A REVIEW ON BULK QUEUE WITH SERVER BREAKDOWN MODELS

Rani R and Indhira K

This review article presents an overview of bulk arrival and bulk service with breakdown QM’s. The concept of bulk arrivals and bulk service has a new significance in the world of reality. To prevent the problem of traffic congestion, researchers must concentrate their efforts on developing models and processes to address the issue. Numerical methods of QM’s are critical in many industries, notably in production lines, to alleviate traffic congestion. This study seeks to give analysts, researchers, and industry professionals enough information to model congestion problems and extract various performance indicators to improve the QS’s.

Cite: Rani R and Indhira K A REVIEW ON BULK QUEUE WITH SERVER BREAKDOWN MODELS. Reliability: Theory & Applications. 2024, June 2(78): 25-34, DOI: https://doi.org/10.24412/1932-2321-2024-278-25-34

COMPARATIVE ANALYSIS OF METHODS FOR ESTIMATING ELECTRICITY LOSSES IN PROBLEMS OF OPERATIONAL OPTIMIZATION OF POWER SYSTEM MODES 

V.Kh. Nasibov R.R. Alizade E.J. Isgenderov

The distribution of unscheduled capacity corresponding to the difference between current and forecast values should be carried out according to the criterion of minimum costs for the units involved to cover this capacity. In operational management, the optimization of power distribution is the process of adjusting the regime for active power, obtained during its short-term planning and optimization. Some of the optimization parameters, such as the relative increase in energy consumption and a measure of the efficiency of the use of water resources, can be determined in the optimization of short-term regimes and used in the optimization of operational regimes. Other parameters included in the operational optimization equation are either calculated during operational control using telemetered parameters, or are set. During the operational optimization of the regime, unscheduled power between stations must be distributed in such a way as to ensure the same relative increases in energy consumption at power plant units, taking into account the relative increases in power losses in the network from the power of these stations. The article considers a comparison of two methods for the operational assessment of the relative increments of power losses for the tasks of operational optimization of the mode by active power. 

Cite: V.Kh. Nasibov R.R. Alizade E.J. Isgenderov COMPARATIVE ANALYSIS OF METHODS FOR ESTIMATING ELECTRICITY LOSSES IN PROBLEMS OF OPERATIONAL OPTIMIZATION OF POWER SYSTEM MODES . Reliability: Theory & Applications. 2024, June 2(78): 35-41, DOI: https://doi.org/10.24412/1932-2321-2024-278-35-41

TRANSIENT AND METAHEURISTIC COST SCRUTINY OF MX/G(A, B)/1 RETRIAL QUEUE WITH RANDOM FAILURE UNDER EXTENDED BERNOULLI VACATION WITH IMPATIENT CUSTOMERS

Rani R and Indhira K

The transient and metaheuristic cost analysis of a MX/G(a, b)/1 retrial queue with random failure during an extended Bernoulli vacation with impatient clients is covered in this study. Any batch that arrives and discovers the server is busy, down, or on vacation joins an orbit. In the alternative, only one new customer from the group joins the service right away, while the others join the orbit. After providing each service, the server either waits to serve the following customer with probability (1 − θ) or goes on vacation with probability θ. It has been found that these systems express steady-state solutions and are dependent on time probability generating functions in consideration of their Laplace transforms. We also discuss a few exceptional and particular instances. After that, the impact of different parameters on the system’s effectiveness is evaluated. We are also talking about ANFIS. Additional approaches employed in this study to swiftly determine the system’s optimum cost include genetic algorithms (GA), artificial bee colonies (ABC), and particle swarm optimization (PSO). We also examined the graph-based convergence of several optimization algorithms.

Cite: Rani R and Indhira K TRANSIENT AND METAHEURISTIC COST SCRUTINY OF MX/G(A, B)/1 RETRIAL QUEUE WITH RANDOM FAILURE UNDER EXTENDED BERNOULLI VACATION WITH IMPATIENT CUSTOMERS. Reliability: Theory & Applications. 2024, June 2(78): 42-63, DOI: https://doi.org/10.24412/1932-2321-2024-278-42-63

APPLICATION OF AUTOMATIC MONITORING AND CONTROL SYSTEMS FOR RELIABILITY OF POWER TRANSMISSION LINES 

S.V. Rzayev, I.A. Guseynova 

The main aspects of the use of automatic monitoring and control systems in order to increase the reliability of power lines are considered. The article highlights modern technologies and techniques that make it possible to quickly identify and prevent possible emergency situations on power transmission lines. The advantages of automated systems compared to traditional monitoring and control methods are discussed, and examples of research and practical applications of such systems are presented. The results obtained can be useful for energy specialists and engineers involved in the design, operation and maintenance of power transmission lines, as well as for developers and manufacturers of automated monitoring and control systems. 

Cite: S.V. Rzayev, I.A. Guseynova  APPLICATION OF AUTOMATIC MONITORING AND CONTROL SYSTEMS FOR RELIABILITY OF POWER TRANSMISSION LINES . Reliability: Theory & Applications. 2024, June 2(78): 64-69, DOI: https://doi.org/10.24412/1932-2321-2024-278-64-69

THE TRIANGLE-G FAMILY OF DISTRIBUTIONS: PROPERTIES, SUB-MODELS, ESTIMATION AND APPLICATION IN LIFETIME STUDIES 

Habibah Rahman 

This paper pictures the importance and the generalization of a new family of distribution developed on Triangle distribution. The new family provides some useful expansions, properties and a suitable alternative to some of existing models with same and higher number of parameters. Exponential distribution (one parameter) and Inverse Weibull distribution (Two parameter) play the role of sub-models. This new family distribution is used as a statistical model to estimate the parameters using the maximum likelihood estimation method. A complete study of Percentage points has been tabled. Two real-world data sets are investigated, demonstrating the suggested model's capacity to fit a variety of data sets along with some other models. 

Cite: Habibah Rahman  THE TRIANGLE-G FAMILY OF DISTRIBUTIONS: PROPERTIES, SUB-MODELS, ESTIMATION AND APPLICATION IN LIFETIME STUDIES . Reliability: Theory & Applications. 2024, June 2(78): 70-84, DOI: https://doi.org/10.24412/1932-2321-2024-278-70-84

RESEARCH OF ELECTROMECHANICAL DEVICES WITH LEVITATION ELEMENTS IN CONTROL SYSTEMS 

G.S. Kerimzade, G.V. Mamedova 

The work examines the main technical indicators of electromechanical converters callers with levitation elements, a generalized design method has been developed tions, as well as design diagrams and functional dependencies of the main varieties of electromechanical devices with elements of levitation. Analytical expressions for the levitation coefficient as a function of the dimensions of the magnetic core and coefficient factor of force multiplicity, technical characteristics of levitation material element, set superheat temperature. A mathematical model has been compiled for based on the parameters of the current mode and forces from the equations of electrical, magnetic, mechanical and thermal circuits of the magnetic system. As a result, the main dimensions of the magnetic system and dimensionless quantities. Analytic expressions for the main dimensions, the specified values of the winding overheating temperature are taken into account, input and output parameters, the condition of uniformity of the magnetic field in the working air nom gap. The optimal values of the dimensions of the magnetic circuit, active resistors have been determined winding voltages are minimal, resulting in minimization of losses active capacities. 

Cite: G.S. Kerimzade, G.V. Mamedova  RESEARCH OF ELECTROMECHANICAL DEVICES WITH LEVITATION ELEMENTS IN CONTROL SYSTEMS . Reliability: Theory & Applications. 2024, June 2(78): 85-90, DOI: https://doi.org/10.24412/1932-2321-2024-278-85-90

A SOFTWARE RELIABILITY PREDICTION AND MANAGEMENT INCORPORATING CHANGE POINTS BASED ON TESTING EFFORT

Anup Kumar Behera, Priyanka Agarwal

This paper proposes a procedure for formulating the software reliability growth model using the non-homogeneous poisson process. We consider the software reliability growth model, which includes imperfect debugging, change points, and testing effort. Nevertheless, when formulating their software reliability models, the majority of scientists make the assumption of a constant detection rate per fault. When software is tested, they all suppose that each fault has an equal chance of being detected and that the rate is equal between generations. In practice, the fault detection rate varies depending on the test teams’ abilities, program size, and software properties. Troubleshooting, even in the most realistic situations relevant to the error reintroduction rate due to incomplete debugging phenomena. In this case, changes in error detection and error introduction rates during software development program. Therefore, here we incorporate the generalized logic test workload function and change points. Parameters in software reliability modeling. Estimated using the least squares estimation method unknown parameters of the new model. Therefore, in our newly proposed model, we collect software testing data. use data from a practical application to illustrate the proposed model. Experimental results show that the proposed SRGM framework for imperfect debugging of integrated test jobs and change points has fairly accurate prediction capabilities.

