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EXPLORING NOVEL EXTENSION OF SUJA DISTRIBUTION: UNVEILING PROPERTIES AND DIVERSE APPLICATIONS

C. Subramanian, M. Subhashree, Aafaq A. Rather

This research article introduces and explores the area biased techniques of the Suja distribution, presenting novel derivations and insights. The estimation of the one-parameter area biased Suja distribution is accomplished using maximum likelihood, providing a robust framework for modeling real-world data. A comprehensive study of several statistical properties is conducted to unveil the characteristics and behaviors of this new model. To demonstrate its practical applicability, the proposed distribution is applied to real data of weather temperature. The analysis showcases the distribution's effectiveness in capturing the intricacies of temperature patterns, revealing its potential utility in weather modeling and related applications. The research contributes to the advancement of statistical modeling techniques and enriches our understanding of the Suja distribution's versatility in handling diverse datasets.

Cite:  C. Subramanian, M. Subhashree, Aafaq A. Rather EXPLORING NOVEL EXTENSION OF SUJA DISTRIBUTION: UNVEILING PROPERTIES AND DIVERSE APPLICATIONS. Reliability: Theory & Applications. 2023, December 4(76): 32-40, DOI: https://doi.org/10.24412/1932-2321-2023-476-32-40

32-40

STATISTICAL MODELS FOR FORECASTING EMERGENCY SITUATIONS OF A BIOLOGICAL AND SOCIAL CHARACTER

Valery Akimov, Ekaterina Ivanova, Irina Oltyan

The article considers a statistical model for predicting emergency situations of a biological and social nature. Particular attention is paid to the calculation of indicators of resource provision of the medical care system and mortality rates during the spread of the epidemic.

Cite:  Valery Akimov, Ekaterina Ivanova, Irina Oltyan STATISTICAL MODELS FOR FORECASTING EMERGENCY SITUATIONS OF A BIOLOGICAL AND SOCIAL CHARACTER. Reliability: Theory & Applications. 2023, December 4(76): 41-45, DOI: https://doi.org/10.24412/1932-2321-2023-476-41-45

41-45

A NEW EXTENDED EXPONENTIATED DISTRIBUTION WITH PROPERTIES AND APPLICATIONS

K. Selvakumar, Jameel A. Ansari, K. Kavitha, C. Subramanian, D. Vedavathi Saraja, Arshad Ahmad Khan, Rashid A. Ganaie, Aafaq A. Rather, Maryam Mohiuddin

This manuscript focuses on the statistical properties and estimation methods of the exponentiated Suja distribution, which is characterized by two parameters: scale and shape. From a frequentist perspective, our primary emphasis is on estimation techniques. Additionally, we derive statistical and reliability characteristics for the model. We explore various estimation procedures, including order statistics, entropies, reliability analysis, and the maximum likelihood method. To assess the model's superiority and practical utility, we analyze real lifetime data sets. Overall, this study provides a comprehensive analysis of the exponentiated Suja distribution, offering insights into its statistical properties, estimation techniques, and real-life applications.

Cite: K. Selvakumar, Jameel A. Ansari, K. Kavitha, C. Subramanian, D. Vedavathi Saraja, Arshad Ahmad Khan, Rashid A. Ganaie, Aafaq A. Rather, Maryam Mohiuddin A NEW EXTENDED EXPONENTIATED DISTRIBUTION WITH PROPERTIES AND APPLICATIONS. Reliability: Theory & Applications. 2023, December 4(76): 46-56, DOI: https://doi.org/10.24412/1932-2321-2023-476-46-56

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LEVERAGING AUXILIARY VARIABLES: ADVANCING MEAN ESTIMATION THROUGH CONDITIONAL AND UNCONDITIONAL POST-STRATIFICATION

