: https://doi.org/10.24412/1932-2321-2025-182-339-349

OPTIMIZING INVENTORY OF DETERIORATING PRODUCTS WITH PRICE-DEPENDENT DEMAND USING QUANTUM-BEHAVED AGTO VARIANTS	350-362

Muragesh Math, D.Gopinath, B. S.Biradar

Preservation of a product is an important issue in the inventory control system. It prevents the deterioration effect of the products while these are stored in the warehouse/showroom. Considering deterioration effect of the product and preservation technology, an inventory model of non-instantaneous deteriorating items is developed with the demand dependent on the selling price of the product. Two different preservation rates are considered. Shortages are allowed partially with two different backlogging rates. Due to consideration of three-parameter Weibull distributed deterioration and preservation facility, the corresponding optimization problems are highly nonlinear. So, these problems cannot be solved analytically due to nonlinearity. To overcome this situation, different variants of quantum-behaved Artificial Gorilla Troops Optimizer (AGTO) are used. To illustrate and validate the proposed model, a numerical example is considered and solved for each case, and compared the results with the different variants of AGTO algorithms. Finally, a sensitivity analysis is performed to study the effect of changes of different parameters of the model on the optimal policy.

Cite: Muragesh Math, D.Gopinath, B. S.Biradar OPTIMIZING INVENTORY OF DETERIORATING PRODUCTS WITH PRICE-DEPENDENT DEMAND USING QUANTUM-BEHAVED AGTO VARIANTS. Reliability: Theory & Applications. 2025, March 1(82):350-362. DOI: https://doi.org/10.24412/1932-2321-2025-182-350-362

APPLICATION OF FUZZY LOGIC IN AGRICULTURAL NETWORK ANALYSIS FOR OPTIMIZING CROP PRODUCTION	363-372

Mushtaq A. Lone, S. A. Mir, Sushil Kumar, Aafaq A. Rather, Danish Qayoom, S. Ramki

This study investigates the application of fuzzy logic and fuzzy set theory in agricultural networking to identify the optimal paths for different crop production activities. Traditionally networking methods often face challenges with incomplete and uncertain data, which are prevalent in agriculture. Fuzzy logic using decagonal fuzzy number offers a more versatile method of handing imprecise data. In this study decagonal fuzzy numbers are defuzzified by rolling averages with a window of three to determine the optimal path. The solution of the formulated mathematical programming model is obtained using R software which enabling accurate computation of the best routes in agricultural networks and three different examples were taken and the network diagram is also shown. This paper further shows the scope of agriculture especially network path analysis in agriculture which can enhance decision making, which in turn can rise crop yields and improve agriculture productivity.

Cite: Mushtaq A. Lone, S. A. Mir, Sushil Kumar, Aafaq A. Rather, Danish Qayoom, S. Ramki APPLICATION OF FUZZY LOGIC IN AGRICULTURAL NETWORK ANALYSIS FOR OPTIMIZING CROP PRODUCTION . Reliability: Theory & Applications. 2025, March 1(82):363-372. DOI: https://doi.org/10.24412/1932-2321-2025-182-363-372

A GENERALIZED POWER SUJATHA DISTRIBUTION WITH PROPERTIES AND APPLICATIONS	373-387

Hosenur Rahman Prodhani, Rama Shanker

This paper introduces a generalized power Sujatha distribution as an extension of the two-parameter generalization of Sujatha distribution, initially proposed for analyzing and modeling lifetime data in medical and engineering fields. The existing generalization of Sujatha distribution, being two-parameter, may not always provide a satisfactory fit for certain lifetime data from both theoretical and practical perspectives. The generalized power Sujatha distribution is presented as a comprehensive model, encompassing both the Generalization of Sujatha distribution and the Sujatha distribution as particular cases, specifically for the analysis of data in medical and engineering domains. The paper delves into the statistical properties of the proposed distribution, examining the behavior of its probability density function and cumulative distribution function across varying parameter values. Additionally, the first four raw moments of the distribution are derived and provided. The expressions for the hazard rate function and mean residual life function are obtained, and their behaviors under different parameter values are discussed. Stochastic ordering, a valuable tool for comparing stochastic nature, is also explored. The method of maximum likelihood is discussed for parameter estimation, and a simulation study is conducted to assess the performance of maximum likelihood estimates as sample sizes increase. To validate the applicability of the distribution, two real lifetime data sets from medical and engineering fields are analyzed. The goodness of fit of the generalized power Sujatha distribution is evaluated using the Akaike Information criterion and Kolmogorov-Smirnov statistic. The results demonstrate that the proposed distribution offers a closer fit compared to three-parameter power Quasi Lindley distribution, Three-parameter Sujatha distribution, Generalized gamma distribution, and two-parameter Generalizations of Sujatha distribution, as well as Weibull distribution and one-parameter Sujatha distribution. Given its superior fit over Power Quasi Lindley and Weibull distributions, particularly in the context of modeling and analyzing data from medical and engineering fields, the paper concludes by recommending the generalized power Sujatha distribution as the preferred choice over the considered distributions for such applications.

Cite: Hosenur Rahman Prodhani, Rama Shanker A GENERALIZED POWER SUJATHA DISTRIBUTION WITH PROPERTIES AND APPLICATIONS . Reliability: Theory & Applications. 2025, March 1(82):373-387. DOI: https://doi.org/10.24412/1932-2321-2025-182-373-387

RELAY CONTACTOR SYSTEM AS A MEANS OF CONTROLLING A LINEAR ELECTRIC DRIVE	388-396

G.S. Kerimzade, G.V. Mamedova

The energy sector is currently undergoing rapid change as a result of advances in technology, changes in consumer demand and the desire for more sustainable and efficient energy sources. Against the background of these changes, the problems of process management and optimization in the energy system are particularly relevant. One of the main directions in this field is the application of control systems through different-purpose control apparatus that can effectively react to changes in the environment and dynamically adapt to new conditions. The future development of the theory and practice of automatic control is related to the determination of the maximum possibilities of the systems and their construction, which are the best according to any technical and economic indicator. It is the research and development of control systems through apparatus in the energy sector, taking into account modern requirements and technological possibilities. Control systems are widely used in various fields of technology, they are applied in the automation of production processes and calculations. Positive results are obtained when simulating the system using different parameter values for different types of interference signals. Management systems with the use of hardware can be successfully applied in the real working conditions of energy enterprises and can ensure optimal use of resources, reduction of operating costs and minimization of negative effects on the environment. This article discusses the characteristics of relay-contactor control systems. Relay contactor equipment controls electric drives powered by electric motors from a network with a constant voltage, which are widely used in all industries. Relay-contactor control systems are control systems built on a relay-contactor element base and designed to automate the operation of engines. With the help of such control systems, operations such as turning the engine on and off, choosing the direction and speed of rotation, starting and braking the engine, creating temporary pauses in movement, protective shutdown of the engine and stopping the mechanism are automated. These operations are necessary to perform the movement of the working body of the mechanism according to technological conditions. An electric drive, made on the basis of a relay-contactor control system, is a simple, unregulated electric drive of direct or alternating current, mainly for general industrial use, for example, electric drive of cranes, elevators, conveyors, fans, pumps, some transport devices, etc.

Cite: G.S. Kerimzade, G.V. Mamedova RELAY CONTACTOR SYSTEM AS A MEANS OF CONTROLLING A LINEAR ELECTRIC DRIVE . Reliability: Theory & Applications. 2025, March 1(82):388-396. DOI: https://doi.org/10.24412/1932-2321-2025-182-388-396

KERNEL SMOOTHING OF THE MEAN PERFORMANCE FOR HOMOGENEOUS CONTINUOUS TIME SEMI-MARKOV PROCESS	397-412

Tayeb Hamlat, Fatiha Mokhtari, Saadia Rahmani

The main goal of the present paper is to propose a systematic approach to model performance measurements within the context of continuous-time semi-Markov processes with a finite state space. Specifically, the mean performance is estimated using the kernel method. The uniform strong consistency and the asymptotic normality of the proposed estimator is investigated. Furthermore, a non-parametric kernel estimation of the expected cumulative operational time is addressed. The constructed estimator is proved to be consistent and to converge to a normal random variable as the time of observation becomes large. As an illustration example, a simulation study has been conducted in order to highlight the efficiency as well as the superiority of our method to the standard empirical method.

Cite: Tayeb Hamlat, Fatiha Mokhtari, Saadia Rahmani KERNEL SMOOTHING OF THE MEAN PERFORMANCE FOR HOMOGENEOUS CONTINUOUS TIME SEMI-MARKOV PROCESS. Reliability: Theory & Applications. 2025, March 1(82):397-412. DOI: https://doi.org/10.24412/1932-2321-2025-182-397-412

CHARACTERIZATION OF SOME GENERALIZED DISTRIBUTIONS USING ORDER STATISTICS	413-424

Haseeb Athar, Mohd. Amir

The Lindley distribution has been useful for fitting lifetime data. In recent times, several authors studied the extension of the original Lindley distribution. In this paper, we introduced the two general classes of distributions, which include all earlier versions of Lindley distributions. These general classes are characterized using conditional expectations of order statistics. Further, there results are applied to characterize several known distributions like Lindley, X-Lindley, power Lindley, Lindley-Pareto, Ailamujia, power Ailamujia, Lindley-Weibull, length-biased exponential, inverse Lindley, inverse power Lindley and inverted length biased exponential distributions.

Cite: Haseeb Athar, Mohd. Amir CHARACTERIZATION OF SOME GENERALIZED DISTRIBUTIONS USING ORDER STATISTICS. Reliability: Theory & Applications. 2025, March 1(82):413-424. DOI: https://doi.org/10.24412/1932-2321-2025-182-413-424

CONSTRUCTION OF GAMMA ZERO-INFLATED POISSON DOUBLE SAMPLING PLANS	425-438

Priyadharshini R, Shalini K

In a well-supervised production framework, non-conformities occur seldom, resulting in a more number of zeros in the count of non-conformities. The zero-inflated Poisson (ZIP) distribution is a suitable model for handling zero inflation. Double sampling plan (DSP) is a precise quality inspection method where a decision on the approval or rejection of a lot is made after reviewing two samples, providing stronger conclusions than single sampling plan (SSP). In practice, decision-making for submitted lots requires a consistent assessment of both within-lot and between-lot variations, which can be addressed using Bayesian methodology. A Bayesian approach integrates prior knowledge and provides more information for making decisions about the approval or rejection of a lot. This article focuses on the designing of Bayesian DSPs; employing a Gamma prior to the parameter in the Poisson component of ZIP distribution the operating characteristic (OC) function is derived. Examples are provided to assess Gamma-ZIP (GZIP) DSPs. The significance of GZIP DSPs over conventional ZIP DSPs is also presented.

Cite: Priyadharshini R, Shalini K CONSTRUCTION OF GAMMA ZERO-INFLATED POISSON DOUBLE SAMPLING PLANS . Reliability: Theory & Applications. 2025, March 1(82):425-438. DOI: https://doi.org/10.24412/1932-2321-2025-182-425-438

A STUDY ON COMPARISON OF VARIOUS CONTINUOUS SAMPLING AND SKIP-LOT SAMPLING PLAN PROCEDURES	439-444

S. Suganya, K. Pradeepa Veerakumari

This paper explains the brief review of skip-lot sampling plan procedures followed by continuous sampling plan procedures. Also, various types of skip-lot sampling plans are compared with continuous sampling plans. The efficiency of SkSP-T is tested on comparison with various skip-lot sampling plans using Single Sampling Plan. A new system of skip-lot sampling plan of type SkSP-T is compared with other skip-lot sampling plans. Different types of skip-lot sampling plans namely SkSP-2, SkSP-3, SkSP-V and SkSP-R. The tables are constructed for various combinations of various parameters using various numerical methods.