Cite: Anup Kumar Behera, Priyanka Agarwal A SOFTWARE RELIABILITY PREDICTION AND MANAGEMENT INCORPORATING CHANGE POINTS BASED ON TESTING EFFORT. Reliability: Theory & Applications. 2024, June 2(78): 91-100, DOI: https://doi.org/10.24412/1932-2321-2024-278-91-100

A COMPREHENSIVE ANALYSIS OF JUCHEZ DISTRIBUTION: EXPLORING STRUCTURAL PROPERTIES AND APPLICATIONS 

Rashid A. Ganaie, R. Shenbagaraja, T. Vivekananda3 and Aafaq A. Rather, Manzoor A. Khanday, Asgar Ali 

This article introduces an innovative extension of the Juchez distribution, referred to as the length-biased Juchez distribution. This distribution, a specific instance of the broader weighted distribution, is thoroughly explored in terms of mathematical and statistical properties. Parameter estimation is accomplished through the application of maximum likelihood estimation techniques. To highlight the practical significance of this new distribution, a comprehensive analysis is conducted using two real-life lifetime datasets. The findings underscore the relevance and applicability of the proposed distribution in modeling and analyzing diverse datasets. 

Cite: Rashid A. Ganaie, R. Shenbagaraja, T. Vivekananda3 and Aafaq A. Rather, Manzoor A. Khanday, Asgar Ali  A COMPREHENSIVE ANALYSIS OF JUCHEZ DISTRIBUTION: EXPLORING STRUCTURAL PROPERTIES AND APPLICATIONS . Reliability: Theory & Applications. 2024, June 2(78): 101-114, DOI: https://doi.org/10.24412/1932-2321-2024-278-101-114

MISSING DATA IMPUTATION VIA OPTIMIZATION APPROACH: AN APPLICATION TO K-MEANS CLUSTERING OF EXTREME TEMPERATURE 

Geovert John D. Labita, Bernadette F. Tubo 

This paper introduces an optimization approach to impute missing data within the 𝐾-means cluster analysis framework. The proposed method has been applied to Philippine climate data over the previous 18 years (2006-2023) with the goal of classifying the regions according to average annual temperature including the maximum and minimum. This dataset contains missing values which is the result of the weather stations’ measurement failure for some time and there is no chance of recovery. As an effect, the regional groupings are greatly affected. This paper adapts a modified method of missing value imputation suitable for climate data clustering, inspired by the work of Bertsimas et al. (2017). The proposed methodology focuses on imputing missing values within observations by finding the value that minimizes the distance between the observation and a cluster centroid in which the Mahalanobis distance is used as the similarity measure. Consequently, the outcomes of clustering obtained through this optimization approach were compared with certain imputation techniques namely Mean Imputation, Expectation-Maximization algorithm, and MICE. The assessment of the derived clusters was conducted using the silhouette coefficient as the performance metric. Results revealed that the proposed imputation gave the highest silhouette scores which means that most of the observations were being clustered appropriately as compared to the results using other imputation algorithms. Moreover, it was found out that most of the areas showing the features of extreme condition are located in the middle part of the country. 

Cite: Geovert John D. Labita, Bernadette F. Tubo  MISSING DATA IMPUTATION VIA OPTIMIZATION APPROACH: AN APPLICATION TO K-MEANS CLUSTERING OF EXTREME TEMPERATURE . Reliability: Theory & Applications. 2024, June 2(78): 115-123, DOI: https://doi.org/10.24412/1932-2321-2024-278-115-123

WEIGHTED TRANSMUTED MUKHERJEE-ISLAM DISTRIBUTION WITH STATISTICAL PROPERTIES 

Danish Qayoom, Aafaq A. Rather

In this study, we employ a weighted transformation approach to introduce a novel model that generalises the Transmuted Mukherjee-Islam distribution. The resulting generalized distribution is referred to as the Weighted Transmuted Mukherjee-Islam (WTMI) distribution The paper thoroughly explores the probability density function (PDF) and the corresponding cumulative distribution function (CDF) associated with the WTMI distribution. A thorough investigation of the distinctive structural properties of the proposed model is conducted, including survival function, conditional survival function, hazard function, cumulative hazard function, mean residual life, moments, moment generating function (MGF), characteristics function (CF), cumulant generating function (CGF), likelihood ratio test, ordered statistics, entropy measures, and Bonferroni and Lorenz curves. The maximum likelihood estimation method is employed for the precise estimation of model parameters.

Cite: Danish Qayoom, Aafaq A. Rather WEIGHTED TRANSMUTED MUKHERJEE-ISLAM DISTRIBUTION WITH STATISTICAL PROPERTIES . Reliability: Theory & Applications. 2024, June 2(78): 124-137, DOI: https://doi.org/10.24412/1932-2321-2024-278-124-137

BAYESIAN ESTIMATION OF P(X ≤ Y) FOR POWER-SERIES MODEL

Soumik Halder, Sudhansu S. Maiti and Mriganka Mouli Chowdhury

When the probability distributions for the stress (X) and strength (Y) are different members of the power series family, the expressions of the stress-strength reliability function, R = P(X ≤ Y), are derived. Apart from stress-strength reliability, it has applications in statistical tolerancing, measurement of demand-supply system performance, genetic trait hereditary measure, bio-equivalence study, etc. The Bayes’ estimates of R under squared error and Precautionary losses are derived for various combinations of distributions of X and Y like binomial, Poisson, negative binomial, and geometric. As in practice, the availability of prior parameters is difficult; the empirical Bayes estimation procedure has been adopted to get their estimates from observed data. Simulation results have been reported, and estimates of posterior risks are compared. In the context of real Soccer games, the Bayes estimates are enumerated and compared with their classical counterparts.

Cite: Soumik Halder, Sudhansu S. Maiti and Mriganka Mouli Chowdhury BAYESIAN ESTIMATION OF P(X ≤ Y) FOR POWER-SERIES MODEL. Reliability: Theory & Applications. 2024, June 2(78): 138-155, DOI: https://doi.org/10.24412/1932-2321-2024-278-138-155

IDENTIFYING THE PROBABILITY DISTRIBUTION MODELS OF ECONOMIC LOSSES DUE TO NATURAL DISASTERS

Ashish Jha, Vikas Kumar Sharma, Abhimanyu Singh Yadav

Natural catastrophes have a tremendous influence on the environment and our economy, which has raised significant concerns and spurred scientific research. Several studies have been done to model the economic losses brought on by natural disasters. In this article, we primarily concentrate on examining the distributions of economic losses resulting from big catastrophes including wildfires, earthquakes, droughts, volcanic eruptions, and harsh weather. We recommend utilizing five well-known statistical distributions, including the Weibull, Log-logistics, Gamma, Generalized Pareto, and Lognormal distributions since we observe the skewed forms of the empirical distributions. We employ the maximum likelihood technique for each distribution for the available data sets in order to estimate the distributions. The parameter estimations are numerically computed using the PSO method. We select the distribution that best fits the economic losses using the Akaike Information Criterion and Kolmogorov-Smirnov statistics. We discovered that the Log-logistic distribution is the distribution that fits the total economic losses caused by all-natural disasters the best.

Cite: Ashish Jha, Vikas Kumar Sharma, Abhimanyu Singh Yadav IDENTIFYING THE PROBABILITY DISTRIBUTION MODELS OF ECONOMIC LOSSES DUE TO NATURAL DISASTERS. Reliability: Theory & Applications. 2024, June 2(78): 156-169, DOI: https://doi.org/10.24412/1932-2321-2024-278-156-169

STOCHASTIC ANALYSIS OF THE UTENSIL INDUSTRY SUBJECT TO REPAIR FACILITY

Hanumanolla Indrasena Reddy, Mohit Yadav and Hemant Kumar

The availability and profit values of the utensil industry are analyzed using the regenerative point graphical technique. The utensil industry contains three different units where two units can work with reduced capacity. It is considered that units C and D may be in a complete failed state through partial failure but unit B is in only complete failed state. When a unit is completely failed then the system is in failed state. An expert technician is available to repair the failed unit. Failure and repair times are independent of each other. The distribution of the failure time is general and repair time is exponential. Various parameters such as mean time to system failure, availability, busy period of the server, expected number of server visits and profit values are calculated with the help of tables.

Cite: Hanumanolla Indrasena Reddy, Mohit Yadav and Hemant Kumar STOCHASTIC ANALYSIS OF THE UTENSIL INDUSTRY SUBJECT TO REPAIR FACILITY. Reliability: Theory & Applications. 2024, June 2(78): 170-177, DOI: https://doi.org/10.24412/1932-2321-2024-278-170-177

STOCHASTIC ANALYSIS OF A COMPLEX REPAIRABLE SYSTEM WITH A CONSTRAIN ON THE NUMBER OF REPAIRS 

Late Dr. K. Shankar Bhat, Miriam Kalpana Simon 

Reliability characteristics of repairable systems have been studied in the past in great detail by numerous researchers. Their findings are based mainly on the significant assumption that the repairs are carried out by one or more repair facilities, and the process of repair renews the functional behavior of the components or units in the system. In other words, the statistical properties of the components or units can be restored by carrying out the repair upon failure. This means that failed units may be treated “as good as new” after each repair. In many practical situations we observe that in the process of making a unit as good-as-new, considerable damage will be done to the operational ability of the repair facility, which may reflect upon the repair rates of the units in subsequent repairs. Intuitively, we expect that the average repair time of a unit to increase after each repair. This paper makes an attempt to incorporate these concepts in a two unit warm standby redundant system in which the efficiency, equivalently, repair capacity of the repair facility decreases upon each repair. Subsequently, the process of repair may not contribute significantly in improving the system reliability. In order to increase the system reliability and that the system might be available in the long run, an optimum replacement of the repair facility in terms of the mean time to system failure (MTSF) is suggested. 