G.R.V. Triveni, Faizan Danish

This article presents a novel class of estimators designed for post-stratification to estimate the mean of a study variable using information from auxiliary variables. Through a rigorous examination of bias and Mean Square Error (MSE), we demonstrate the potential to improve estimation accuracy up to the first order of approximation. We also thoroughly explore both Conditional and Unconditional post-stratification properties, enhancing our understanding of the estimator's performance. To assess the effectiveness of our proposed estimator, we conduct a comprehensive numerical illustration. The results affirm its superiority over existing estimators in both Conditional and Unconditional Poststratification scenarios, exhibiting the highest Percentage Relative Efficiency. Additionally, graphical analysis reveals that Conditional post- stratification outperforms Unconditional post-stratification. These findings underscore the significant practical value of our proposed estimator in enhancing the accuracy of mean estimation in post-stratification studies. By accurately estimating population parameters, our novel class of estimators contributes to more informed decision-making in various fields of study. The utilization of auxiliary variables allows for better utilization of available information and leads to more reliable and robust conclusions. Overall, the novel class of estimators introduced in this article represents a valuable contribution to the field of post-stratification. As researchers continue to explore and apply these estimators, they have the potential to revolutionize data analysis methods, becoming indispensable tools for survey and research design. The improvements in estimation accuracy brought about by these estimators are particularly crucial in situations where reliable data is scarce or challenging to obtain, making them invaluable for decision-makers and researchers alike. With the increased accuracy and efficiency of our proposed estimators, they provide a pathway for better resource allocation, cost-effective decision-making, and improved policy formulation. Policymakers and researchers can confidently rely on these estimators to produce more accurate results and achieve better outcomes in various domains. In conclusion, the novel class of estimators for post-stratification presented in this article opens up new avenues for advancing statistical estimation methods. The fusion of auxiliary variables with traditional poststratification techniques represents a powerful approach to enhance estimation accuracy. Embracing and incorporating these estimators into research practices will undoubtedly bring us closer to making data-driven decisions that have a meaningful impact on society.

Cite: G.R.V. Triveni, Faizan Danish LEVERAGING AUXILIARY VARIABLES: ADVANCING MEAN ESTIMATION THROUGH CONDITIONAL AND UNCONDITIONAL POST-STRATIFICATION. Reliability: Theory & Applications. 2023, December 4(76): 57-68, DOI: https://doi.org/10.24412/1932-2321-2023-476-57-68

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ASSESSMENT OF GENERALIZED LIFETIME PERFORMANCE INDEX FOR LINDLEY DISTRIBUTION USING PROGRESSIVE TYPE-II SAMPLES

Abhimanyu S Yadav, Mahendra Saha, Amartya Bhattacharya, Arindam Gupta

A meaningful subject of discourse in manufacturing industries is the assessment of the lifetime performance index. In manufacturing industries, the lifetime performance index is used to measure the performance of the product. A generalized lifetime performance index (GLPI) is defined by taking into consideration the median of the process measurement when the lifetime of products follows a parametric distribution may serve better the need of quality engineers and scientists in industry. The present study constructs various point estimators of the GLPI based on progressive type II right censored data for the Lindley distributed lifetime in both classical and Bayesian setup. We perform Monte Carlo simulations to compare the performances of the maximum likelihood and Bayes estimates with a gamma prior of Cy (L) under progressive type-II right censoring scheme. Finally, the validity of the model is adjudged through analysis of a data set.

Cite: Abhimanyu S Yadav, Mahendra Saha, Amartya Bhattacharya, Arindam Gupta ASSESSMENT OF GENERALIZED LIFETIME PERFORMANCE INDEX FOR LINDLEY DISTRIBUTION USING PROGRESSIVE TYPE-II SAMPLES. Reliability: Theory & Applications. 2023, December 4(76): 69-86, DOI: https://doi.org/10.24412/1932-2321-2023-476-69-86

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EXPLORING THE LENGTH BIASED TORNUMONKPE DISTRIBUTION: PROPERTIES, ESTIMATIONS AND PRACTICAL APPLICATIONS

D. Vedavathi Saraja, B. Jayakumar, Madhulika Mishra, Priya Deshpande, C. Subramanian, Rashid A. Ganaie, Aafaq A. Rather, Bilal Ahmad Bhat

In this study, we introduce a novel extension of the Tornumonkpe distribution, known as the length biased Tornumonkpe distribution. This distribution holds particular significance as it belongs to the family of weighted distributions, specifically the length biased variant. Through an in-depth analysis, we explore the mathematical and statistical properties of this distribution, shedding light on its unique characteristics. To estimate the model parameters of this new distribution, we employ the well-established technique of maximum likelihood estimation. This allows us to accurately determine the parameters and enhance our understanding of the distribution's behavior. To demonstrate the practical applicability and advantages of the length biased Tornumonkpe distribution, we showcase its performance using a real-life time data set. Through this empirical examination, we investigate the distribution's superiority and flexibility, providing valuable insights into its potential use in various domains.