Cite: S. Suganya, K. Pradeepa Veerakumari A STUDY ON COMPARISON OF VARIOUS CONTINUOUS SAMPLING AND SKIP-LOT SAMPLING PLAN PROCEDURES . Reliability: Theory & Applications. 2025, March 1(82):439-444. DOI: https://doi.org/10.24412/1932-2321-2025-182-439-444

DECISION SUPPORT SYSTEM OF EVAPORATING SYSTEM OF SUGAR PLANT	445-453

Parveen Sihmar, Vikas Modgil

This paper addresses an analysis methodology for assessing the efficacy of a evaporating system in a sugar industry. A stochastic Petri nets technique is employed to simulate the interactions between the subsystems. A software package, "Petri module," from GRIF, was licensed. The performability of subsystems has been evaluated, and fluctuations in repair and failure rates have been observed. The maintenance order priority was assigned to the subsystems of the evaporating system based on the criticality of failure. Finally, a decision support system is implemented to assist maintenance personnel in making more informed decisions during the development of maintenance policies. It has been noted that the evaporator is an essential component that requires the complete attention of the plant manager.

Cite: Parveen Sihmar, Vikas Modgil DECISION SUPPORT SYSTEM OF EVAPORATING SYSTEM OF SUGAR PLANT . Reliability: Theory & Applications. 2025, March 1(82):445-453. DOI: https://doi.org/10.24412/1932-2321-2025-182-445-453

MODELING RELIABILITY IN k-OUT-OF-m SYSTEMS WITH UNEQUAL LOAD SHARING USING PROPORTIONAL CONDITIONAL REVERSE HAZARD RATE	454-471

Sukumar V. Rajguru, Santosh. S. Sutar

This paper explores a load-sharing model within a k-out-of-m system, where multiple components work together to handle a shared load. Such systems are prevalent in various engineering and industrial applications. While previous studies have focused on equal load-sharing rules, this research emphasizes systems operating under an unequal load-sharing rule, which has a significant impact on the system’s reliability and performance. Specifically, the paper examines a k-out-of-m load-sharing system modeled using the proportional conditional reverse hazard rate model, incorporating unequal load sharing. We have derived expressions for the probability density function and cumulative distribution function of system failure. To illustrate the model, they use a 2-out-of-4 configuration with Weibull baseline distributions. The maximum likelihood estimation method is employed to estimate the model parameters, and the performance of these estimates is evaluated through a simulation study, assessing both bias and mean square errors. Additionally, the practical applicability of the model is demonstrated through the analysis of two real datasets.

Cite: Sukumar V. Rajguru, Santosh. S. Sutar MODELING RELIABILITY IN k-OUT-OF-m SYSTEMS WITH UNEQUAL LOAD SHARING USING PROPORTIONAL CONDITIONAL REVERSE HAZARD RATE. Reliability: Theory & Applications. 2025, March 1(82):454-471. DOI: https://doi.org/10.24412/1932-2321-2025-182-454-471

IMPROVING VARIANCE PRECISION IN POPULATION STUDIES: THE ROLE OF POST-STRATIFICATION AND AUXILIARY DATA	472-482

M. I. Khan, S. Qurat Ul Ain, M. Younis Shah

In this study, we propose an enhanced estimator for the finite population variance in the context of post-stratified sampling, incorporating an auxiliary variable to improve accuracy. We derive expressions for the bias and mean square error (MSE) of the proposed estimator, providing an approximation accurate up to the first order. The theoretical analysis highlights the conditions under which the proposed estimator yields lower bias and reduced MSE, making it a more efficient alternative to traditional methods. To evaluate the practical performance of this estimator, we apply it to two real-world data sets, where our results demonstrate a marked improvement in efficiency over existing estimators. The numerical findings confirm that, in post-stratified sampling, the proposed estimator significantly enhances the precision of variance estimation, especially when the auxiliary variable is highly correlated with the study variable. This work not only contributes a more efficient estimator but also provides valuable insights into the application of auxiliary information in post-stratified sampling designs.

Cite: M. I. Khan, S. Qurat Ul Ain, M. Younis Shah IMPROVING VARIANCE PRECISION IN POPULATION STUDIES: THE ROLE OF POST-STRATIFICATION AND AUXILIARY DATA . Reliability: Theory & Applications. 2025, March 1(82):472-482. DOI: https://doi.org/10.24412/1932-2321-2025-182-472-482

A COMPARATIVE STUDY ON PARAMETER ESTIMATION TECHNIQUES FOR THE DISCRETE INVERSE RAYLEIGH DISTRIBUTION	483-492

Haripriya M, Radhika A, Jeslin J

This article explores into the Discrete Inverse Rayleigh Distribution, a novel discrete analogue of the continuous Inverse Rayleigh distribution, formulated by inverting a continuous Rayleigh random variable. The Discrete Inverse Rayleigh Distribution can effectively capture a range of hazard rate shapes, exhibiting either unimodal or monotonic decreasing behaviors depending on parameter values. To estimate the parameters of this distribution, we examine four distinct methods: a heuristic algorithm, a probability paper plotting technique designed for the Inverse Rayleigh, the method of moments, and the method of proportions. Each method offers unique strengths and presents different computational requirements and precision levels. Through rigorous simulation studies, we assess the accuracy and reliability of these methods, evaluating their performance across a variety of scenarios. Our results indicate that the methods of moments and proportions encounter significant difficulties when estimating parameters for right-skewed Discrete Inverse Rayleigh distributions. These challenges are primarily due to numerical instability and poor convergence properties under certain parameter configurations, which can limit their practical applicability in these cases. In contrast, both the probability paper plotting method and the heuristic algorithm demonstrate robustness and enhanced accuracy, especially in the context of right-skewed distributions. The probability paper plot is notably effective due to its reliance on graphical techniques that simplify parameter estimation in complex, non-monotonic datasets, whereas the heuristic algorithm provides a more computationally efficient solution without sacrificing precision. To validate the utility of the Discrete Inverse Rayleigh Distribution, we compare its performance with the Discrete Rayleigh Distribution by fitting both models to a real-world dataset. The comparative analysis leverages the Akaike Information Criterion (AIC) to quantitatively assess model fit. Our findings underscore the advantages of the Discrete Inverse Rayleigh Distribution, particularly in applications where discrete data exhibits non-monotonic hazard rates, highlighting its superior fit over the traditional Discrete Rayleigh in this context. This study contributes to the growing toolkit for discrete time-to-event data modeling, offering insights into effective parameter estimation strategies and demonstrating the value of the Discrete Inverse Rayleigh Distribution for specialized discrete hazard rate analysis.

Cite: Haripriya M, Radhika A, Jeslin J A COMPARATIVE STUDY ON PARAMETER ESTIMATION TECHNIQUES FOR THE DISCRETE INVERSE RAYLEIGH DISTRIBUTION . Reliability: Theory & Applications. 2025, March 1(82):483-492. DOI: https://doi.org/10.24412/1932-2321-2025-182-483-492

DESIGNING SINGLE SAMPLING PLANS BASED ON ZERO-INFLATED BINOMIAL DISTRIBUTION	493-499

Sangeetha S, Shalini K, Hemalatha R

Withdrawal



LEVERAGING RANK SET SAMPLING FOR ENHANCED STRESS-STRENGTH ESTIMATION IN THE CONTEXT OF NAKAGAMI DISTRIBUTION	500-514

Surinder Kumar, Rahul Shukla, Bhupendra Meena, Shivendra Pratap Singh

This study addresses the estimation of the stress-strength reliability model, where stress and strength both following the Nakagami distribution. While conventional approaches have relied on simple random sampling (SRS) for estimating reliability models, recent research suggests that ranked set sampling (RSS) offers a more efficient alternative. RSS yields more informative samples compared to SRS, potentially enhancing the accuracy of reliability estimations. Our investigation focuses on deriving maximum likelihood estimators (MLEs) for stress-strength under both SRS and RSS methodologies. To evaluate the comparative efficacy of these sampling techniques, we conduct a comprehensive Monte Carlo simulation study. The results of this analysis provide compelling evidence that RSS-based estimators outperform their SRS counterparts in terms of efficiency and precision. This research contributes to the growing body of literature supporting the adoption of RSS in reliability engineering. By demonstrating the superior performance of RSS in the context of Nakagami-distributed stress-strength models, we offer valuable insights for researchers and practitioners seeking to optimize their estimation procedures in reliability analysis.

Cite: Surinder Kumar, Rahul Shukla, Bhupendra Meena, Shivendra Pratap Singh LEVERAGING RANK SET SAMPLING FOR ENHANCED STRESS-STRENGTH ESTIMATION IN THE CONTEXT OF NAKAGAMI DISTRIBUTION . Reliability: Theory & Applications. 2025, March 1(82):500-514. DOI: https://doi.org/10.24412/1932-2321-2025-182-500-514

EVALUATION OF PARAMETRIC ESTIMATION METHODS FOR THE GAMMA DISTRIBUTION USING MAXIMUM LIKELIHOOD AND BAYESIAN APPROACHES IN A CENSORED LIFE-TESTING STRATEGY WITH MARKOV CHAIN MONTE CARLO SIMULATIONS	515-527

Christian Akrong Hesse, Dominic Buer Boyetey, Emmanuel Dodzi Kpeglo, Albert Ayi Ashiagbor

The goal of this study was to address the computational challenges associated with parametric estimation of the gamma distribution by evaluating the performance of the maximum likelihood and maximum a-posteriori estimation methods within the framework of Markov Chain Monte Carlo simulations. This was done by first assuming a censored life-testing strategy that terminates on the rth failure from a given sample of n electronic devices. Second, we obtained the joint distribution function of the first r-order statistic by arranging the r values in order of magnitude. Finally, we explored through the Markov Chain Monte Carlo framework using the maximum likelihood and maximum a-posteriori to estimate the gamma distribution parameters. The findings of this study suggest that both estimation methods were not significantly different from the actual hypothesized parameter values. Further, we observed that irrespective of the prior distribution used for the Bayesian maximum a-posteriori Markov Chain Monte Carlo estimation, the resulting parametric estimates of the gamma distribution remain the same, confirming the assertion that the Bayesian maximum a-posteriori Markov Chain Monte Carlo approach is a valuable tool for informative posterior analysis. The study’s uniqueness lies in adopting a censored life-testing strategy centered on the joint distribution function of the first r-order statistic.

Cite: Christian Akrong Hesse, Dominic Buer Boyetey, Emmanuel Dodzi Kpeglo, Albert Ayi Ashiagbor EVALUATION OF PARAMETRIC ESTIMATION METHODS FOR THE GAMMA DISTRIBUTION USING MAXIMUM LIKELIHOOD AND BAYESIAN APPROACHES IN A CENSORED LIFE-TESTING STRATEGY WITH MARKOV CHAIN MONTE CARLO SIMULATIONS . Reliability: Theory & Applications. 2025, March 1(82):515-527. DOI: https://doi.org/10.24412/1932-2321-2025-182-515-527

ENHANCING LINDLEY DISTRIBUTION PARAMETER ESTIMATION WITH HYBRID BAYESIAN AVERAGE MODEL FOR FUZZY DATA	528-542

Abbarapu Ashok, Nadiminti Nagamani

With the ultimate goal of increasing parameter estimate accuracy, this study will examine and assess a number of estimating techniques used with the Lindley distribution in the context of fuzzy data. Gibbs sampling, Bootstrapping Sampling, MCMC, MH, and a unique hybrid methodology that combines these approaches via Bayesian model averaging were also studied. The research looks at several sample sizes ranging from 15 to 100 and repeats the estimate method 10,000 times for each size. Fuzzy data are created using established fuzzy systems, and the performance of each approach is measured using average values (AV), mean squared errors (MSE), coverage probabilities, and confidence interval lengths. The findings show that the hybrid technique consistently produces estimates closer to the genuine parameter value of one across all sample sizes, with smaller mean squared errors than individual methods. Furthermore, the hybrid method’s confidence intervals preserve coverage probabilities that are consistent with the targeted confidence level, demonstrating the method’s trustworthiness in statistical inference. Overall, the results show that the hybrid technique improves estimate accuracy and reliability, providing a strong foundation for parameter estimation in the Lindley distribution framework using fuzzy data.