Cite: Late Dr. K. Shankar Bhat, Miriam Kalpana Simon  STOCHASTIC ANALYSIS OF A COMPLEX REPAIRABLE SYSTEM WITH A CONSTRAIN ON THE NUMBER OF REPAIRS . Reliability: Theory & Applications. 2024, June 2(78): 178-187, DOI: https://doi.org/10.24412/1932-2321-2024-278-178-187

BAYESIAN ANALYSIS OF EXTENDED MAXWELL-BOLTZMANN DISTRIBUTION USING SIMULATED AND REAL-LIFE DATA SETS

Nuzhat Ahad, S.P. Ahmad, J.A. Reshi

The objective of the study is to use Bayesian techniques to estimate the scale parameter of the 2Kth order weighted Maxwell-Boltzmann distribution (KWMBD). This involved using various prior assumptions such as extended Jeffrey’s, Hartigan’s , Inverse-gamma and Inverse-exponential, as well as different loss functions including squared error loss function (SELF), precautionary loss function (PLF), Al Bayyati’s loss function (ALBF), and Stein’s Loss Function (SLF).The maximum likelihood estimation (MLE) is also obtained. We compared the performances of MLE and bayesian estimation under each prior and its associated loss functions. And demonstrated the effectiveness of Bayesian estimation through simulation studies and analyzing real-life datasets.

Cite: Nuzhat Ahad, S.P. Ahmad, J.A. Reshi BAYESIAN ANALYSIS OF EXTENDED MAXWELL-BOLTZMANN DISTRIBUTION USING SIMULATED AND REAL-LIFE DATA SETS. Reliability: Theory & Applications. 2024, June 2(78): 188-201, DOI: https://doi.org/10.24412/1932-2321-2024-278-188-201

STUDY ON ACCEPTANCE SAMPLING PLAN BASED ON PERCENTILES  FOR EXPONENTIATED GENERALIZED INVERSE RAYLEIGH DISTRIBUTION

S Jayalakshmi, Aleesha A

An acceptance sampling plan is a sampling procedure with a set of rules for making decisions about a lot of products. The decision is based on the number of defectives in a sample. The sampling inspection plans which are developed for taking decision about a lot based on lifetime of the product are called reliability sampling plans. In this paper, we have developed Acceptance sampling plan (ASP) based on truncated life tests when the lifetime of a product follows the exponentiated generalized inverse Rayleigh distribution (EGIR). The minimum sample sizes needed to ensure the specified life percentile are obtained for a fixed value of the consumer`s confidence level. The operating characteristic values according to the different quality levels are obtained and the minimum ratios of the mean life to the specified life are calculated. The important tables based on the suggested acceptance sampling plan are calculated and illustrated.

Cite: S Jayalakshmi, Aleesha A STUDY ON ACCEPTANCE SAMPLING PLAN BASED ON PERCENTILES  FOR EXPONENTIATED GENERALIZED INVERSE RAYLEIGH DISTRIBUTION. Reliability: Theory & Applications. 2024, June 2(78): 202-208, DOI: https://doi.org/10.24412/1932-2321-2024-278-202-208

A NEW BAYESIAN CONTROL CHART FOR PROCESS MEAN USING EMPIRICAL BAYES ESTIMATES

Souradeep Das and Sudhansu S. Maiti

This article develops a new control chart for the mean using empirical Bayes estimates. We assume that the quality characteristic of the proposed control chart follows a normal distribution with unknown mean and variance. Both the parameters have known prior probability distributions. In practice, the parameters of priors are unknown and are estimated using the empirical Bayes approach. For the performance assessment of the new control chart, the Average Run Length (ARL) procedure is used while the process is in control and out of control. A real-life example is also considered to evaluate the performance of the proposed control chart.

Cite: Souradeep Das and Sudhansu S. Maiti A NEW BAYESIAN CONTROL CHART FOR PROCESS MEAN USING EMPIRICAL BAYES ESTIMATES. Reliability: Theory & Applications. 2024, June 2(78): 209-217, DOI: https://doi.org/10.24412/1932-2321-2024-278-209-217

COMPARISON OF SINGLE SERVER RETRIAL QUEUING PERFORMANCE  USING FUZZY QUEUING MODEL AND INTUITIONISTIC FUZZY QUEUING MODEL WITH INFINITE CAPACITY 

S. Aarthi

A single server retrial fuzzy queuing model is presented in this study. An unreliable 𝐹𝑀/𝐹𝑀/1 fuzzy retrial queue with a virtually unlimited retrial orbit and a standard queue is investigated. After an unspecified amount of time has elapsed and the server is workable and inactive, orbit patrons don't rejoin the regular queue, but instead, enter the server momentarily. Customers who arrive and discover the server is engaged or has struggled are placed in the regular queue, whereas customers who are disrupted are always placed in orbit. The model's prosecution proportions are also calculated in a hazy environment. The main goal of this investigation is to compare the efficacy of a single server retrial queuing system based on fuzzy queuing theory and intuitionistic fuzzy queuing theory. The arrival, service, failure, orbit, and repair rates are documented using triangular and triangular intuitionistic fuzzy numbers. The evaluation metrics for the fuzzy queuing theory model are proffered as a range of possible values, whereas the intuitionistic fuzzy queuing theory model encompasses a wide range of values. An approach is conducted to discover quality measures using a design protocol in which the fuzzy values are left alone and not repurposed to crisp values, allowing us to draw research findings in an ambiguous future. Two numerical problems are solved to emphasize the method's protracted survivability. 

Cite: S. Aarthi COMPARISON OF SINGLE SERVER RETRIAL QUEUING PERFORMANCE  USING FUZZY QUEUING MODEL AND INTUITIONISTIC FUZZY QUEUING MODEL WITH INFINITE CAPACITY . Reliability: Theory & Applications. 2024, June 2(78): 218-231, DOI: https://doi.org/10.24412/1932-2321-2024-278-218-231

THE LENGTH-BIASED WEIGHTED WILSON HILFERTY DISTRIBUTION AND ITS APPLICATIONS 

Shivendra Pratap Singh, Surinder Kumar, Naresh Chandra Kabdwal

In this article, we propose a new length-biased weighted form of Wilson Hilferty distribution named as Length-Biased Weighted Wilson Hilferty Distribution. The various Statistical properties of the proposed distribution like, reliability function, hazard rate function, reverse hazard rate function, moment generating function, quantile function, the coefficient of variation etc. are considered to understand its nature. Furthermore, we have used the method of maximum likelihood for estimation of the parameters of proposed distribution. Also, we obtain the Shannon’s entropy, stochastic ordering, Lorenz and Bonferroni curves. The performance of the proposed distribution is compared with competitive distributions using two real data sets. 

Cite: Shivendra Pratap Singh, Surinder Kumar, Naresh Chandra Kabdwal THE LENGTH-BIASED WEIGHTED WILSON HILFERTY DISTRIBUTION AND ITS APPLICATIONS . Reliability: Theory & Applications. 2024, June 2(78): 232-246, DOI: https://doi.org/10.24412/1932-2321-2024-278-232-246

A TWO NON-IDENTICAL UNIT STANDBY SYSTEM WITH CORRELATED PREVENTIVE MAINTENANCE TIME AND TIME TO PREVENTIVE MAINTENANCE AND INVERSE GAUSSIAN REPAIR TIME DISTRIBUTION 

Anju Rani, Rakesh Gupta, Pradeep Chaudhary

The paper deals with the cost benefit analysis of a two non-identical unit cold standby system model with the implementation of preventive maintenance (PM) on the priority unit after it has operated for a random duration. The objective is to evaluate the economic viability and performance of such system. A single repairman is consistently available within the system, responsible for both PM and repair of each failed unit. The priority in repair is given to priority (p) unit over ordinary (o) unit. The failure time distribution of each unit is assumed to be exponential while the repair time distribution of both the unit is taken as inverse Gaussian. The PM time and time to PM of the priority unit are correlated having their joint distributions as bivariate exponential. By considering the regenerative point technique, various measures of system effectiveness are obtained. 

Cite: Anju Rani, Rakesh Gupta, Pradeep Chaudhary A TWO NON-IDENTICAL UNIT STANDBY SYSTEM WITH CORRELATED PREVENTIVE MAINTENANCE TIME AND TIME TO PREVENTIVE MAINTENANCE AND INVERSE GAUSSIAN REPAIR TIME DISTRIBUTION . Reliability: Theory & Applications. 2024, June 2(78): 247-257, DOI: https://doi.org/10.24412/1932-2321-2024-278-247-257

ON ESTIMATION AND PREDICTION FOR THE XLINDLEY DISTRIBUTION BASED ON RECORD DATA

F. Zanjiran, S.M.T.K. MirMostafaee

This paper investigates the estimation of the unknown parameter in the XLindley distribution using record values and inter-record times, both in classical and Bayesian frameworks. It also delves into Bayesian prediction of a future record value. We also study the problem of estimation and prediction for the XLindley distribution based on lower records alone. A simulation study, as well as an analysis of a real data example, are conducted for comparison and illustration. The numerical findings underline that including the inter-record times in the study may enhance the performance of the estimators and predictors.