Cite: D. Vedavathi Saraja, B. Jayakumar, Madhulika Mishra, Priya Deshpande, C. Subramanian, Rashid A. Ganaie, Aafaq A. Rather, Bilal Ahmad Bhat EXPLORING THE LENGTH BIASED TORNUMONKPE DISTRIBUTION: PROPERTIES, ESTIMATIONS AND PRACTICAL APPLICATIONS. Reliability: Theory & Applications. 2023, December 4(76): 87-98, DOI: https://doi.org/10.24412/1932-2321-2023-476-87-98

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ENHANCING ENGINEERING SCIENCES WITH UMA DISTRIBUTION: A PERFECT FIT AND VALUABLE CONTRIBUTIONS

R. A. Ganaie, C. Subramanian, V. P. Soumya, R. Shenbagaraja, Mahfooz Alam, D. Vedavathi Saraja, Rushika Kinjawadekar, Aafaq A. Rather, Showkat A. Dar

In this study, we introduce a novel class of distributions called the length biased Uma distribution. This distribution is a specific instance of the broader weighted distribution family, known for its versatility in various applications. We explore the structural properties of the length biased Uma distribution and propose a robust parameter estimation technique based on maximum likelihood estimation. To assess its efficacy, we apply the newly introduced distribution to two real-world datasets, evaluating its flexibility and performance in comparison to existing models. The results obtained demonstrate the potential of the length biased Uma distribution as a valuable addition to the repertoire of statistical distributions, offering valuable insights for a wide range of practical applications.

Cite: R. A. Ganaie, C. Subramanian, V. P. Soumya, R. Shenbagaraja, Mahfooz Alam, D. Vedavathi Saraja, Rushika Kinjawadekar, Aafaq A. Rather, Showkat A. Dar ENHANCING ENGINEERING SCIENCES WITH UMA DISTRIBUTION: A PERFECT FIT AND VALUABLE CONTRIBUTIONS. Reliability: Theory & Applications. 2023, December 4(76): 99-111, DOI: https://doi.org/10.24412/1932-2321-2023-476-99-111

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A NOVEL EXTENSION OF INVERSE EXPONENTIAL DISTRIBUTIONS: A HEAVY-TAILED MODEL WITH UPSIDE DOWN BATHTUB SHAPED HAZARD RATE

Jabir Bengalath, Bindu Punathumparambath

Heavy-tailed distributions have garnered interest due to their advantageous statistical and reliability characteristics, rendering them valuable in applied fields such as economics, finance, and risk management. Such distributions offer robust properties, making them pertinent to studies in various areas like econometrics, statistics, and insurance. Thus, the primary objective of this paper is to propose a Two parameter right skewed- upside down bathtub type, heavy tailed distribution, which is a generalisation of Inverse Exponential distribution and is referred to as Modi Inverse Exponential distribution. We derive several mathematical and statistical features, including quantile function, mode, median, skewness, kurtosis, and mean deviation. Additionally, the reliability and hazard rate functions are also derived. Stochastic ordering and order statistics of the proposed distribution were derived. We also investigate the tail behaviour of the proposed model. Furthermore, estimation methods such as maximum likelihood estimation and its asymptotic confidence bound, percentile method, and Cramer-von-Mises method were examined. To demonstrate the appropriateness of the suggested model, we have considered two distinct real datasets along with three distinct models and concluded that the proposed model is more adaptable.

Cite: Jabir Bengalath, Bindu Punathumparambath A NOVEL EXTENSION OF INVERSE EXPONENTIAL DISTRIBUTIONS: A HEAVY-TAILED MODEL WITH UPSIDE DOWN BATHTUB SHAPED HAZARD RATE. Reliability: Theory & Applications. 2023, December 4(76): 112-127, DOI: https://doi.org/10.24412/1932-2321-2023-476-112-127

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A NOVEL METHODOLOGY IN DEVELOPING STRESS-STRENGTH RELIABILITY MODEL FOR WEIBULL DISTRIBUTION: A COMPARISON OF ARTIFICIAL NEURAL NETWORK (ANN) AND RESPONSE SURFACE ANALYSIS (RSA)

Dr. Saurabh L. Raikar, Prof. Rajesh S. Prabhu Gaonkar

Stress strength interference theory is widely used in evaluating the reliability of mechanical components. Various interference models have been developed when stress and strength follow a wide range of distributions. But when stress and strength follow Weibull distribution, a closed form of interference model is not available. This paper deals with developing a methodology for obtaining a closed form interference model for a given application when the stress and strength follow Weibull distribution. The method of artificial neural network (ANN) and response surface analysis (RSA) are used in modelling and analysis. The validation experiment has been conducted and the error obtained shows that the proposed methodology performs reasonably well.