Cite: Abbarapu Ashok, Nadiminti Nagamani ENHANCING LINDLEY DISTRIBUTION PARAMETER ESTIMATION WITH HYBRID BAYESIAN AVERAGE MODEL FOR FUZZY DATA. Reliability: Theory & Applications. 2025, March 1(82):528-542. DOI: https://doi.org/10.24412/1932-2321-2025-182-528-542

UNRELIABLE M/G/1 QUEUE WITH GENERAL RETRIAL TIME, WORKING VACATION AND SETUP TIME	543-556

Hadjadj Houari , Arrar Nawel , Lahcene Yahiaoui

In the current article, a retrial queuing system with working vacations, interruptions, setup time, and perfect repair is analyzed. The scenario includes a server taking working vacations during empty periods without a complete halt of servicing customers; however, the rates of service remain reduced. Further, a setup time is included here, implying that if the server remains idle when a new customer enters, the state changes to inactive plus a setup duration before restarting operation. In this phase of setup, the setup failure happens and is replaced immediately before the server can proceed to normal operations. In addition to this, automatic power-off to conserve energy is there when no customer comes while the server is in vacation mode. Customers who find that the server cannot be accessed spend time waiting in retrial orbit instead of entering a normal queue. Here they’re encouraged to try again for service after a random time. The steady state probability generating functions for system size and retrial group size are obtained by analyzing the system dynamics through the supplementary variable technique (SVT). Reliability and optimization analyses will be included in what will be studied from the system. Reliability concerns evaluating the chances of the server being available at different failure and repair sites while in the system, while optimization looks at the best configuration of system parameters that will work towards achieving greater efficiency and reduced delays. Explicit mathematical formulations can be obtained under ergodicity conditions describing the system size distribution and sojourn time and state probabilities. For a practical realization of the model, which numerically experiments would be carried out in Python, the theoretical results were validated. Such results therefore hold information on how direct retrials, setup times, service rates, and repair mechanisms affect overall system behavior. They also provide strong evidence for trade-offs between energy conservation on the one hand and reliability together with continuous service on the other. The proposed model together with practical implementation thus produces very significant inferences relevant to real service models in which the optimization of resources and efficiency of operation are critical.

Cite: Hadjadj Houari , Arrar Nawel , Lahcene Yahiaoui UNRELIABLE M/G/1 QUEUE WITH GENERAL RETRIAL TIME, WORKING VACATION AND SETUP TIME. Reliability: Theory & Applications. 2025, March 1(82):543-556. DOI: https://doi.org/10.24412/1932-2321-2025-182-543-556

ESTIMATING THE POPULATION MEAN USING STRATIFIED DOUBLE UNIFIED RANKED SET SAMPLING FOR ASYMMETRIC DISTRIBUTIONS	557-572

Mohammed Ahmed Alomair, Chainarong Peanpailoon, Roohul Andrabi, Tundo, Khalid Ul Islam Rather

In this study, we propose a novel sampling technique known as Stratified Unified Ranked Set Sampling (SDURSS) and evaluate its efficiency for estimating population means. SDURSS is designed to enhance the estimation accuracy by integrating concepts from ranked set sampling with stratified sampling. Our results demonstrate that the SDURSS estimator generally exhibits superior efficiency compared to SRS, particularly in complex distribution scenarios. While SDURSS often performs more efficiently than SSRS and SRSS, its performance relative to these methods varies depending on the specific distribution and sample size. In several cases, SDURSS outperforms SSRS and SRSS, highlighting its potential benefits in practical applications. The findings suggest that SDURSS is a promising alternative to traditional sampling methods, offering improved efficiency and potentially more accurate estimates of population means. This research underscores the value of exploring advanced sampling techniques to enhance statistical estimation, particularly in scenarios involving asymmetric distributions where traditional methods may be less effective.

Cite: Mohammed Ahmed Alomair, Chainarong Peanpailoon, Roohul Andrabi, Tundo, Khalid Ul Islam Rather ESTIMATING THE POPULATION MEAN USING STRATIFIED DOUBLE UNIFIED RANKED SET SAMPLING FOR ASYMMETRIC DISTRIBUTIONS . Reliability: Theory & Applications. 2025, March 1(82):557-572. DOI: https://doi.org/10.24412/1932-2321-2025-182-557-572

A SIGNIFICANT STUDY ON ROBUST MEASURE OF LOCATION PARAMETERS USING DATA DEPTH APPROACHES	573-579

Kalaivani S

Data depth procedures are statistical methods used to measure the centrality or depth of a point within a multivariate dataset. These procedures provide a way to quantify how deep or outlying a point is relative to the overall distribution of the data. This study explores various data depth procedures to find reliable location estimations in cases like with and without outliers. In this paper, various depth procedures, such as Mahalanobis depth, Halfspace depth, Euclidean depth, Simplicial depth, and Projection depth, are studied and compared. The efficiency of these depth functions is evaluated using real datasets and simulation studies with R software.

Cite: Kalaivani S A SIGNIFICANT STUDY ON ROBUST MEASURE OF LOCATION PARAMETERS USING DATA DEPTH APPROACHES. Reliability: Theory & Applications. 2025, March 1(82):573-579. DOI: https://doi.org/10.24412/1932-2321-2025-182-573-579

OPTIMIZING A LINEAR FRACTIONAL FUNCTION OVER AN INTEGER EFFICIENT SET	580-590

Leila YOUNSI-ABBACI

Over recent decades, significant advancements have been made in optimization over the efficient set. This paper introduces a novel exact algorithm designed to optimize a linear fractional objective function over the integer efficient set of a multi-objective linear programming problem (MOILP). Without enumerating all efficient solutions, our method employs a selection strategy to iteratively improve the primary objective while progressively refining the feasible region and excluding dominated points. By exploring edge connections within the truncated feasible space, the proposed algorithm ensures convergence to the global optimal value in a finite number of iterations. A numerical example demonstrates the algorithm’s effectiveness and practical application. This approach addresses critical challenges in multiobjective integer programming, particularly the nonconvexity of the efficient set and the absence of explicit feasible set descriptions.

Cite: Leila YOUNSI-ABBACI OPTIMIZING A LINEAR FRACTIONAL FUNCTION OVER AN INTEGER EFFICIENT SET. Reliability: Theory & Applications. 2025, March 1(82):580-590. DOI: https://doi.org/10.24412/1932-2321-2025-182-580-590

A MODIFIED INCIDENT EDGE PATH ALGORITHM FOR EFFICIENT SHORTEST PATH SOLUTIONS IN PIPELINE NETWORKS AND URBAN NAVIGATION SYSTEMS	591-600

Kanchana M, Kavitha K

The article describes how to utilize the Modified Incident Edge Path Algorithm (MIEPA) to identify the cheapest transit option and the best route. The MIEPA algorithm, which is based on graph theory, is simple to use and can potentially be employed to major smart logistics challenges such as pipeline networks and Google Maps. It evaluates the most optimal approach to minimize transportation expenses using MATLAB. The algorithm ensures that each node gets visited and determines the shortest path from the origin to all other nodes. The running time complexity and theorem of the new method are presented, and the algorithm is compared to the existing algorithm. The proposed MIEPA addresses negative weights and prevents negative cycles. It has used two real-world problems to evaluate the suggested algorithm.

Cite: Kanchana M, Kavitha K A MODIFIED INCIDENT EDGE PATH ALGORITHM FOR EFFICIENT SHORTEST PATH SOLUTIONS IN PIPELINE NETWORKS AND URBAN NAVIGATION SYSTEMS. Reliability: Theory & Applications. 2025, March 1(82):591-600. DOI: https://doi.org/10.24412/1932-2321-2025-182-591-600

ON SOME PROPERTIES AND APPLICATIONS OF THE MODI-FRECHET DISTRIBUTION	601-619

Akhila P., Girish Babu M.

In this paper we introduce a novel expansion of Frechet distribution from Modi family of probability distributions. The important statistical properties like moments, stochastic ordering, and entropy are studied in this paper. Two distinct characterizations of the proposed distribution are derived through the hazard rate function and truncated moments. The statistical inference about the parameters of the new distribution is studied using the method of maximum likelihood estimation. To study the flexibility and practical utility of the distribution, two real-life data sets from the reliability sector and from the biomedical field were analyzed. An extensive simulation study is also conducted to validate the accuracy and consistency of the estimation techniques.

Cite: Akhila P., Girish Babu M. ON SOME PROPERTIES AND APPLICATIONS OF THE MODI-FRECHET DISTRIBUTION. Reliability: Theory & Applications. 2025, March 1(82):601-619. DOI: https://doi.org/10.24412/1932-2321-2025-182-601-619

BAYESIAN ESTIMATION OF INVERSE AILAMUJIA DISTRIBUTION USING DIFFERENT LOSS FUNCTIONS	620-631

Aijaz Ahmad, Manzoor A. Khanday, Sonali Kedar Powar, Aafaq A. Rather, C. Subramanian

This paper focuses on the Bayesian estimation of the parameter of the inverse Ailamujia distribution, employing advanced prior structures and diverse loss functions. Specifically, the extended Jeffreys’ prior and gamma prior are utilized to derive the Bayesian estimators. Estimation is performed under various loss functions, including squared error, entropy, precautionary, and Linex loss functions, ensuring a comprehensive analysis. To demonstrate the practical applicability and comparative performance of these estimators, an empirical investigation is conducted using a real dataset. The findings highlight the adaptability and effectiveness of the proposed Bayesian approach across different estimation scenarios.

Cite: Aijaz Ahmad, Manzoor A. Khanday, Sonali Kedar Powar, Aafaq A. Rather, C. Subramanian BAYESIAN ESTIMATION OF INVERSE AILAMUJIA DISTRIBUTION USING DIFFERENT LOSS FUNCTIONS . Reliability: Theory & Applications. 2025, March 1(82):620-631. DOI: https://doi.org/10.24412/1932-2321-2025-182-620-631

ENHANCING EMOTION RECOGNITION WITH MULTIMODEL APPROACH USING DEEP NEURAL NETWORKS	632-644

Dr. Komal Anadkat, Ayush Solanki, Dhruva Patel, Vraj Thakkar

Recognizing and extracting different emotions, and then validating those emotions have become important for enhancing human-computer interaction. Emotions play a crucial role in social interactions, facilitating rational decision-making and perception. Previously researched emotion recognition models have typically focused on a single input type like images, text, or audio, where each model can identify the emotion of a person through a single source like facial expressions, voice, social media posts, etc. However, these uni-model approaches are limited because they rely on just one type of data, which often misses the full range of emotional cues. To overcome these limitations, multi-model emotion recognition techniques are proposed which are useful for detecting emotions through a person’s facial expressions, speech, social media status, and then EEG data. Model fusion techniques have been applied to detect the most accurate emotion for a particular person through fusion of all the models. A recognition rate-based weighting approach is proposed for model fusion, wherein models are assigned weights proportional to their individual recognition rates. This approach enhances overall performance by combining the outputs of various models with higher emphasis on those with better accuracy. The decision fusion-based multi- model emotion recognition model is proposed which achieved a maximum of 87%. accuracy using a bi-model approach and 92% accuracy with a tri-model approach. The weighted decision fusion approach assigns more weight to the model which is more accurate and achieved 93% accuracy. The proposed recognition rate-based weighting approach for fusion has provided significant results, achieving approximately 93% accuracy with 0.900 and 0.904 Cohen kappa and Mathew score respectively using facial expression, speech, and social media text modalities on combined dataset. The proposed model achieved 63% accuracy on a real-world collected dataset without considering EEG data and improved to 73% if EEG is also considered.