Cite: F. Zanjiran, S.M.T.K. MirMostafaee ON ESTIMATION AND PREDICTION FOR THE XLINDLEY DISTRIBUTION BASED ON RECORD DATA. Reliability: Theory & Applications. 2024, June 2(78): 258-272, DOI: https://doi.org/10.24412/1932-2321-2024-278-258-272

IMPROVED DEGRADATION TEST USING INVERSE GAUSSIAN PROCESS FOR SIMPLE STEP-STRESS MODEL 

G. Sathya Priyanka, S. Rita, M. Iyappan

The accelerated Degradation testing (ADT) experiments are important technical methods in reliability studies. Different type of accelerating degradation models has developed with the time and can be used in different types of situations. However, it has become necessary for the manager to test how many numbers of unit should be tested at a particular stress level so that the cost of testing is less. Accelerated Degradation testing (ADT) is preferred to be used in mechanized industries to obtain the required information about the reliability of product components and materials in a short period of time. Accelerated test conditions involve higher than usual pressure, temperature, voltage, vibration or any other combination of them. Data collected at such accelerated conditions are extrapolated through a physically suitable statistical model to estimate the lifetime distribution at design condition stress the life data collected from the high stresses the need to be extrapolated to estimate the life distribution under the normal-use condition. A special class of the ADT is the step-stress testing which regularly increases the stress levels at some pre-fixed time points until the test unit fails. Such experiments allow the experimenter to run the test units at higher-than-usual stress conditions in order to secure failures more quickly. The Inverse Gaussian process is flexible in incorporating random effects and explanatory variables. The different types of models based on IG process are random drift model, random volatility model and random drift- volatility model. In this paper we have considered random drift model for the study on stochastic degradation models for simple step-stress model using inverse Gaussian process observed in degradation problems. 

Cite: G. Sathya Priyanka, S. Rita, M. Iyappan IMPROVED DEGRADATION TEST USING INVERSE GAUSSIAN PROCESS FOR SIMPLE STEP-STRESS MODEL . Reliability: Theory & Applications. 2024, June 2(78): 273-281, DOI: https://doi.org/10.24412/1932-2321-2024-278-273-281

CONSTRUCTION OF DOUBLE SAMPLING INSPECTION PLANS FOR LIFE TESTS BASED ON LOMAX DISTRIBUTION 

A. Pavithra and R. Vijayaraghavan

A life test is a random experiment performed on manufactured products such as electrical and electronic components to estimate their life period based on a randomly chosen components. The lifespan of a component is considered as a random variable that follows a certain continuous-type distribution, called the lifetime distribution. Reliability sampling is one of the decision-making methodologies in product control and deals with inspection procedures for sentencing one or more lots or batches of items submitted for inspection. The concept of sampling plans for life tests involving with two random samples is employed in the present study under the assumption that the lifetime random variable is described by the Lomax distribution. A procedure based on mean / median life criterion is developed for designing the optimum plans with minimum sample sizes when two points on the desired operating characteristic curve are prescribed to ensure protection to the producer and the consumer.

Cite: A. Pavithra and R. Vijayaraghavan CONSTRUCTION OF DOUBLE SAMPLING INSPECTION PLANS FOR LIFE TESTS BASED ON LOMAX DISTRIBUTION . Reliability: Theory & Applications. 2024, June 2(78): 282-290, DOI: https://doi.org/10.24412/1932-2321-2024-278-282-290

A COMPREHENSIVE STUDY OF LENGTH-BIASED TRANSMUTED DISTRIBUTION 

Danish Qayoom, Aafaq A. Rather

In this study, we explore a new probability distribution termed as the Length-Biased Transmuted Mukherjee-Islam (LBTMI) distribution. This exploration enhances the conventional Transmuted Mukherjee-Islam distribution by integrating a weighted transformation approach. The paper examines the probability density function and the corresponding cumulative distribution function associated with the LBTMI distribution. A comprehensive examination of the unique structural properties of the proposed model is carried out, including the survival function, conditional survival function, hazard function, cumulative hazard function, mean residual life, moments, moment generating function (MGF), characteristic function (CF), cumulant generating function (CGF), likelihood ratio test, ordered statistics, entropy measures, and Bonferroni and Lorenz curves. To ensure precise estimation of model parameters, the study employs the maximum likelihood estimation method, contributing significantly to the advancement of statistical modelling in this domain. 

Cite: Danish Qayoom, Aafaq A. Rather A COMPREHENSIVE STUDY OF LENGTH-BIASED TRANSMUTED DISTRIBUTION . Reliability: Theory & Applications. 2024, June 2(78): 291-304, DOI: https://doi.org/10.24412/1932-2321-2024-278-291-304

THE EXPECTED FISHER INFORMATION MATRIX OF POISSON HALF LOGISTIC MODEL

Ibrahim Abdullahi, Aminu Suleiman Mohammed and Sani Musa

This study delves into the computation and evaluation of the expected Fisher information matrix within the context of the Poisson-type I half logistic (PHL) distribution. Leveraging confidence intervals and their associated coverage probabilities, our investigation aimed to study the performance of information matrix by the maximum likelihood method in estimating parameters. Our results unveiled a consistent trend: as the sample size expanded, a reduction in the length of the confidence interval was observed, and the 95% asymptotic confidence interval’s coverage probability aligned within the expected nominal size. This serves as a testament to the accuracy and robustness of the information matrix’s performance within the PHL distribution framework. Also, tested using some real data set. 

Cite: Ibrahim Abdullahi, Aminu Suleiman Mohammed and Sani Musa THE EXPECTED FISHER INFORMATION MATRIX OF POISSON HALF LOGISTIC MODEL. Reliability: Theory & Applications. 2024, June 2(78): 305-313, DOI: https://doi.org/10.24412/1932-2321-2024-278-305-313

BULK ARRIVING RETRIAL QUEUE WITH G-QUEUE AND RENEGING CLIENTS

J. Bharathi, S. Nandhini, Nur Aisyah Abdul Fataf

We consider a server queue with negative clients (G-Queue) in this effort, where clients are serviced one after the other in batches in a system of variable size. Additionally, we presumptively have a general distribution for the service times, delay times, and repair times. For various states, we concrete the probability-generating functions for the number of customers in the orbit. We scrutinize a single server queue with batches of reneging or balking clients in a system of variable size in this work. Different performance measures and unique situations are examined. The outcomes of this work have applications in satellite communication, software-design for various computer-communication systems and mailing systems among other things.

Cite: J. Bharathi, S. Nandhini, Nur Aisyah Abdul Fataf BULK ARRIVING RETRIAL QUEUE WITH G-QUEUE AND RENEGING CLIENTS. Reliability: Theory & Applications. 2024, June 2(78): 314-323, DOI: https://doi.org/10.24412/1932-2321-2024-278-314-323

A BAYESIAN APPROACH FOR CHRIS-JERRY DISTRIBUTION USING VARIOUS LOSS FUNCTIONS 

Dr. G Meenakshi and Balachandar.B

The paper introduces a Bayesian approach for estimating parameters of the Chris-Jerry distribution, focusing on the use of a conjugate prior, specifically the gamma prior. The Bayesian estimation method is developed with a various loss function, offering a robust framework for parameter estimation. symmetric loss function and Linex loss functions are commonly used in Bayesian statistics to balance the trade-off between bias and variance. The central idea is to derive the Bayes estimate of the distribution parameter by leveraging the properties of the conjugate gamma prior. Conjugate priors simplify the Bayesian analysis by ensuring that the posterior distribution belongs to the same family as the prior, facilitating analytical calculations. The proposed methodology is implemented and validated through numerical illustrations using. This involves applying the developed Bayesian estimation framework to real-world data or simulated scenarios, demonstrating its effectiveness and practical applicability. The numerical and simulation studies are done by using r software 

Cite: Dr. G Meenakshi and Balachandar.B A BAYESIAN APPROACH FOR CHRIS-JERRY DISTRIBUTION USING VARIOUS LOSS FUNCTIONS . Reliability: Theory & Applications. 2024, June 2(78): 324-332, DOI: https://doi.org/10.24412/1932-2321-2024-278-324-332

PROFIT AND AVAILABILITY ANALYSIS OF UTENSIL INDUSTRY SUBJECT TO REPAIR FACILITY

Amit Kumar, Pinki Kumari

The main objective of the paper is to optimize the availability and profit values of the utensil industry. There are three distinct units in the utensil industry and two of them work in reduced state. It is assumed that unit A is failed in complete failure mode while units B and C completely failed through partial failure mode. The system is in a failing condition when one of the units completely fails. There is a qualified technician to fix the fault in the system. Timelines for failure and repair are unrelated to one another. The repair time is exponential while the failure time distribution is general. Many factors, including mean time to system failure, availability, busy period, estimated number of server visits and profit values are calculated from tables.

Cite: Amit Kumar, Pinki Kumari PROFIT AND AVAILABILITY ANALYSIS OF UTENSIL INDUSTRY SUBJECT TO REPAIR FACILITY. Reliability: Theory & Applications. 2024, June 2(78): 333-340, DOI: https://doi.org/10.24412/1932-2321-2024-278-333-340

ANALYSIS OF THE MULTIPLE WORKING VACATIONS, BATCH SERVICE AND RENEGING QUEUING SYSTEM UNDER SINGLE SERVER POLICY

Lidiya P, K Julia Rose Mary

In this paper, we analysed the multiple working vacation queuing model with reneging under a single server policy. Reneging describes the situation where a customer or entity decides to leave the queue before being served. The presence of reneging behaviour affects queue and service efficiency, as customers leaving the queue prematurely can impact overall system performance and customer satisfaction. In this model, customers arrive at a service facility and form a queue to be served by a single server. The arrival follows the Poisson distribution, and the service follows the exponential process. Batches of customers are served under the General Bulk Service Rule. In GBSR, rather than individual customer arriving at a queue one by one, customers arrive in groups or batches. Thus, each batch of service contains a minimum of ′a′ units and a maximum of ′b′ units of customers. The steady-state equation, the various performance measures for the system, and particular cases of the described model are derived.

Cite: Lidiya P, K Julia Rose Mary ANALYSIS OF THE MULTIPLE WORKING VACATIONS, BATCH SERVICE AND RENEGING QUEUING SYSTEM UNDER SINGLE SERVER POLICY. Reliability: Theory & Applications. 2024, June 2(78): 341-350, DOI: https://doi.org/10.24412/1932-2321-2024-278-341-350

CRITICAL ANALYSIS OF FAILURE AND REPAIR RATES OF POLY-TUBE MANUFACTURING PLANT USING PSO 

Shakuntla Singla, Diksha Mangla, Umar Muhammad Modibbo, A.K. Lal 

A proper maintenance strategy is essential for the optimal performance of poly tube manufacturing to ensure high reliability. It involves a complex structure consisting of many components interconnected in series or parallel configurations. This project's contribution is the development of a method for evaluating the performance of an industrial system using previously unknown data. The RAM index, influenced by failure and repair rates, has been devised to identify the system's most critical component that impacts reliability, availability, and maintainability, collectively known as RAM. For performance analysis, a Markov-based simulation system model has been formulated and resolved to refine the results through particle swarm optimization (PSO). The transition diagram facilitates the construction of ordinary differential equations (ODEs), which represent various operational states such as full capacity, reduced capacity, and failure. These ODEs are then solved using initial and boundary condition. 

Cite: Shakuntla Singla, Diksha Mangla, Umar Muhammad Modibbo, A.K. Lal  CRITICAL ANALYSIS OF FAILURE AND REPAIR RATES OF POLY-TUBE MANUFACTURING PLANT USING PSO . Reliability: Theory & Applications. 2024, June 2(78): 351-364, DOI: https://doi.org/10.24412/1932-2321-2024-278-351-364

A STUDY ON THE IMPACT OF TRANSFORMING PARAMETER IN BOX - COX TRANSFORMATION FOR NON-NORMAL DATA TO ENHANCE PROCESS CAPABILITY

J. Krishnan and R. Vijayaraghavan

Process Capability Analysis (PCA) helps to improve and monitor the quality of the manufacturing products in industries. The most commonly and traditionally applied indices are process capability index and process capability ratio. Many statistical tests require the condition that the data to be approximately normally distributed. When it comes to reality the data often do not follow a normal distribution. In such instances, different approaches are employed. Box-Cox Transformation (BCT) is one such methodology that is often used by quality practitioners relying on single transforming parameter lamda to transform the non-normal data into normal data. The widely used approach to decide the transforming parameter lamda is based on the rounded value of lamda instead of an optimal value of lamda. There are two transforming expressions available in BCT method. The choice of the value for lamda in BCT can have a significant impact on the results. This paper concentrates on the impact of data transformation in BCT method through two different expressions based on an optimal as well as a rounded value of lamda. The influence made by the estimates of process capability and process performance indices is also studied in this paper. The result of the analysis clearly indicates that the optimal value of lamda when employed in the first BCT transformation expression to estimate the process capability indices for non-normal data provides improvised results. For data analysis, Ms-Excel and Minitab 21 software has been used in this study.

Cite: J. Krishnan and R. Vijayaraghavan A STUDY ON THE IMPACT OF TRANSFORMING PARAMETER IN BOX - COX TRANSFORMATION FOR NON-NORMAL DATA TO ENHANCE PROCESS CAPABILITY. Reliability: Theory & Applications. 2024, June 2(78): 365-376, DOI: https://doi.org/10.24412/1932-2321-2024-278-365-376

ANALYSIS OF PERSONALIZED STRESS RECOGNITION IN THE OFFICE ENVIRONMENT

Jigna Jadav, Dr. Uttam Chauhan 

In today's fast-paced lifestyle, pursuing holistic well-being has increased interest in monitoring and managing stress levels. Heart rate variability (HRV), a non-invasive measure of autonomic nervous system activity, has emerged as a valuable tool for assessing individual responses to stress. This study focuses on utilizing the capabilities of the Apple Watch to collect continuous HRV data in real-world contexts. A diverse dataset from individuals working in software companies was gathered, including HRV recordings during various stress-inducing scenarios. By employing HRV Time Domain, Frequency Domain, and Nonlinear features, the study uses Principal Component Analysis (PCA) to extract relevant features, considering the personalized nature of stress reactions. Addressing variations in stress responses among individuals, the study introduces an innovative approach using Long Short-Term Memory (LSTM) networks. A hybrid model, combining feature selection, dimensionality reduction, and ensemble techniques, is developed to predict stress levels based on individualized HRV patterns. Rigorous training and validation reached to an 88% accuracy rate. These findings demonstrate the effectiveness of the proposed methodology. The LSTM model accurately forecasts stress responses, highlighting the potential of Apple Watch-acquired HRV data for stress assessment. Beyond prediction, the study enhances understanding of the complex interplay between HRV dynamics and unique stress reactions. This novel approach, leveraging Apple Watch features and intelligent computing, offers a personalized method to predict stress levels using K-Means Clustering Algorithm. Through integrating K-means clustering and person-specific HRV analysis, the research endeavours to advance our comprehension of the intricate interplay between physiological responses and stressors. The study offers a novel perspective on stress response variations by delving into the distinct autonomic patterns characterizing each cluster. It sets the stage for developing targeted interventions and personalized stress management strategies. 

Cite: Jigna Jadav, Dr. Uttam Chauhan  ANALYSIS OF PERSONALIZED STRESS RECOGNITION IN THE OFFICE ENVIRONMENT. Reliability: Theory & Applications. 2024, June 2(78): 377-389, DOI: https://doi.org/10.24412/1932-2321-2024-278-377-389

SURVIVAL PROBABILITY AND MEAN RESIDUAL LIFE TIMES OF SHOCK MODEL WITH ADDITIONAL RISK 

Abhijeet Jadhav and S. B. Munoli

A shock model with two types of shocks functioning in the presence of an additional risk is proposed. Survival probability and mean residual life times of the proposed models are derived and assessed through the data of life testing experiment. Model validation and estimation of survival probability and mean residual life times is done through simulation studies. Comparison of survival probabilities and mean residual life times of models functioning without and with additional risk is made. 

Cite: Abhijeet Jadhav and S. B. Munoli SURVIVAL PROBABILITY AND MEAN RESIDUAL LIFE TIMES OF SHOCK MODEL WITH ADDITIONAL RISK . Reliability: Theory & Applications. 2024, June 2(78): 390-399, DOI: https://doi.org/10.24412/1932-2321-2024-278-390-399

APPLICATION OF NON-DESTRUCTIVE TESTING METHODS AND EVALUATION OF CONDITION OF REINFORCED CONCRETE FRAMING 

Alena Rotaru 

The condition evaluation for reinforced concrete framing requires comprehensive analysis of the factors influencing their performance such as strength, protective layer thickness, rebar diameter, thermal conductivity, humidity, adhesion of coatings, etc. Non-destructive methods are especially relevant when the characteristics of concrete and rebars are unknown and the scope of testing is considerable. Non-destructive testing allows to effectively monitor the conditions of technical devices, structures and buildings and enables to evaluate the timeliness and quality of repair and maintenance of a facility. Non-destructive testing provides the most reliable characteristics of the parameters defining the technical condition of the facilities under test. Non-destructive testing of the structural strength is applied in those areas, which have been exposed to loads due to natural and man-made contingencies. 

Cite: Alena Rotaru  APPLICATION OF NON-DESTRUCTIVE TESTING METHODS AND EVALUATION OF CONDITION OF REINFORCED CONCRETE FRAMING . Reliability: Theory & Applications. 2024, June 2(78): 400-407, DOI: https://doi.org/10.24412/1932-2321-2024-278-400-407

APPLICATION OF POLAR COORDINATES IN THE SUMMATION OF THE GAUSSIAN DISTRIBUTION

James DANIEL, Kayode AYINDE, Emmanuel Erhuvwu DUDU, Okechukwu Ijeoma EBERECHUKWU

This work applies the polar coordinates system of advanced calculus in the summation of the Gaussian distribution. In trying to achieve this aim, sub-concepts such as complex variables, gamma function of half, error function, and the relation between the error function and the standard normal distribution were defined and explained at various stages of the work. The embedded theorem which seems to be a new theorem also came up in the body of the work.