Cite: Dr. Komal Anadkat, Ayush Solanki, Dhruva Patel, Vraj Thakkar ENHANCING EMOTION RECOGNITION WITH MULTIMODEL APPROACH USING DEEP NEURAL NETWORKS . Reliability: Theory & Applications. 2025, March 1(82):632-644. DOI: https://doi.org/10.24412/1932-2321-2025-182-632-644

OVERVOLTAGE AT THE TRANSFORMER WHEN DISCONNECTING CLOSE ASYMMETRICAL SHORT CIRCUITS	645-657

Nahid Mufidzade, Gulgaz Ismayilova

This article examines overvoltages at the inputs of high-voltage (HV) and low-voltage (LV) transformers rated at 110/6 kV and 110/10 kV, focusing on scenarios involving grounded and isolated neutrals during short circuits near the transformers. The study finds that with an isolated neutral, overvoltages resulting from a phase-to-ground short circuit reach the highest levels, as anticipated. However, the disconnection of all types of asymmetrical short circuits—whether with an isolated or grounded neutral—yields even greater, potentially excessive overvoltages. This occurs because the windings of undamaged transformer phases remain partially energized during disconnection, leading to significant currents being interrupted. The magnetic energy from these currents converts to electrical energy, resulting in substantial voltage increases, characterized as pulsed overvoltages lasting several microseconds. Implementing switches with shunt resistance can reduce these overvoltages considerably, though the remaining levels may still exceed acceptable thresholds. To mitigate the risk of such excessive overvoltages, installing surge arresters at the inputs of high-voltage transformers is recommended, ensuring that transformer input overvoltages remain within permissible limits.

Cite: Nahid Mufidzade, Gulgaz Ismayilova OVERVOLTAGE AT THE TRANSFORMER WHEN DISCONNECTING CLOSE ASYMMETRICAL SHORT CIRCUITS . Reliability: Theory & Applications. 2025, March 1(82):645-657. DOI: https://doi.org/10.24412/1932-2321-2025-182-645-657

OPTIMIZING BAYESIAN REPETITIVE GROUP SAMPLING PLAN FOR QUALITY CONTROL TO ENHANCE DECISION MAKING EFFICIENCY IN MODERN MANUFACTURING	658-672

P. Sivakumar1, V. Kaviyarasu, V. Devika

This article introduces an approach to optimize the design of Repetitive Group Sampling (RGS) plan in the context of quality control for modern manufacturing processes. The primary objective of this study is to enhance decision-making efficiency by applying Bayesian principles to develop optimal sampling plans. In modern manufacturing environment, the industries are using the advanced technologies and machineries to maintain the quality of their products. The existence of defects would consequently be highly rare in such production. In such situation, Zero Inflated Poisson (ZIP) distribution is a more appropriate probability distribution rather than the usual Poisson distribution. Further, manufacturing industries often use a variety of manpower and materials to produce their products in various production streams. This may lead to have more quality variation in between lots and hence, the lot quality will vary over lots. The lots that arise from such a production process will be unstable, and quality variations among the units are often heterogeneous in nature. In such situation, the Bayesian sampling plans under Zero Inflated Poisson distribution would be more effective and alternative for traditional sampling plans. This paper studies the designing and selection of Bayesian Repetitive Group Sampling (BRGS) Plan under the conditions of Gamma-Zero Inflated Poisson distribution (G-ZIP). To investigate the effectiveness of this plan, a comparison between the proposed BRGS plan and various existing sample plans is made. Further, we provided the procedure and tables with the suitable numerical illustration to compute the optimal sampling plan.

Cite: P. Sivakumar1, V. Kaviyarasu, V. Devika OPTIMIZING BAYESIAN REPETITIVE GROUP SAMPLING PLAN FOR QUALITY CONTROL TO ENHANCE DECISION MAKING EFFICIENCY IN MODERN MANUFACTURING . Reliability: Theory & Applications. 2025, March 1(82):658-672. DOI: https://doi.org/10.24412/1932-2321-2025-182-658-672

PERFORMANCE ANALYZATION OF ERLANG SERVICE MODEL UNDER TRIANGULAR FUZZY NUMBER BY USING THE L-R FUZZY APPROACH	673-682

Dr. V. P. Anuja

A traditional mathematical technique for analyzing line-waiting delays and overcrowding is queuing theory. It addresses the number of patrons in line as well as numerous other queue-related issues. Developing an Erlang service model in a fuzzy environment is our study’s goal. This study aims to investigate the anticipated number of patients in the line as well as the queuing system’s waiting time. To achieve this, we applied the L-R strategy under triangular fuzzy numbers and the alpha-cuts method. To measure various linguistic aspects in queuing systems, the fuzzy approach has been used. The findings showed that waiting times are determined using recommended techniques and that the fuzzy Erlang model is stable. Finally, we provide numerical examples to show the capabilities of the suggested method.

Cite: Dr. V. P. Anuja PERFORMANCE ANALYZATION OF ERLANG SERVICE MODEL UNDER TRIANGULAR FUZZY NUMBER BY USING THE L-R FUZZY APPROACH. Reliability: Theory & Applications. 2025, March 1(82):673-682. DOI: https://doi.org/10.24412/1932-2321-2025-182-673-682

DEVELOPMENT OF NEW METHODS FOR PROTECTING SUBSTATION AND OVERHEAD LINES FROM OVERVOLTAGES	683-689

N.M. Piriyeva, N.S. Mammadov, S.V. Rzayeva

This article explores various methods and devices used for protecting overhead lines and substations from surges, particularly those induced by lightning strikes. Traditional surge protection methods such as lightning rods, arresters, and grounding systems are discussed, highlighting their limitations and challenges, especially in long-distribution networks. The study examines the development and implementation of novel surge protection devices, including nonlinear surge arresters, frequency-dependent devices (FDD), and multi-chamber arresters. Special attention is given to FDD, which utilizes ferromagnetic materials to create frequency-dependent resistance, effectively suppressing high-frequency overvoltages. Experimental results demonstrate the efficacy of FDD in reducing the amplitude of lightning-induced overvoltage pulses and enhancing the lightning resistance of overhead lines and substations. However, challenges such as insufficient information on device effectiveness, limited ohmic resistance at high frequencies, and size constraints hinder widespread adoption. The article concludes by emphasizing the need for further research to optimize FDD designs, increase active resistance, and assess operational effectiveness to facilitate broader deployment across different voltage classes.

Cite: N.M. Piriyeva, N.S. Mammadov, S.V. Rzayeva DEVELOPMENT OF NEW METHODS FOR PROTECTING SUBSTATION AND OVERHEAD LINES FROM OVERVOLTAGES . Reliability: Theory & Applications. 2025, March 1(82):683-689. DOI: https://doi.org/10.24412/1932-2321-2025-182-683-689

A MODIFIED WEIGHTED DISTRIBUTION - APPLICATION ON DIABETES MELLITUS AND PANCREATIC CANCER DATA	690-699

Praseeja C B, Prasanth C B, C Subramanian, Unnikrishnan T

This research article attempts to establish and explore a case of two parameter Nwikpe distribution and termed it as Area Biased C2N distribution. As the characteristics of Hydrogen per Oxide(H2O2) is quite different from that of Water (H2O) even though both are the different combinations of the same elements Oxygen & Hydrogen, the characteristics of initial distribution is also entirely different from that of the area biased modified distribution. The implemented new distribution has distinct structural characteristics, and its parameters are estimating using maximum likelihood estimation. Utilizing biomedical data, the new distribution’s application has been examining to ascertain its superiority and utility. One lifetime data set shows the mean reduction in blood glucose (mg/dL) after three days of the first usage of the Metformin medicine from a random sample of 130 patients from a hospital at Chennai, TamilNadu with type 2 diabetes mellitus by testing the FBS-Fasting Blood Glucose. The another set of lifetime data shows the mean reduction in blood glucose (mg/dL) after each dosage of the FIASP insulin-medicine in alternate days of a pancreatic cancer patient, noted for 63 days randomly. Both data set is going to fit to the new distribution and analyze them, to determine the supremacy and usefulness.

Cite: Praseeja C B, Prasanth C B, C Subramanian, Unnikrishnan T A MODIFIED WEIGHTED DISTRIBUTION -APPLICATION ON DIABETES MELLITUS AND PANCREATIC CANCER DATA. Reliability: Theory & Applications. 2025, March 1(82):690-699. DOI: https://doi.org/10.24412/1932-2321-2025-182-690-699

EXPLORING QUADRASOPHIC FUZZY SET: APPLICATIONS IN ASSESSING STRESS LEVELS AND SELF-ESTEEM CONNECTIONS	700-714

G. Aruna, J. Jesintha Rosline, A. Anthoni Amali

The ambiguous environment has been addressed with a variety of fuzzy sets and their extensions. The Quadrasophic Fuzzy Set is one of the generalization of Fuzzy set to handle imprecise information efficiently. It is defined with two new parameters. In this artifact, we defined the operations, theorems, and relations of the Quadrasophic Fuzzy Set with pertinent examples. We also established a comparison study with other existing models. Additionally, the integration of Quadrasophic Fuzzy data with the TOPSIS approach to solve the Multi Criteria Decision Making problem is proposed and illustrated by examining the relationship between employee stress levels and their self-esteem, which can trigger obsessive-compulsive disorder, using real-life data. The results are analyzed with SPSS software.

Cite: G. Aruna, J. Jesintha Rosline, A. Anthoni Amali EXPLORING QUADRASOPHIC FUZZY SET: APPLICATIONS IN ASSESSING STRESS LEVELS AND SELF-ESTEEM CONNECTIONS. Reliability: Theory & Applications. 2025, March 1(82):700-714. DOI: https://doi.org/10.24412/1932-2321-2025-182-700-714

BAYESIAN GLM: A NON-INFORMATIVE APPROACH FOR PARAMETER ESTIMATION IN EXPONENTIAL DISPERSION REGRESSION MODELS	715-727

Ibrahim Sadok, Mourad Zribi

This paper proposes a novel Bayesian approach to parameter estimation in exponential dispersion regression models (EDRM). By employing a non-informative prior distribution, we offer a flexible and robust framework that avoids the need for subjective prior specification. To efficiently sample from the posterior distribution, we develop an importance-sampling algorithm tailored to the EDRM. Through a real-world data analysis, we demonstrate the efficacy of our proposed method in providing accurate and reliable parameter estimates. This research contributes to the advancement of Bayesian statistical modeling techniques and offers valuable insights for practitioners in various fields.

Cite: Ibrahim Sadok, Mourad Zribi BAYESIAN GLM: A NON-INFORMATIVE APPROACH FOR PARAMETER ESTIMATION IN EXPONENTIAL DISPERSION REGRESSION MODELS. Reliability: Theory & Applications. 2025, March 1(82):715-727. DOI: https://doi.org/10.24412/1932-2321-2025-182-715-727

IMPLEMENTATION OF THE MAXIMUM PERMISSIBLE OVERLOAD CAPACITY OF A DC MOTOR	728-733

Rafig Sultanov, Elbrus Ahmedov, Nadir Aliyev

DC motors, due to their wide applicability in various industrial sectors, necessitate precise control of their overload capacity to ensure safe and efficient operation. This study presents a comprehensive methodology for assessing the maximum permissible overload capacity of a DC motor. The core of this methodology lies in the derivation and application of the electromechanical characteristic equation of an electric drive with current cutoff. This equation serves as the foundation for constructing the electromechanical characteristics of the drive, providing a detailed representation of the motor's performance under varying operational conditions. A novel circuit is proposed, featuring an automatic adjustment mechanism for the cut-off current setting based on the speed of the electric drive. This adaptive circuit design ensures that the motor operates within its maximum permissible overload capacity, thereby optimizing performance and preventing potential damage due to excessive loads. By leveraging this advanced control methodology, the reliability and efficiency of DC motors in industrial applications can be significantly enhanced. This approach not only maximizes the motor's operational capabilities but also contributes to the overall safety and longevity of the electric drive systems.

Cite: Rafig Sultanov, Elbrus Ahmedov, Nadir Aliyev IMPLEMENTATION OF THE MAXIMUM PERMISSIBLE OVERLOAD CAPACITY OF A DC MOTOR . Reliability: Theory & Applications. 2025, March 1(82):728-733. DOI: https://doi.org/10.24412/1932-2321-2025-182-728-733

THE ROLE OF MODERN GROUNDING DEVICES IN ENSURING THE STABILITY OF POWER SYSTEMS	734-742

I.N. Rahimli, A.L. Bakhtiyarov, G.K. Abdullayeva

The article focuses on investigating the impact of grounding device parameters on the stability of power systems under external disturbances, such as short circuits and lightning strikes. The study examines transient processes in power systems, including the analysis of rotor angle variations in generators and voltage recovery. Numerical modeling based on the equations of synchronous generators and electromagnetic transient processes is employed. A comparative analysis of various grounding device configurations is conducted, taking into account their resistance and the system's recovery time. The research results identify the optimal parameters of grounding devices that minimize the recovery time of power systems and enhance their overall stability. The findings can be utilized in the design and operation of power systems with improved reliability.

Cite: I.N. Rahimli, A.L. Bakhtiyarov, G.K. Abdullayeva THE ROLE OF MODERN GROUNDING DEVICES IN ENSURING THE STABILITY OF POWER SYSTEMS . Reliability: Theory & Applications. 2025, March 1(82):734-742. DOI: https://doi.org/10.24412/1932-2321-2025-182-734-742

RELIABILITY, AVAILABILITY AND MAINTAINABILITY OF A BOILER IN THERMAL POWER PLANT– A CASE STUDY	743-753

K. Sunitha, T. Sumathi Uma Maheshwari, M. Tirumala Devi, A. Satyanarayana4

Many countries face problems in electricity generation. Boilers play an important role in a power plant. Sudden failures of a power plant boiler components cause loss of production and high maintenance cost. Due to unplanned and irregular maintenance, which can ultimately increase the production cost of electricity. This is a common challenge faced by power plant operators worldwide. The present study aims to examine and analyze the failure times of a boiler at a thermal power plant and identify its critical failure expectancy and system reliability. The data was collected over a long period and was analyzed using statistical methods. In this study, the hypothesis has been proposed to choose the best analysis. Furthermore, reliability, availability, and maintainability analysis were carried out under discrete analysis. The analysis included identifying the probability distribution of the failure times, identifying critical failure expectancy, and determining system reliability.

Cite: K. Sunitha, T. Sumathi Uma Maheshwari, M. Tirumala Devi, A. Satyanarayana4 RELIABILITY, AVAILABILITY AND MAINTAINABILITY OF A BOILER IN THERMAL POWER PLANT– A CASE STUDY. Reliability: Theory & Applications. 2025, March 1(82):743-753. DOI: https://doi.org/10.24412/1932-2321-2025-182-743-753

PROBABILISTIC INVENTORY MODEL FOR DETERIORATING ITEMS WITH UNCERTAIN DEMAND UNDER PENTAGONAL FUZZY ENVIRONMENT	754-772

Ashish Negi, Ompal Singh

Using a pentagonal fuzzy framework, this research presents a probabilistic inventory model for deteriorating items under an uncertain demand. Degeneration of items puts a company’s financial ability to meet its objectives at risk. Few models have synchronized optimization over this whole scenario with all components, according to a survey of the literature. It deals with the difficulties of inventory control in situations where demand is represented by fuzzy sets but is not precisely known. The model offers a clearer and more useful understanding of demand uncertainty by defuzzifying pentagonal fuzzy numbers using the Graded Mean Integration Representation (GMIR) approach. The goal of the study is to optimize inventory levels in order to minimize total costs, which include holding, degradation, shortage, and purchase. These components are included into a mathematical model, and numerical scenarios are shown to compare the both potential strategies. The sensitivity of the solution and decision variables with respect to different inventory characteristics is examined in both crisp and fuzzy settings. Fuzzy logic is integrated into the model to provide a strong framework for making decisions when dealing with ambiguous demand and the complications that come with deteriorating inventory. The paper includes numerical examples and sensitivity analyses to demonstrate the model™s effectiveness and practical relevance. These findings provide valuable guidance for inventory managers aiming to improve decision-making and operational efficiency in contexts with fuzzy demand and deteriorating products. At the optimal position, the total cost is relatively inelastic to an increase in base deterioration rate and more elastic to a decrease in it. Although the crisp example is marginally less efficient per unit cost, total costs are lower than in the fuzzy case, which is to be expected given the fuzzy case’s potential for superior results.

Cite: Ashish Negi, Ompal Singh PROBABILISTIC INVENTORY MODEL FOR DETERIORATING ITEMS WITH UNCERTAIN DEMAND UNDER PENTAGONAL FUZZY ENVIRONMENT. Reliability: Theory & Applications. 2025, March 1(82):754-772. DOI: https://doi.org/10.24412/1932-2321-2025-182-754-772

RELIABILITY ANALYSIS OF A POWER DISTRIBUTION SYSTEM WITH TWO TRANSFORMERS AND SIX FEEDERS	773-786

Syed Mohd Rizwan, Satish Tanavade, Kajal Sachdeva, Syed Zegham Taj

The article explores the reliability and sensitivity of a power distribution substation. It includes an analysis based on real maintenance data collected from a 33/11kV electrical power distribution substation, which features a set of two 6 MVA power transformers supplying power through a total of six outgoing feeders (three feeders per transformer). The study documents faults observed in both transformers and all six outgoing feeders. The reliability of the substation is evaluated using various indices such as availability, repair durations, and expected repair frequencies for different failure types. The analysis employs Markov processes and regenerative point techniques. In addition to reliability, the study includes a profit analysis of the substation. It presents graphical representations of key parameters. Furthermore, a sensitivity analysis is conducted to assess how variations in parameters impact the availability and profitability of the substation components. Substation economics is also established to assess the operational viability.

Cite: Syed Mohd Rizwan, Satish Tanavade, Kajal Sachdeva, Syed Zegham Taj RELIABILITY ANALYSIS OF A POWER DISTRIBUTION SYSTEM WITH TWO TRANSFORMERS AND SIX FEEDERS . Reliability: Theory & Applications. 2025, March 1(82):773-786. DOI: https://doi.org/10.24412/1932-2321-2025-182-773-786

A NEW FAMILY OF LINDLEY DISTRIBUTIONS FEATURING BIMODAL CASES	787-799

Festus C. Opone, Jacob C. Ehiwario, Sunday A. Osagie, John N. Igabari, Nosakhare Ekhosuehi

Several lifetime distributions have been developed in literature to handle different real-world scenario. Most of these distributions were developed to model a unimodal (symmetric or asymmetric) data. Only a hand-full of these distributions exhibits a bimodal property. This paper explores a new family of Lindley distributions featuring a bimodal property. We introduce five different sub-families of the T-Power Lindley{Y} family based on the quantile function of the uniform, exponential, Frechet, log-logistic and logistic distributions. Useful mathematical properties of the proposed T-Power Lindley{Y} family of distributions are derived and sub-models were the random variable T follows the one-parameter Topp- Leone, exponential, exponentiated exponential, Weibull and Gumbel distributions are introduced. From the graphical representation of the density function of these sub-models, we observe that the shape of the density function accommodates a decreasing (reversed-J), left-skewed, right-skewed, symmetric, as well as a bimodal shape. In order to illustrate the usefulness and performance of the proposed T-Power Lindley{Y} family of distributions, the Gumbel Power Lindley (GPL) distribution belonging to the proposed family of distribution was employed to fit a bimodal data set alongside with the beta-Normal distribution. Result obtained from the analysis revealed that the Gumbel Power Lindley (GPL) distribution compares favourably better than the beta-Normal distribution. The density fits of the distributions for the data set was also investigated to support the claim.

Cite: Festus C. Opone, Jacob C. Ehiwario, Sunday A. Osagie, John N. Igabari, Nosakhare Ekhosuehi A NEW FAMILY OF LINDLEY DISTRIBUTIONS FEATURING BIMODAL CASES. Reliability: Theory & Applications. 2025, March 1(82):787-799. DOI: https://doi.org/10.24412/1932-2321-2025-182-787-799

OPTIMIZING TWO-WAREHOUSE INVENTORY MODEL FOR DETERIORATING ITEMS WITH GENERALIZED EXPONENTIAL DEMAND, PARTIAL BACKLOGGING, AND INFLATION USING BACTERIAL FORAGING OPTIMIZATION	800-813

Garima Sethi, Ajay Singh Yadav, Chaman Singh

This paper presents a novel two-warehouse inventory model for degrading products, where the demand rate is governed over time by a generalized exponential function. Two real-world supply chain challenges that are taken into account in the model are the economic effects of inflation and partial backlog. By reducing the whole cost, which includes holding, shortage, and degradation charges, the Bacterial Foraging Optimization (BFO) method maximizes inventory management. The effectiveness of the model is validated through a comprehensive numerical example, and graphical representations demonstrate the impact of key factors on system performance. The results demonstrate how BFO may be used to complex inventory problems, giving supply chain managers crucial data as they try to balance cost-effectiveness and demand fluctuations in an inflationary environment. This approach highlights the need of advanced optimization techniques in improving decision-making processes for degrading products in a two-warehouse scenario.

Cite: Garima Sethi, Ajay Singh Yadav, Chaman Singh OPTIMIZING TWO-WAREHOUSE INVENTORY MODEL FOR DETERIORATING ITEMS WITH GENERALIZED EXPONENTIAL DEMAND, PARTIAL BACKLOGGING, AND INFLATION USING BACTERIAL FORAGING OPTIMIZATION. Reliability: Theory & Applications. 2025, March 1(82):800-813. DOI: https://doi.org/10.24412/1932-2321-2025-182-800-813

SURVIVAL ANALYSIS OF A STOCHASTIC MODEL ON CARDIOVASCULAR SYSTEM CONSIDERING POSSIBILITES OF DAMAGE, FAILURE AND RECOVERY OF HEART	814-826

Shikha Bhardwaj, Rajeev Kumar

The present paper deals with survival analysis of a stochastic model on cardiovascular system considering possibilities of damage, failure and recovery of heart. The analysis is based upon a stochastic model for the system considering different kinds of damage and failure of heart at different situations. The treatments and recovery of heart are taken in to account. On complete failure of heart, transplantation of the heart is also considered. The model has been analyzed by determining important measures of effectiveness using Markov process and regenerative point technique. Sensitivity analysis has also been done to select important parameters for enhancing the survivability of the system.