Cite: James DANIEL, Kayode AYINDE, Emmanuel Erhuvwu DUDU, Okechukwu Ijeoma EBERECHUKWU APPLICATION OF POLAR COORDINATES IN THE SUMMATION OF THE GAUSSIAN DISTRIBUTION. Reliability: Theory & Applications. 2024, June 2(78): 408-424, DOI: https://doi.org/10.24412/1932-2321-2024-278-408-424

REGRESSION MODEL OF ARC OVERVOLTAGE DURING SINGLE-PHASE NON-STATIONARY GROUND FAULTS IN NEUTRAL ISOLATED NETWORKS

Najaf Orujov, Huseyngulu Guliyev, Sara Alimammadova

In order to perform insulation tests of electrical equipment under load in neutral insulated networks, it is necessary to create an artificial overvoltage, and at this time, it is necessary to determine the mathematical relationships between the single-phase non-stationary ground and the closing parameters. In the case of single-phase non-stationary earth faults, the dependencies between important parameters such as overvoltage frequency, earth fault resistance and earth fault angle obey complex laws. Therefore, for practical conditions, adequate mathematical models should be developed that allow to know the interdependencies of such parameters. In this work, the problem of analytical determination of the relationship between the overvoltage generated in neutral insulated networks as a result of non-stationary earth faults, the earth fault resistance and the earth fault angle was considered. For this purpose, a regression equation was obtained for the dependence of the overvoltage frequency on the ground fault resistance and the ground fault angle, and the corresponding spatial description was given. The obtained results confirmed the existence of a strong correlation between these parameters and can be used for practical purposes. 

Cite: Najaf Orujov, Huseyngulu Guliyev, Sara Alimammadova REGRESSION MODEL OF ARC OVERVOLTAGE DURING SINGLE-PHASE NON-STATIONARY GROUND FAULTS IN NEUTRAL ISOLATED NETWORKS. Reliability: Theory & Applications. 2024, June 2(78): 425-433, DOI: https://doi.org/10.24412/1932-2321-2024-278-425-433

ANALYSIS OF A SINGLE SERVER SYSTEM WITH HETEROGENEOUS ARRIVAL, HETEROGENEOUS SERVICE, SYSTEM FAILURE AND MAINTENANCE 

Mohammed Shapique A, Vaithiyanathan A

This paper investigates a single-server queuing system with heterogeneous service, failure, and maintenance. The proposed model features a server acting as both the main and backup server. System failure can occur at any stage. When a failure happens, instead of stopping the service entirely, the main server functions as a backup, providing service at a reduced rate. Once all jobs in the system have been serviced, the backup server enters the maintenance state. Following the repair process during maintenance, the server transitions to an idle state, awaiting incoming jobs. Explicit expressions for both transient and steady-state behaviours of the system are derived. Additionally, key system performance metrics are discussed in this paper, accompanied by graphical illustrations to visualize system size probabilities and performance indices.

Cite: Mohammed Shapique A, Vaithiyanathan A ANALYSIS OF A SINGLE SERVER SYSTEM WITH HETEROGENEOUS ARRIVAL, HETEROGENEOUS SERVICE, SYSTEM FAILURE AND MAINTENANCE . Reliability: Theory & Applications. 2024, June 2(78): 434-445, DOI: https://doi.org/10.24412/1932-2321-2024-278-434-445

ON CERTAIN CLASSES OF CONFORMALLY FLAT LORENTZIAN PARA-KENMOTSU MANIFOLDS

K. L. Sai Prasad, P. Naveen and S. Sunitha Devi

In this present paper, we classify and explore the geometrical significance of a class of Lorentzian almost paracontact metric manifolds namely Lorentzian para-Kenmotsu (briefly LP-Kenmotsu) mani-folds whenever the manifolds are either conformally flat or conformally symmetric. It was found that a conformally flat LP-Kenmotsu manifold is of constant curvature and a conformally symmetric LP-Kenmotsu manifold is locally isomorphic to a unit sphere. At the end, we obtain the scalar curvature of ϕ-conformally flat LP-Kenmotsu manifolds.

Cite: K. L. Sai Prasad, P. Naveen and S. Sunitha Devi ON CERTAIN CLASSES OF CONFORMALLY FLAT LORENTZIAN PARA-KENMOTSU MANIFOLDS. Reliability: Theory & Applications. 2024, June 2(78): 446-453, DOI: https://doi.org/10.24412/1932-2321-2024-278-446-453

ESTIMATION OF HAZARD AND SURVIVAL FUNCTION FOR COMPETING RISKS USING KERNEL AND MIXTURE MODEL IN BIMODAL SETUP 

A. M. Rangoli, A. S. Talawar 

Aim of the present paper is to find suitable model for bimodal data. We have modelled mixture of two Weibull distributions in the presence of competing risks and also used Epanechnikov kernel to estimate hazard and survival functions. We considered prostate cancer data for application of the mixture model and kernel. We used maximum likelihood estimation (MLE) to estimate parameters of the mixture model, as the equations have no closed form, so we considered expectation–maximization (EM) algorithm. The mixture model and kernel gave good fit to the bimodal data. The prostate cancer data consists of three causes, we have estimated hazard function for these three causes using mixture model and kernel. The asymptotic confidence interval for the parameters of mixture model to all three causes were estimated. Also compared survival curve of mixture model with kernel and Kaplan-Meier survival curves for all the three causes. 

Cite: A. M. Rangoli, A. S. Talawar  ESTIMATION OF HAZARD AND SURVIVAL FUNCTION FOR COMPETING RISKS USING KERNEL AND MIXTURE MODEL IN BIMODAL SETUP . Reliability: Theory & Applications. 2024, June 2(78): 454-466, DOI: https://doi.org/10.24412/1932-2321-2024-278-454-466

EXPLORE THE DYNAMICS OF MANUFACTURING INDUSTRIES: RELIABILITY ANALYSIS THROUGH STOCHASTIC PROCESS MODELING 

Sonia, Shakuntla Singla 

In nowadays, the chief attention of the researcher is to study how the reliability analysis of manufacturing industrial systems by using the stochastic process. This topic tells us, how the manufacturing industries perform over time with the help of mathematical models which include randomness and uncertainty. Through stochastic processes we examine the reliability of these systems, technologists can recognize possible failure points and develop tactics to improve overall performance and effectiveness. The reliability of a manufacturing industrial system can be examined through a stochastic process, which permits for the estimate of failure rates and maintenance agendas. This analysis can lead to more well-organized and cost-effective procedure of the system. In this study, the researcher analysed the possibility plan for reliability through many distributions such as the normal distribution, gamma distribution, weibull distribution, and exponential distribution. The result of the study was prepared using Minitab software. The result of the study shows that the normal distribution of reliability fits best in comparison to the gamma, weibull, and exponential distributions. 

Cite: Sonia, Shakuntla Singla  EXPLORE THE DYNAMICS OF MANUFACTURING INDUSTRIES: RELIABILITY ANALYSIS THROUGH STOCHASTIC PROCESS MODELING . Reliability: Theory & Applications. 2024, June 2(78): 467-471, DOI: https://doi.org/10.24412/1932-2321-2024-278-467-471

MULTICOMPONENT RELIABILITY UNDER PATHWAY MODEL

T. PRINCY

In this paper, we consider a system with a finite number of components. It is assumed that the system architecture is a series format. The system fails when any one of the components fails. The case where the lifetimes of the components, are independently distributed and have pathway density is considered. Then the survival function, hazard function, the expected time to failure, general moments, etc. of the system lifetime are computed. It is shown that the hazard function can have many types of shapes, including bathtub shapes. The estimation of stress-strength reliability is considered based on the method of maximum likelihood estimation when both stress and strength variables follow the pathway model. Finally, to show the applicability of the proposed model in a real-life scenario, remission time data from cancer patients is analyzed.

Cite: T. PRINCY MULTICOMPONENT RELIABILITY UNDER PATHWAY MODEL. Reliability: Theory & Applications. 2024, June 2(78): 472-486, DOI: https://doi.org/10.24412/1932-2321-2024-278-472-486

ON AN INTERNAL DEPENDENCE OF SIMULTANEOUS MEASUREMENTS

Valentin Vankov Iliev

In this paper we show that there exists an internal dependence of the simultaneous measurements made by the two pairs of linear polarizers operated in each leg of the apparatus in Aspect’s version of Einstein-Podolsky-Rosen Gedankenexperiment. The corresponding Shannon-Kolmogorov’s information flow linking a polarizer from one leg to a polarizer from the other leg is proportional to the absolute value of this function of dependence. It turns out that if Bell’s inequality is violated, then this information flow is strictly positive, that is, the experiment performed at one leg is informationally dependent on the experiment at the other leg. By throwing out the sign of absolute value, we define the signed information flow linking a polarizer from one leg to a polarizer from the other leg which, in turn, reproduces the probabilities of the four outcomes of the simultaneous measurements, predicted by quantum mechanics. We make an attempt to illustrate the seeming random relation between the total information flow, the total signed information flow, and the violation of Bell’s inequality in terms of a kind of uncertainty principle.