Cite: Shikha Bhardwaj, Rajeev Kumar SURVIVAL ANALYSIS OF A STOCHASTIC MODEL ON CARDIOVASCULAR SYSTEM CONSIDERING POSSIBILITES OF DAMAGE, FAILURE AND RECOVERY OF HEART . Reliability: Theory & Applications. 2025, March 1(82):814-826. DOI: https://doi.org/10.24412/1932-2321-2025-182-814-826

SAMPLING INSPECTION SCHEMES WITH SWITCHING RULES FOR LIFE TESTS BASED ON EXPONENTIAL DISTRIBUTION	827-834

A. Pavithra, R. Vijayaraghavan

A life test is a random experiment which is performed on manufactured items such as electric and electronic components in order to estimate their lifetime by selecting the items randomly from the production process. The lifetime / lifespan of the product is a random variable that follows a specific continuous-type probability distribution, called the lifetime distribution. Reliability sampling, which is one among the classifications of product control techniques, deals with inspection procedures for sentencing one or more lots or batches of items submitted for inspection. An acceptance sampling scheme is a combination of sampling inspection plans with switching rules for changing from one plan to another. A switching rule is an instruction within a sampling scheme for changing from one sampling plan to another of greater or lesser severity of sampling based on the demonstrated quality history. In this paper, the concept of sampling schemes for life tests with a switching rule involving two samples under the assumption that the lifetime random variable follows an exponential distribution is introduced. A procedure is developed for designing the optimum sampling schemes with minimum sample sizes when two points on the desired operating characteristic curve are prescribed providing protection to the producer and the consumer.

Cite: A. Pavithra, R. Vijayaraghavan SAMPLING INSPECTION SCHEMES WITH SWITCHING RULES FOR LIFE TESTS BASED ON EXPONENTIAL DISTRIBUTION. Reliability: Theory & Applications. 2025, March 1(82):827-834. DOI: https://doi.org/10.24412/1932-2321-2025-182-827-834

USE OF MEDIAN BASED ESTIMATOR TO MITIGATE OUTLIER’S EFFECT THROUGH S2 CHART	835-847

Sonam Jaiswal

In this paper, we consider an upper-sided Phase II variance chart with probability limits in case of unknown parameter because the quality practitioner interested in monitoring increased variance of the process parameter. It is well established that when the Phase I data are contaminated with spurious observations, performance of the chart is suspected to deviate from what is normally expected. Therefore, we propose an improved performance of one-sided variance chart under the exceedance probability criterion for a fixed in-control average run length using the absolute deviation from median estimator. Under the exceedance probability criteria, the chart is designed so that the user can get more confidence in their in-control average run length values. The proposed chart is compared with the existing chart in case of contaminated and non-contaminated observations. Result shows that performance of variance chart shows robust performance when using absolute deviation from median estimator. Finally, an example has been provided in the favour of our proposed study.

Cite: Sonam Jaiswal USE OF MEDIAN BASED ESTIMATOR TO MITIGATE OUTLIER’S EFFECT THROUGH S2 CHART . Reliability: Theory & Applications. 2025, March 1(82):835-847. DOI: https://doi.org/10.24412/1932-2321-2025-182-835-847

ADVANCED STATISTICAL APPROACH TO FAILURE DATA WITH GAMMA AND WEIBULL DISTRIBUTIONS	848-854

Vijayan S, Kavitha S

This paper aims to systematically investigate the utility of the Gamma and Weibull distributions, focusing on their application to biomedical datasets and clarifying their mathematical and statistical properties. By analyzing lifetime data across various disciplines, the research emphasizes the effectiveness and flexibility of these distributions in capturing the complexities of biomedical data. It underscores the importance of parameters such as standard error, log-likelihood, Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC) in value estimation. The findings suggest that both distributions provide valuable insights into the underlying data, with practical implications for reliability engineering and failure analysis. Moreover, the study demonstrates that the Weibull distribution offers a better fit to the given data than the Gamma distribution due to its adaptability, which yields superior results. A key contribution of this study is the proposal of a model based on estimating the Conditional Weibull distribution for feature parameters, which accurately predicts a finite mixture of two-parameter Weibull distributions initially verified on datasets.

Cite: Vijayan S, Kavitha S ADVANCED STATISTICAL APPROACH TO FAILURE DATA WITH GAMMA AND WEIBULL DISTRIBUTIONS . Reliability: Theory & Applications. 2025, March 1(82):848-854. DOI: https://doi.org/10.24412/1932-2321-2025-182-848-854

BAYESIAN PARAMETER ESTIMATION FOR TRANSMUTED WEIBULL DISTRIBUTION WITH CENSORING RATES AND VARIOUS LOSS FUNCTIONS	855-864

Jeslin J, Radhika A, Haripriya M

Statistical distributions are essential tools for describing and predicting real-world phenomena, though recent advancements in data collection have made it challenging to fit existing probability models to many practical datasets. While non-parametric models are sometimes recommended, parametric models retain substantial popularity due to their interpretability and flexibility. The quadratic rank transmutation map (QRTM) technique has been used to create new families of non-Gaussian distributions, known as transmuted distributions, which allow for modifications in moments, skewness, and kurtosis, thus increasing flexibility. The transmuted Weibull distribution (TWD) has gained attention for applications in reliability, survival analysis, and lifetime data analysis. This article focuses on a Bayesian analysis of the transmuted Weibull distribution, a generalization of the traditional Weibull model that addresses its limitations, particularly for datasets exhibiting non-monotonic failure rates. Bayesian parameter estimation is performed using a Markov Chain Monte Carlo (MCMC) algorithm, with both non-informative and informative priors. We calculate Bayes estimators (BEs) and posterior risks (PRs) under different loss functions, including the Absolute Error Loss Function (AELF), precautionary loss function (PLF), and quadratic loss function (QLF). Simulation studies evaluate the Bayes estimators' performance, investigating the effects of various priors, sample sizes, and censoring rates on estimation accuracy and credible interval width. Real-world data applications highlight the practical utility of the Bayesian approach for the TWD, showing consistent results with increasing sample sizes and underscoring the robustness of the MCMC algorithm for parameter estimation. The article is structured as follows: the TWD’s parameters, including scale, shape, and transmutation, are estimated under different loss functions and priors. Bayesian credible intervals (BCIs) are also computed. Both uncensored and censored data environments are considered, with varying sample sizes and censoring rates. Posterior risks for each estimator are analyzed to assess performance, and two real datasets are used to illustrate the flexibility and applicability of the proposed distribution. This study lays a foundation for future research, such as exploring mixtures of transmuted Weibull distributions or conducting Bayesian analyses for record values.

Cite: Jeslin J, Radhika A, Haripriya M BAYESIAN PARAMETER ESTIMATION FOR TRANSMUTED WEIBULL DISTRIBUTION WITH CENSORING RATES AND VARIOUS LOSS FUNCTIONS . Reliability: Theory & Applications. 2025, March 1(82):855-864. DOI: https://doi.org/10.24412/1932-2321-2025-182-855-864

OPTIMIZATION OF EQUIPMENT RELIABILITY BASED ON A NEURO-FUZZY APPROACH: CASE OF A FLOUR MILL	865-882

Ngnassi Djami Aslain Brisco

The main objective of this paper is to present an innovative approach combining fuzzy logic and artificial neural networks to optimize equipment reliability in the specific context of a flour mill. Faced with the challenges of performance and profitability in this industrial sector, the neuro-fuzzy methodology has been developed to meet the challenges related to the complexity and uncertainty inherent in equipment reliability management. The first part of the paper provides an overview of the problem, introducing the key concepts of reliability and maintenance, while highlighting the particular challenges of the milling industry. This paper also outlines the advantages of the neuro-fuzzy approach for optimizing equipment reliability. The methodology for developing the neuro-fuzzy model is detailed in the second part. It covers the construction of the fuzzy inference system, the design of the neural network structure, as well as the training and optimization steps of the model. The case study conducted in a flour mill is presented in the third part. After a description of the company and its equipment system, the collection and analysis of reliability data are presented, as well as the implementation of the developed neuro-fuzzy model. The results obtained demonstrate that this methodology makes it possible to better anticipate failures, optimize maintenance interventions, and reduce associated costs. Sensitivity analysis and comparison with other optimization methods confirm the validity and operational and economic benefits of the proposed approach.

Cite: Ngnassi Djami Aslain Brisco OPTIMIZATION OF EQUIPMENT RELIABILITY BASED ON A NEURO-FUZZY APPROACH: CASE OF A FLOUR MILL . Reliability: Theory & Applications. 2025, March 1(82):865-882. DOI: https://doi.org/10.24412/1932-2321-2025-182-865-882

ENHANCING INTRUSION DETECTION SYSTEM RELIABILITY USING GWO-SOMNN (GREY WOLF OPTIMIZATION WITH SELF-ORGANIZING MAP NEURAL NETWORK)	883-896

Archana Gondalia, Apurva Shah

In today’s fast-changing technological environment, the number of Internet-connected devices has grown significantly, raising the risk of cybersecurity threats for both individuals and organizations. Network Intrusion Detection Systems (NIDS) have become vital tools for protecting networks from these increasing threats. This paper presents a GWO-SOMNN approach (Gray Wolf Optimization with Self-Organizing Map Neural Network) that combines Grey Wolf Optimization (GWO), Self-Organizing Maps (SOM) and Neural Networks (NN) for feature selection and classification on the UNSW-NB15 dataset. The proposed method leverages GWO to optimize feature selection, reducing the dataset’s dimensionality and computational load, while SOM is employed for clustering and visualizing high-dimensional data. Neural Networks are then used for effective classification of network attacks. The GWO-SOMNN approach is evaluated on the UNSW-NB15 dataset, and its performance is measured in terms of 97.18% accuracy and 97.15% F1-score for binary classification and 82.41% accuracy and 78.92% F1-score for multiclass classification. The results demonstrate significant improvements over traditional methods, particularly in enhancing the classification of both binary and multi-class network attacks. These findings highlight the potential of this integrated approach in developing more efficient and accurate network intrusion detection systems.

Cite: Archana Gondalia, Apurva Shah ENHANCING INTRUSION DETECTION SYSTEM RELIABILITY USING GWO-SOMNN (GREY WOLF OPTIMIZATION WITH SELF-ORGANIZING MAP NEURAL NETWORK). Reliability: Theory & Applications. 2025, March 1(82):883-896. DOI: https://doi.org/10.24412/1932-2321-2025-182-883-896

ANALYSIS OF AN ENCOURAGED ARRIVAL MARKOVIAN QUEUE WITH SINGLE WORKING VACATION, IMPATIENCE AND RENEGING OF CUSTOMERS	897-902

V. Narmadha, P. Rajendran

In this paper, we analyze a single server markovian queueing model with encouraged arrivals that undergoes a single working vacation. Additionally, we consider the impatience and reneging behavior of customers in the queue during the working vacation period. Customers arrive at the system following a Poisson distribution. The server goes on vacation when the system is empty and stays on vacation for a random period that follows an exponential distribution. During the working vacation period, the server continues to provide service at a slower rate. After the vacation, the server returns to the regular service period and continues providing service at the regular busy period rate if there are one or more customers in the system, or it remains idle until a new customer arrives. During the working vacation, customers in the queue become impatient and renege from the system, with the reneging time assumed to follow an exponential distribution. The system is characterised as a quasi-birth-death process, and the stationary probabilities are derived using the probability generating function method. Some numerical analysis is also carried out to show the effect of encouraged arrivals on performance measures.

Cite: V. Narmadha, P. Rajendran ANALYSIS OF AN ENCOURAGED ARRIVAL MARKOVIAN QUEUE WITH SINGLE WORKING VACATION, IMPATIENCE AND RENEGING OF CUSTOMERS . Reliability: Theory & Applications. 2025, March 1(82):897-902. DOI: https://doi.org/10.24412/1932-2321-2025-182-897-902

IMPACT OF DESIGN AND CONSTRUCTION ERRORS ON THE STRUCTURAL RELIABILITY OF STEEL INDUSTRIAL BUILDINGS	903-917

Andrey Lipin, Seymur Bashirzade, Mukhlis Hajiyev, Rafail Garibov

Errors in design and construction critically undermine the structural reliability of industrial buildings, putting property, the environment, and human safety at risk. In this regard, the present research work is intended to investigate how such mistakes influence the performance of the main structural components and the stability of steel industrial buildings. Detailed finite element analysis was performed using DIANA FEA for solid modeling and SAP2000 for beam modeling to assess global structural performance. This includes, among others, the insufficiency of local reinforcement in compressed members and eccentricity in column connections. It was performed to analyze the local and global buckling behaviors, deviations in symmetry, and inefficiency of the bracing systems. Consequently, it reveals a significant reduction in load-bearing capacity due to reinforcement deficiencies in the compressed elements and eccentricity, while a structural loss in integrity becomes highly significant at symmetry deviations, especially in horizontal loads. This study provides critical insights into mitigating design and construction errors to enhance the reliability of industrial steel buildings.

Cite: Andrey Lipin, Seymur Bashirzade, Mukhlis Hajiyev, Rafail Garibov IMPACT OF DESIGN AND CONSTRUCTION ERRORS ON THE STRUCTURAL RELIABILITY OF STEEL INDUSTRIAL BUILDINGS . Reliability: Theory & Applications. 2025, March 1(82):903-917. DOI: https://doi.org/10.24412/1932-2321-2025-182-903-917

COST AND RELIABILITY OPTIMIZATION OF A COMPLEX SYSTEM USING MULTI-OBJECTIVE GREY WOLF OPTIMIZATION TECHNIQUE	918-927

Anuj Kumar, Ganga Negi, Mangey Ram, Sangeeta Pant, Sushil Chandra Dimri

Modern engineering systems increasingly focus on multi-objective optimization. Nature-inspired optimization techniques have shown superior efficiency and effectiveness compared to many traditional methods across various parameters. This work demonstrates the reliability and cost optimization of a complex bridge system using the Multi-Objective Grey Wolf Optimization algorithm (MOGWO). The bridge system in question is a series-parallel system. A key performance highlight is the use of an archive for search agents to generate a Pareto optimal front (PoF) with a minimal number of iterations. Among the various solutions in the PoF, the solution set that best meets the multi-objective criteria is preferred. Additionally, statistical analyses are conducted to further validate the competitiveness of the results.

Cite: Anuj Kumar, Ganga Negi, Mangey Ram, Sangeeta Pant, Sushil Chandra Dimri COST AND RELIABILITY OPTIMIZATION OF A COMPLEX SYSTEM USING MULTI-OBJECTIVE GREY WOLF OPTIMIZATION TECHNIQUE . Reliability: Theory & Applications. 2025, March 1(82):918-927. DOI: https://doi.org/10.24412/1932-2321-2025-182-918-927

EXPLORING AN EXTENDED RAYLEIGH DISTRIBUTION: MODELING AND APPLICATIONS IN REAL LIFE SCENARIOS	928-941

Aadil Ahmad Mir, S.P. Ahmad

In this manuscript, we propose a new extension of the Rayleigh distribution, named as Ratio Transformation Rayleigh Distribution (RTRD), which offers superior fits compared to the Rayleigh distribution and several of its known generalizations. We derive various properties of the proposed distribution, including moments, moment generating function, hazard rate, conditional moments, Bonferroni and Lorenz curves, mean residual life, mean waiting time, Renyi entropy and order statistics. The unknown parameters are estimated using the maximum likelihood estimation procedure. An extensive simulation study is conducted to illustrate the behavior of the maximum likelihood estimators (MLEs) based on Mean Square Errors. The flexibility of the new distribution is demonstrated by applying it to two real data sets. Comparative analysis with the Rayleigh distribution, Weighted Rayleigh distribution, Exponentiated Rayleigh distribution and Transmuted Rayleigh distribution reveals that RTRD outperforms these competing distributions based on Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Akaike Information Criterion Corrected (AICC) and other goodness of fit measures.

Cite: Aadil Ahmad Mir, S.P. Ahmad EXPLORING AN EXTENDED RAYLEIGH DISTRIBUTION: MODELING AND APPLICATIONS IN REAL LIFE SCENARIOS. Reliability: Theory & Applications. 2025, March 1(82):928-941. DOI: https://doi.org/10.24412/1932-2321-2025-182-928-941

THE MARSHALL-OLKIN EXTENDED SHANKER DISTRIBUTION AND ITS APPLICATIONS	942-956

Sara Ziari, S.M.T.K. MirMostafaee

In this paper, we introduce the Marshall–Olkin extended Shanker distribution, as an extension of the Shanker distribution, using the Marshall-Olkin approach. Several important properties of the new distribution, such as the hazard rate function, moments, incomplete moments, mean deviations, Lorenz and Bonferroni curves, and Rényi entropy are explored. The estimation of the parameters is discussed with the help of the maximum likelihood method. The performance of the estimators is evaluated using a simulation study. Two real data applications are developed in order to assess the flexibility and power of the new distribution. The goodness of fit criteria reveal that the new model may provide a better fit than the Shanker distribution and other competing models that belong to the Marshall-Olkin G family of distributions.

Cite: Sara Ziari, S.M.T.K. MirMostafaee THE MARSHALL-OLKIN EXTENDED SHANKER DISTRIBUTION AND ITS APPLICATIONS . Reliability: Theory & Applications. 2025, March 1(82):942-956. DOI: https://doi.org/10.24412/1932-2321-2025-182-942-956

ANALYSIS OF THERMAL PROCESSES IN A CONTROLLED ASYNCHRONOUS MOTOR	957-965

S.Y. Shikhaliyeva

This article examines the reliability and risks associated with technical systems involved in the conversion of mechanical energy to electrical energy, focusing on the thermal dynamics of electric machines. It explores the processes of heat generation due to energy losses, primarily heat dissipation, and the effects of temperature increases on the longevity and performance of the machine. The cooling systems essential for managing heat transfer and minimizing overheating are analyzed, considering factors such as heat conduction, convection, and radiation, as well as the role of electrohydraulic and aerodynamic systems in optimizing heat exchange. Special attention is given to the impact of temperature fluctuations on the insulation materials of electric machines, with an emphasis on how overheating accelerates insulation degradation and reduces machine lifespan. The paper further discusses the intricate relationship between cooling efficiency, machine power, and the economic implications of designing effective thermal management systems. Moreover, the challenges of selecting and optimizing cooling strategies in electric machine design are highlighted, considering both technical and economic factors. Lastly, the study delves into ventilation calculations necessary to ensure efficient airflow and cooling, using practical equations and methods for determining pressure loss and fan performance, underscoring the complexity and importance of achieving optimal temperature conditions for long-term, reliable machine operation.

Cite: S.Y. Shikhaliyeva ANALYSIS OF THERMAL PROCESSES IN A CONTROLLED ASYNCHRONOUS MOTOR . Reliability: Theory & Applications. 2025, March 1(82):957-965. DOI: https://doi.org/10.24412/1932-2321-2025-182-957-965

ENHANCING ENERGY SYSTEM RELIABILITY: MODERN APPROACHES AND SOLUTIONS	966-971

Sh.V. Ismayilova, Z.A. Isgandarova, K.M. Mukhtarova

The article analyzes methods for improving the reliability of energy systems considering the SAIDI and SAIFI indicators, which reflect the duration and frequency of power outages. Approaches are discussed, including the implementation of intelligent monitoring systems, Automated Distribution Management Systems (ADMS), as well as distributed generation and redundancy. The study confirms that the integrated use of these technologies significantly enhances network reliability, reducing SAIDI and SAIFI indices, and evaluates the economic efficiency of these solutions, demonstrating their long-term profitability.

Cite: Sh.V. Ismayilova, Z.A. Isgandarova, K.M. Mukhtarova ENHANCING ENERGY SYSTEM RELIABILITY: MODERN APPROACHES AND SOLUTIONS . Reliability: Theory & Applications. 2025, March 1(82):966-971. DOI: https://doi.org/10.24412/1932-2321-2025-182-966-971

SELECTION OF A BAYESIAN DOUBLE SAMPLING PLAN THROUGH MARKOV DEPENDENCE METHOD IN DRUG DISCOVERY	972-980

Kaviyarasu V, Karthick

Most of the pharmaceutical firms have worked hard to maintain quality in their manufacturing products like medicines and biological instruments using the principles of statistical quality control to optimize the fault model. In this field, one of the pioneering statistical methods is acceptance sampling by attributes. A sampling plan is used to assess the quality of goods, keep an eye on the quality of the materials, and confirm whether or not the yields are defect-free or not. When posterior knowledge about the parameter is known, the Bayesian strategy provides a more robust statistical method for reaching a suitable conclusion. In this article a new Bayesian double sampling plan under stochastic modeling was established. This is achieved by various characteristics of sampling plan explicit by its random variable and its probability function. This plan is studied through the Gamma- Poisson model to safeguard both the producer and consumer by minimizing the Average Sample Number and Total Cost. Necessary tables and figures are constructed for the selection of optimal plan parameters and suitable illustrations are provided that are applicable under pharmaceutical industries.

Cite: Kaviyarasu V, Karthick SELECTION OF A BAYESIAN DOUBLE SAMPLING PLAN THROUGH MARKOV DEPENDENCE METHOD IN DRUG DISCOVERY. Reliability: Theory & Applications. 2025, March 1(82):972-980. DOI: https://doi.org/10.24412/1932-2321-2025-182-972-980

OPTIMIZATION ANALYSIS OF UNRELIABLE MULTI-SERVER QUEUEING SYSTEM WITH BERNOULLI SCHEDULE WORKING VACATION, THRESHOLD-BASED RECOVERY POLICY, AND IMPATIENCE	981-995

Hayat Ramdani, Amina Angelika Bouchentouf, Lahcene Yahiaoui

This paper analyzes an unreliable multi-server queueing system incorporating working vacations, Bernoulli interruptions, breakdowns with a threshold recovery policy, balking, abandonment, and retention. During the break period, if there are customers in the queue, the servers may either resume normal service or continue their vacation. Customers arriving while the system is saturated are rejected. Failures occur unexpectedly but only when at least one customer is present in the system. Recovery procedures remain in effect until the total number of customers surpasses a predefined threshold. Using matrix-analytic methods, we derive steady-state solutions and explicit formulas for various performance indicators. Further, we explore cost parameter optimization.

Cite: Hayat Ramdani, Amina Angelika Bouchentouf, Lahcene Yahiaoui OPTIMIZATION ANALYSIS OF UNRELIABLE MULTI-SERVER QUEUEING SYSTEM WITH BERNOULLI SCHEDULE WORKING VACATION, THRESHOLD-BASED RECOVERY POLICY, AND IMPATIENCE. Reliability: Theory & Applications. 2025, March 1(82):981-995. DOI: https://doi.org/10.24412/1932-2321-2025-182-981-995

CLASSICAL AND BAYESIAN ESTIMATION OF EXPONENTIATED INVERSE RAYLEIGH DISTRIBUTION BASED ON RECORD VALUES	996-1008

Iftkhar Khan, Zaki Anwar, Zakir Ali

In this article explores two approaches for estimating the parameters of the exponentiated inverse Rayleigh distribution (EIRD) using record values: Classical estimation and Bayesian estimation. In classical estimation, maximum likelihood estimators (MLE’s) and the asymptotic confidence intervals are derived based on the observed Fisher information matrix of the parameters. In Bayesian estimation, estimators of the parameters are obtained under the square error loss function. This involves using Tierney-Kadane’s approximation (TK) and Markov chain Monte Carlo (MCMC) methods for Bayesian computation. Additionally, the article constructs the highest posterior credible intervals of the parameters using the MCMC method. To evaluate the performance of these estimators, a Monte Carlo simulation study is conducted to compare their behavior. Finally, a real data analysis is presented to illustrate the application of the methods discussed in the article.