Cite: Valentin Vankov Iliev ON AN INTERNAL DEPENDENCE OF SIMULTANEOUS MEASUREMENTS. Reliability: Theory & Applications. 2024, June 2(78): 487-494, DOI: https://doi.org/10.24412/1932-2321-2024-278-487-494

MAXWELL-GOMPERTZ DISTRIBUTION: PROPERTIES AND APPLICATIONS 

Alfred Adewole Abiodun, Aliyu Ismail Ishaq, Olakiitan Ibukun Adeniyi, Ifeanyi Vivian Omekam, Jumoke Popoola, Olubimpe Mercy Oladuti and Eunice Ohunene Job 

This paper proposed a three parameter Maxwell-Gompertz distribution as an extension of Gompertz distribution. Some statistical properties of the distribution such as moments, survival and hazard functions, quantile function, Rényi entropy and order statistics were derived. Maximum likelihood method was used to estimate the model parameters. A simulation study was carried out in order to gain an insight into the performance on small, moderate and large samples. The flexibility of the new distribution was empirically demonstrated in comparison to four other extensions of Gompertz distributions using two real life datasets. 

Cite: Alfred Adewole Abiodun, Aliyu Ismail Ishaq, Olakiitan Ibukun Adeniyi, Ifeanyi Vivian Omekam, Jumoke Popoola, Olubimpe Mercy Oladuti and Eunice Ohunene Job  MAXWELL-GOMPERTZ DISTRIBUTION: PROPERTIES AND APPLICATIONS . Reliability: Theory & Applications. 2024, June 2(78): 495-508, DOI: https://doi.org/10.24412/1932-2321-2024-278-495-508

DETERMINATION OF VITERBI PATH FOR 3 HIDDEN AND 5 OBSERVABLE STATES USING HIDDEN MARKOV MODEL 

T. Raja jithendar, M. Tirumala Devi, and G. Saritha

Hidden markov model (HMM) is a statistical markov model in which the system being modeled and is assumed to be a markov process with unobservable (i.e., Hidden) states. In HMM, the state is not directly visible but the output depend on the state is visible. Each state has a probability distribution over the possible output tokens. The model is referred to as a hidden markov model even if these parameters are known exactly. The viterbi is one of the estimate underlying state path in hidden markov models. In this paper, viterbi path is derived using hidden markov model. 

Cite: T. Raja jithendar, M. Tirumala Devi, and G. Saritha DETERMINATION OF VITERBI PATH FOR 3 HIDDEN AND 5 OBSERVABLE STATES USING HIDDEN MARKOV MODEL . Reliability: Theory & Applications. 2024, June 2(78): 509-515, DOI: https://doi.org/10.24412/1932-2321-2024-278-509-515

APPLICATION OF EXTENDED LOMAX DISTRIBUTION ON THE RELIABILITY ANALYSIS OF SOLAR PHOTOVOLTAIC SYSTEM 

Anas Sani Maihulla, Ibrahim Yusuf, Michael Khoo B. C., and Ameer Abdullahi Hassan 

In this study, a novel distribution called the Extended-Lomax distribution which generalizes the existing Lomax distribution and has increasing and decreasing shapes for the hazard rate function was proposed. Various structural properties of the new proposed distribution are derived including the survival function, hazard function, and rth moment. The probability density function (PDF) plots indicated that the distribution is skewed to the right. To estimate the parameters of the newly proposed distribution, two estimation methods which include the Maximum likelihood approach and Method of Moments was employed. The main objective of the proposed distribution’s construction was to increase the adaptability of the current Lomax distributions so that they could better suit reliability data sets than alternative candidate distributions with an equivalent number of parameters. This distribution should be able to eliminate the Heavy-tail of the current distribution and model both monotonic and non-monotonic patterns of failure rates. Solar photovoltaic system reliability data was used to evaluate the performance of the proposed Extended Lomax distribution as well as the estimation methods.

Cite: Anas Sani Maihulla, Ibrahim Yusuf, Michael Khoo B. C., and Ameer Abdullahi Hassan  APPLICATION OF EXTENDED LOMAX DISTRIBUTION ON THE RELIABILITY ANALYSIS OF SOLAR PHOTOVOLTAIC SYSTEM . Reliability: Theory & Applications. 2024, June 2(78): 516-525, DOI: https://doi.org/10.24412/1932-2321-2024-278-516-525

CONFIDENCE INTERVALS FOR THE PARAMETER OF THE IWUEZE DISTRIBUTION WITH APPLICATIONS TO MEDICAL AND ENGINEERING DATA 

Wararit Panichkitkosolkul 

One of the lifetime distributions is the Iwueze distribution, which is constructed by combining the exponential and gamma distributions. In this paper, confidence intervals (CIs) are proposed for the parameter of the Iwueze distribution using the likelihood-based, Wald-type, bootstrap-t, and bias-corrected and accelerated (BCa) bootstrap methods. We evaluated the performance of the proposed CI methods through Monte Carlo simulation in terms of their coverage probability (CP) and average length (AL) in various scenarios. Furthermore, we had also derived the explicit formula for the Wald-type CI, which is straightforward for computation. The simulation results showed that the likelihood-based and Wald-type CIs returned satisfactory results according to coverage probabilities, even for the setting of small sample sizes. On the other hand, both the bootstrap-t and BCa bootstrap CIs yield CPs lower than the nominal confidence level when sample sizes are small. However, as the sample sizes increase, the CP of all CIs tend to approach the nominal confidence level. The parameter values also have a minor influence on the CP of all CIs when the sample size is fixed. Moreover, the AL of all CIs decreases as the sample size increases. The Wald-type and likelihood-based CIs have very similar ALs for all parameter values. In general, the bootstrap-t CI tends to yield the shortest interval. The effectiveness of all CIs was demonstrated by applying them to medical and engineering data, yielding results consistent with those of the simulation study. 

Cite: Wararit Panichkitkosolkul  CONFIDENCE INTERVALS FOR THE PARAMETER OF THE IWUEZE DISTRIBUTION WITH APPLICATIONS TO MEDICAL AND ENGINEERING DATA . Reliability: Theory & Applications. 2024, June 2(78): 526-543, DOI: https://doi.org/10.24412/1932-2321-2024-278-526-543

OPTIMIZATION OF PREVENTIVE MAINTENANCE BY A COMPARATIVE APPROACH BASED ON EXACT RESOLUTION METHODS AND GENETIC ALGORITHMS: APPLICATION TO A PRODUCTION UNIT 

Ngnassi Djami A.B., Samon J.B, Nzié W

The control of the maintenance of the industrial installations, in particular of the costs due to the implementation of the preventive policies is very interesting because of the growing importance of this service in the chains of production. The objective of this paper is to minimize the preventive maintenance costs of a production unit. For this, a state of the art on the maintenance cost models according to the policy used is first made, then a synthesis of the optimization methods is made in order to deploy the exact resolution methods and the genetic algorithms. The result of this paper is the proposal of a cost model corresponding to a periodic maintenance policy with minimal repair to the failure and the optimization of the periodicities of the partial revisions of the production unit. 

Cite: Ngnassi Djami A.B., Samon J.B, Nzié W OPTIMIZATION OF PREVENTIVE MAINTENANCE BY A COMPARATIVE APPROACH BASED ON EXACT RESOLUTION METHODS AND GENETIC ALGORITHMS: APPLICATION TO A PRODUCTION UNIT . Reliability: Theory & Applications. 2024, June 2(78): 544-563, DOI: https://doi.org/10.24412/1932-2321-2024-278-544-563

BAYES ESTIMATOR OF PARAMETERS OF BINOMIAL TYPE EXPONENTIAL CLASS SRGM USING GAMMA PRIORS

Rajesh Singh, Kailash R. Kale and Pritee Singh

The Reliability is one of the key characteristics of software that operates flawlessly and in accordance with needs of users. The assessment of Reliability is very important but it is complicated. The oneparameter exponential class failure intensity function is used in this article to quantify the model and assess the software Reliability. The scale parameter and the number of existing total failures are the model's parameters. Using the Bayesian approach, the estimators of parameters are obtained under the assumption that gamma priors are suitable to provide prior information of the parameters. Using risk efficiencies computed under squared error loss, the performance of proposed estimators is studied with their corresponding maximum likelihood estimators. The suggested Bayes estimators are found to outperform over the equivalent maximum likelihood estimators. 

Cite: Rajesh Singh, Kailash R. Kale and Pritee Singh BAYES ESTIMATOR OF PARAMETERS OF BINOMIAL TYPE EXPONENTIAL CLASS SRGM USING GAMMA PRIORS. Reliability: Theory & Applications. 2024, June 2(78): 564-575, DOI: https://doi.org/10.24412/1932-2321-2024-278-564-575

STUDY OF THE FUNCTIONING OF A MULTI-COMPONENT AND MULTI-PHASE QUEUING SYSTEM UNDER THE CONDITIONS OF THE IMPLEMENTATION OF DISRUPTIVE TECHNOLOGIES IN AIR TRANSPORTATION

O. Zaporozhets, M. Katsman, V. Matsiuk, V. Myronenko

The article considers multi-component and multi-stage mathematical models of queuing systems (QS) with the distribution of the incoming flow simultaneously between the system components, which consist of a certain number of service channels and waiting places in the queue. The maintenance of requirements with a lack of time to stay in the service channel and waiting is considered, while the service process in the QS of each component consists of several stages with the corresponding duration, and the full-service period is equal to the sum of such time intervals. The number of components and their parameters correspond to the similar characteristics of the production divisions of the repair enterprise. The study of the effectiveness of the operation of the repair enterprise as a multi-component and multi-stage QS consists in determining the values of the initial parameters of the QS components, taking into account the restrictions imposed on them, in order to obtain the largest values of the probabilities of servicing the requirements of the QS components and the system as a whole. The model is implemented using Any Logic University Researcher, which allows you to combine the principles of system dynamics with the paradigms of agent and discrete-event modelling. The proposed approach to the modelling of maintenance and repair processes by production divisions of the enterprise as a multi-component and multi-phase QS allows to determine the effectiveness of the functioning of such a QS and to obtain arguments for increasing the efficiency of its operation.

Cite: O. Zaporozhets, M. Katsman, V. Matsiuk, V. Myronenko STUDY OF THE FUNCTIONING OF A MULTI-COMPONENT AND MULTI-PHASE QUEUING SYSTEM UNDER THE CONDITIONS OF THE IMPLEMENTATION OF DISRUPTIVE TECHNOLOGIES IN AIR TRANSPORTATION. Reliability: Theory & Applications. 2024, June 2(78): 576-593, DOI: https://doi.org/10.24412/1932-2321-2024-278-576-593

PROFIT ANALYSIS OF REPAIRABLE COLD STANDBY SYSTEM SUBJECT TO REBOOT FACILITY UNDER REFRESHMENTS

Ajay Kumar and Ashish Sharma

This paper relates to the reliability measures analysis of two identical unit system with reboot facility. Initially, one unit of the system is in operative mode and another unit is kept in cold standby mode. A technician is always available with the system to perform repairing and rebooting activities. Here, the system operative unit failed in safe mode and unsafe mode. During unsafe failure, repair activity cannot be done immediately but first rebooting is done to transform unsafe failure into safe failure, and then repair activity is performed as usual. Sometimes, the technician needs refreshments due to continuous work and provides better services after taking refreshments. The unit works like a new one after repair. The failure time of the unit in safe mode, unsafe mode and technician refreshment request time are assumed to be general while the repair time of the unit, rebooting delay time and technician refreshment time are taken as exponential. Reliability measures such as mean time to system failure, availability of the system, busy period of the repairman, the expected number of visits by the technician and profit values are calculated using tables.

Cite: Ajay Kumar and Ashish Sharma PROFIT ANALYSIS OF REPAIRABLE COLD STANDBY SYSTEM SUBJECT TO REBOOT FACILITY UNDER REFRESHMENTS. Reliability: Theory & Applications. 2024, June 2(78): 594-603, DOI: https://doi.org/10.24412/1932-2321-2024-278-594-603

ENHANCING SECURITY IN IOT DEVICES: A LIGHTWEIGHT HYBRID CRYPTOGRAPHIC SYSTEM (LCS) APPROACH 

AMITA SHAH, SANJAY SHAH, DHAVAL PARIKH, NAMIT SHAH

The escalating connectivity of devices in the Internet of Things (IoT) era necessitates robust security measures while accommodating resource constraints. Lightweight cryptography addresses this need, focusing on algorithm development for devices with limited resources. This research proposes the Lightweight Crypto System (LCS) as a hybrid cryptosystem, integrating the Lightweight Symmetric Algorithm (LSA) and the Lightweight Hash Algorithm (LHA). LSA is a modified AES-128 variant, enhancing data confidentiality, while LHA, derived from SHA-256, verifies data integrity. The study evaluates the proposed LCS on criteria such as execution time, memory usage, avalanche effect, collision resistance, and entropy, emphasizing the optimal balance between performance and security achieved by LSA and LHA. The findings position LCS as a compelling solution for securing IoT devices without compromising on stringent security requirements.

Cite: AMITA SHAH, SANJAY SHAH, DHAVAL PARIKH, NAMIT SHAH ENHANCING SECURITY IN IOT DEVICES: A LIGHTWEIGHT HYBRID CRYPTOGRAPHIC SYSTEM (LCS) APPROACH . Reliability: Theory & Applications. 2024, June 2(78): 604-620, DOI: https://doi.org/10.24412/1932-2321-2024-278-604-620

THE EFFICIENT CLASSES OF ESTIMATORS FOR THE PRODUCT OF TWO POPULATION MEANS IN THE EXISTENCE OF NON-RESPONSE UNDER THE STRATIFIED POPULATION-A SIMULATION STUDY

Manish Mishra, B. B. Khare & Sachin Singh

This paper focuses on estimating the product of two population means. Within this paper, we have introduced three distinct classes of estimators for product of two population means. These estimators take into account the known population mean of an auxiliary variable under the framework of stratified random sampling and the presence of non-response in the study variable. Basically, for case (I) we assume the non-response on the study variable and utilize the auxiliary information corresponding to the responding units of the study variable and in case (II), we utilize the complete dataset from the auxiliary variable while also accounting for non-response in the study variable. In case (III) we combined both the information of the auxiliary variable and assumed the non-response on the study variable. Expressions for bias and mean square error have been derived, extending up to the first-order derivative. We have also pinpointed some specific members of the proposed estimator. We have conducted a simulation study to evaluate the valuable insights into the performance of the suggested classes of estimators with the conventional estimator.

Cite: Manish Mishra, B. B. Khare & Sachin Singh THE EFFICIENT CLASSES OF ESTIMATORS FOR THE PRODUCT OF TWO POPULATION MEANS IN THE EXISTENCE OF NON-RESPONSE UNDER THE STRATIFIED POPULATION-A SIMULATION STUDY. Reliability: Theory & Applications. 2024, June 2(78): 621-629, DOI: https://doi.org/10.24412/1932-2321-2024-278-621-629

ANALYSIS OF SINGLE SERVER FEEDBACK RETRIAL QUEUE WITH BERNOULLI WORKING VACATION AND STARTING FAILURE

Keerthiga S and Indhira K

The suggested queueing model describes a single-server feedback retrial queueing system with starting failure, Bernoulli working vacation and vacation interruptions. The server departs on a working vacation as soon as orbit is empty. During the working vacation period, the server provides a slower level of service. The supplementary variable method was utilized to determine the steady-state probability-generating functions for the system and its orbit. If there are consumers in the system at the end of each vacation, the server becomes idle and ready to serve new customers. The average busy time and the average busy cycle are presented as important system performance indicators. Additionally, the adaptive neuro-fuzzy interface system has compared the numerical results with the neuro-fuzzy results. Finally, particle swarm optimization (PSO) where utilized to obtain the best (optimal) cost for the system in this study. We have examined the convergence of these optimization strategies.

Cite: Keerthiga S and Indhira K ANALYSIS OF SINGLE SERVER FEEDBACK RETRIAL QUEUE WITH BERNOULLI WORKING VACATION AND STARTING FAILURE. Reliability: Theory & Applications. 2024, June 2(78): 630-646, DOI: https://doi.org/10.24412/1932-2321-2024-278-630-646

METHOD AND ALGORITHM FOR QUANTITATIVE ANALYSIS OF AVERAGE MONTHLY VALUES OF THE OPERATIONAL RELIABILITY OF OVERHEAD POWER LINES 

Farhadzadeh E.M., Muradaliyev A.Z., Abdullayeva S.A. 

The relevance of ensuring the efficiency of equipment, devices and installations (object) of electric power systems increases every year and becomes the most important problem of maintaining energy security. The decrease in work efficiency is due to a number of factors, but, first, an increase in the relative number of objects, the service life of which exceeds the standard value. An illustration of the methodology for quantifying, comparing and ranking the monthly average values of indicators of the operational reliability of 110 kV overhead power transmission lines and above given in order to identify and restore the wear of the least reliable lines. 

Cite: Farhadzadeh E.M., Muradaliyev A.Z., Abdullayeva S.A.  METHOD AND ALGORITHM FOR QUANTITATIVE ANALYSIS OF AVERAGE MONTHLY VALUES OF THE OPERATIONAL RELIABILITY OF OVERHEAD POWER LINES . Reliability: Theory & Applications. 2024, June 2(78): 647-654, DOI: https://doi.org/10.24412/1932-2321-2024-278-647-654

APPLICATIONS OF SIMULATION AND QUEUING THEORY IN SCOOTER INDUSTRY 

Mohit Yadav, Shruti Gupta and Sandeep Singh 

This paper describes the role of queuing theory in developing queuing networks in companies. Queuing networks can be considered as a collection of nodes where each node stands for a service facility. It is a powerful and versatile tool for modeling facilities in manufacturing products. In the realm of service industries like scooter manufacturing, the queuing theory and simulation play a vital role. These concepts help in predicting queue lengths and waiting durations when multiple scooters are manufactured and distributed using first come first serve discipline. Tables are used to explore the availability of furnished scooters in the companies and their comparative study analyzes the waiting scooters and space availability in the companies.

Cite: Mohit Yadav, Shruti Gupta and Sandeep Singh  APPLICATIONS OF SIMULATION AND QUEUING THEORY IN SCOOTER INDUSTRY . Reliability: Theory & Applications. 2024, June 2(78): 655-660, DOI: https://doi.org/10.24412/1932-2321-2024-278-655-660