Cite: Iftkhar Khan, Zaki Anwar, Zakir Ali CLASSICAL AND BAYESIAN ESTIMATION OF EXPONENTIATED INVERSE RAYLEIGH DISTRIBUTION BASED ON RECORD VALUES. Reliability: Theory & Applications. 2025, March 1(82):996-1008. DOI: https://doi.org/10.24412/1932-2321-2025-182-996-1008

THE POISSON-SUJA DISTRIBUTION AND ITS APPLICATIONS IN BIOLOGICAL COUNT DATA SETS	1009-1019

Rama Shanker, Joyshree Saharia, Kamlesh Kumar Shukla

The Poisson-Suja distribution which is a Poisson mixture of Suja distribution has been proposed. The descriptive statistics based on moments including coefficient of variation, skewness, kurtosis and index of dispersion has been derived and studied. Over-dispersion, unimodality and increasing hazard rate properties of the distribution have been studied. The method of moment and the method of maximum likelihood have been discussed for estimating parameters. Applications and the goodness of fit the distribution and its comparison with other one-parameter discrete distributions have also been presented. It was found more closer fit than other compared distributions. So, it can be considered as good discrete distribution for count datasets.

Cite: Rama Shanker, Joyshree Saharia, Kamlesh Kumar Shukla THE POISSON-SUJA DISTRIBUTION AND ITS APPLICATIONS IN BIOLOGICAL COUNT DATA SETS . Reliability: Theory & Applications. 2025, March 1(82):1009-1019. DOI: https://doi.org/10.24412/1932-2321-2025-182-1009-1019

A NEW TRANSMUTED PROBABILITY MODEL: PROPERTIES AND APPLICATIONS	1020-1034

Khawar Javaid, Bilal Ahmad Para

In this article, we introduced a new three parameter continuous probability model by extending a two parameter log-logistic distribution using the quadratic rank transmutation map technique. We provide a comprehensive description of the statistical properties of the newly introduced model. Robust measures of skewness and kurtosis of the proposed model have also been derived along with the moment generating function, characteristic function, reliability function and hazard rate function of the proposed model. The estimation of the model parameters is performed by maximum likelihood method followed by a Monte Carlo simulation procedure. The applicability of this distribution to modeling real life data is illustrated by two real life examples and the results of comparison to base distribution in modeling the data are also exhibited.

Cite: Khawar Javaid, Bilal Ahmad Para A NEW TRANSMUTED PROBABILITY MODEL: PROPERTIES AND APPLICATIONS. Reliability: Theory & Applications. 2025, March 1(82):1020-1034. DOI: https://doi.org/10.24412/1932-2321-2025-182-1020-1034

MULTI-OBJECTIVE PROBLEM WITH MULTIPLE JOBS ASSIGNED TO A SINGLE MACHINE WITHIN AVAILABLE COST UNDER UNCERTAIN ENVIRONMENT	1035-1048

Aamir Khan, Quazzafi Rabbani, Ahteshamul Haq

The assignment problem is a key challenge in optimization and operations research, finding applications in diverse real-world scenarios. The Hungarian method is a widely employed algorithm for solving this problem, especially in its balanced form. However, for unbalanced assignment problems, where tasks outnumber resources (or vice versa), an extension is necessary. One common approach introduces a dummy resource, but this may leave tasks unassigned. The Modified Hungarian method improves upon the standard algorithm for unbalanced problems, ensuring that all tasks are assigned to real resources. This is achieved by modifying the cost matrix and algorithm steps to accommodate additional tasks and resources. Triangular fuzzy numbers are discussed when exact parameter information is undefined, and fuzzy programming is applied to determine a compromise result. Incorporating cost and profit per resource, the Modified Hungarian algorithm addresses the problem of unspecified job allocations to a single machine by introducing a cost parameter for each machine. The methodology is demonstrated on a numerical example for better comprehension.

Cite: Aamir Khan, Quazzafi Rabbani, Ahteshamul Haq MULTI-OBJECTIVE PROBLEM WITH MULTIPLE JOBS ASSIGNED TO A SINGLE MACHINE WITHIN AVAILABLE COST UNDER UNCERTAIN ENVIRONMENT . Reliability: Theory & Applications. 2025, March 1(82):1035-1048. DOI: https://doi.org/10.24412/1932-2321-2025-182-1035-1048

RELATIONSHIP BETWEEN THE LEIMKUHLER CURVE AND RELIABILITY MEASURE CONCEPTS IN DOUBLE TRUNCATED VARIABLES	1049-1060

Vahideh Asghari, Gholamreza Mohtashami Borzadaran, Hadi Jabbari

This paper investigates the application of Leimkuhler curve and doubly truncated distributions in informetrics. Leimkuhler curve, ranking sources in descending order, emerges as a key tool for identifying efficient information sources. The study introduces a random variable representing the age of cited articles, influencing the probability distribution in retrospective citation analysis. Reliability measures, including mean residual life function and mean past residual life function are employed to analyze engineering and reliability aspects in informometric data. Truncation in probability distributions, particularly the doubly truncated distribution, is explored, revealing its broad applicability. The relationship between the Leimkuhler curve and truncated distributions will also be examined.

Cite: Vahideh Asghari, Gholamreza Mohtashami Borzadaran, Hadi Jabbari RELATIONSHIP BETWEEN THE LEIMKUHLER CURVE AND RELIABILITY MEASURE CONCEPTS IN DOUBLE TRUNCATED VARIABLES. Reliability: Theory & Applications. 2025, March 1(82):1049-1060. DOI: https://doi.org/10.24412/1932-2321-2025-182-1049-1060

MATHEMATICAL ANALYSIS OF THE MECHANICAL PART OF THE DESIGN SCHEME OF THE ELECTRIC DRIVE OF A HYBRID ELECTRIC MACHINE	1061-1069

S.A. Khanahmedova

The paper analyzes the mechanical part of the design scheme of the electric drive of a hybrid electric machine, which is a key stage in the design and research of automatic control systems. The main elements of a mechanical system, a model of a real mechanical system connected to an electric drive, including all moving elements, transmission mechanisms, and actuators that convert electrical energy into mechanical work, are considered. The presented calculation scheme allows you to analyze dynamic processes, i.e. to study the system's behavior over time, to determine stability, fluctuations, and other characteristics. Calculations of various mass systems are performed using the capabilities of the MATLAB/Simulink software package for a three-mass and two-mass system. These models can be used for different systems with different parameters. To draw up a structural diagram, the elements of the mechanical part and the connections between the elements, the types of these connections (rigid, elastic) and the directions of motion transmission are determined. Structural diagrams are used to analyze the dynamic characteristics of the system, determine transients, stability, and vibrations.

Cite: S.A. Khanahmedova MATHEMATICAL ANALYSIS OF THE MECHANICAL PART OF THE DESIGN SCHEME OF THE ELECTRIC DRIVE OF A HYBRID ELECTRIC MACHINE . Reliability: Theory & Applications. 2025, March 1(82):1061-1069. DOI: https://doi.org/10.24412/1932-2321-2025-182-1061-1069

ZERO TRUNCATED POISSON REGRESSION MODEL FOR REPRODUCTIVE PATTERNS ON COUNT DATA	1070-1088

B. Muniswamy, M. V. Lavanya

The number of children ever born is an important measure for understanding fertility patterns, which impact demographic structures and population growth. The problem relates to the modeling of count data that includes the truncation of zero values, specifically focusing on women who have experienced childbirth at least once. This study analyzes the factors that influence the number of children ever born (CEB) among women aged 15 to 50 in Andhra Pradesh, utilizing data from the National Family Health Survey (NFHS-5) conducted from 2019 to 2021. The study used Zero-Truncated Poisson (ZTP) and Zero-Truncated Generalized Poisson (ZTGP) models to identify major determinants, including religion, kind of cooking fuel used, place of delivery, wealth, age, and fertility choices. The ZTP regression model was found to be the best model and identifies significant determinants such as religion, wealth, age, and fertility preferences. The results show that rural residence, Muslim faith, and older age groups are associated with higher CEB, while wealthier women tend to have fewer children. The study shows the importance of implementing focused reproductive health activities, specifically in rural regions, to manage population growth and enhance the health outcomes of both mothers and children.

Cite: B. Muniswamy, M. V. Lavanya ZERO TRUNCATED POISSON REGRESSION MODEL FOR REPRODUCTIVE PATTERNS ON COUNT DATA . Reliability: Theory & Applications. 2025, March 1(82):1070-1088. DOI: https://doi.org/10.24412/1932-2321-2025-182-1070-1088

AN M/G/1 RETRIAL QUEUE WITH WORKING VACATION, NON PERSISTENT CUSTOMERS AND A WAITING SERVER	1089-1099

R. Keerthana

An M/G/1 retrial queue with working vacation, non persistent customers and a waiting server is taken into consideration in this study. Both retrial times and service times are assumed to follow general distribution and the waiting server follows an exponential distribution. Before switching over to a vacation the server waits for some arbitrary amount of time and so is called a waiting server. During the working vacation period customers are served at a lesser rate of service. We obtain the PGF for the number of customers and the mean number of customers in the invisible waiting area which is acquired by utilizing the supplementary variable technique. We compute the waiting time distribution. Out of interest a few special cases are conferred. Numerical outcomes are exhibited.

Cite: R. Keerthana AN M/G/1 RETRIAL QUEUE WITH WORKING VACATION, NON PERSISTENT CUSTOMERS AND A WAITING SERVER. Reliability: Theory & Applications. 2025, March 1(82):1089-1099. DOI: https://doi.org/10.24412/1932-2321-2025-182-1089-1099

REPETITIVE SAMPLING INSPECTION PLAN UNDER TRUNCATED LIFETEST BASED ON ONE PARAMETER POLYNOMIAL EXPONENTIAL DISTRIBUTION	1100-1115

Anumita Mondal, Sudhansu S. Maiti

This article constructs a Repetitive Sampling Inspection Plan under Truncated life test (RSIPTL) when the lifetime follows the One Parameter Polynomial Exponential (OPPE) family of distributions. In RSIPTL, a lot can be accepted or rejected in the first, second, and so on, based on the number of defective items in each sample. The OPPE has infinite support. It has transformed into its unit form to utilize finite support, i.e., having the support (0, 1). The Lindley distribution, a particular choice of the OPPE, has been studied in detail. We obtained the minimum number of items required in a lot to satisfy the consumer risk. Extensive tables are prepared for easy understanding and use of the plan for industrial workers. The RSIPTL is compared with a single sampling plan (SSP) and a two-stage reliability acceptance sampling plan (TSRASP) for Lindley and Exponential distributions. Two data sets are discussed and comparative statements are made with respect to the proposed plan.

Cite: Anumita Mondal, Sudhansu S. Maiti REPETITIVE SAMPLING INSPECTION PLAN UNDER TRUNCATED LIFETEST BASED ON ONE PARAMETER POLYNOMIAL EXPONENTIAL DISTRIBUTION. Reliability: Theory & Applications. 2025, March 1(82):1100-1115. DOI: https://doi.org/10.24412/1932-2321-2025-182-1100-1115