Cite: Dr. Saurabh L. Raikar, Prof. Rajesh S. Prabhu Gaonkar A NOVEL METHODOLOGY IN DEVELOPING STRESS-STRENGTH RELIABILITY MODEL FOR WEIBULL DISTRIBUTION: A COMPARISON OF ARTIFICIAL NEURAL NETWORK (ANN) AND RESPONSE SURFACE ANALYSIS (RSA). Reliability: Theory & Applications. 2023, December 4(76): 128-140, DOI: https://doi.org/10.24412/1932-2321-2023-476-128-140

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RELIABILITY MODELLING OF UTENSILS MANUFACTURING SYSTEM WITH TEMPERATURE DEPENDENT MAINTENANCE

Manisha Gaba, Dalip Singh, Sheetal, Kajal Sachdeva

In this paper, a stochastic model for utensils manufacturing system with preventive maintenance (PM) is analysed in detail. The operation is affected by variation in the temperature dependent maintenance. The entire manufacturing process of utensils goes through four subsystems viz., Circle cutting subsystem 1, Pressing subsystem 2, Spinning subsystem 3 and Polishing & Packing 4. The system has series structure of all the subsystems. The system is put under PM on the winter time and after PM it operates as new. The PM time distributions are considered as arbitrary and the time to failure as well as repair of each subsystem follows a negative exponential distribution. All random variables are statistically independent. Several measures for evaluating the effectiveness of a system, including mean time to system failure (MTSF), system availability (in summer and winter), busy period of repairman and expected number of repairs (in summer and winter) are derived using a regenerative point technique and Markov process. The system is also analysed for particular values of the parameters.

Cite: Manisha Gaba, Dalip Singh, Sheetal, Kajal Sachdeva RELIABILITY MODELLING OF UTENSILS MANUFACTURING SYSTEM WITH TEMPERATURE DEPENDENT MAINTENANCE. Reliability: Theory & Applications. 2023, December 4(76): 141-153, DOI: https://doi.org/10.24412/1932-2321-2023-476-141-153

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OPTIMIZING MULTI-OBJECTIVE MULTI-INDEX TRANSPORTATION PROBLEMS: A SMART ALGORITHMIC SOLUTION WITH LINDO SOFTWARE

Ajjaz Maqbool Dar, K. Selvakumar, S. Ramki, K. M. Karuppasamy, Jameel A. Ansari, Aafaq A. Rather

In the present paper, we create an algorithm to address the transportation problem with numerous objectives and indexes. The transportation problem exists when there are more supply points, more demand points, and various means of transportation are used to meet demand or when moving certain types of goods. The transportation problem may frequently be more complex than the typical form of transportation problem. We create a model that blends fuzzy multi-objective programming and the multiindex transportation problem' by using LINDO software to resolve all related problems. Additionally, the decision-maker may present a variety of data and it may be further improved. The new algorithmfor addressing transport problems in fuzzy environments is demonstrated numerically.

Cite: Ajjaz Maqbool Dar, K. Selvakumar, S. Ramki, K. M. Karuppasamy, Jameel A. Ansari, Aafaq A. Rather OPTIMIZING MULTI-OBJECTIVE MULTI-INDEX TRANSPORTATION PROBLEMS: A SMART ALGORITHMIC SOLUTION WITH LINDO SOFTWARE. Reliability: Theory & Applications. 2023, December 4(76): 154-167, DOI: https://doi.org/10.24412/1932-2321-2023-476-154-167

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CHARACTERIZATION OF NEW QUASI LINDLEY DISTRIBUTION BY TRUNCATED MOMENTS AND CONDITIONAL EXPECTATION OF ORDER STATISTICS

Mohd. Amir, Mohammad Faizan, Rafiqullah Khan

Characterization of a probability distribution plays an important role in probability and statistics. Before a particular probability distribution model is applied to fit the real-world data, it is necessary to confirm whether the given probability distribution satisfies the underlying requirements by its characterization. The aim of this paper is to find characterization results New Quasi Lindley distribution. These results are established using the relation between truncated moments and failure rate functions and conditional expectation of adjacent order statistics. The first characterization result is based on relation between left truncation moment and failure rate function while the second result is based on relation between right truncated moment and reverse failure rate function. In the third characterization result we used conditional expectation of order statistics when the conditioned one is adjacent order statistics. Further, some of its important deductions are also discussed.

Cite: Mohd. Amir, Mohammad Faizan, Rafiqullah Khan  CHARACTERIZATION OF NEW QUASI LINDLEY DISTRIBUTION BY TRUNCATED MOMENTS AND CONDITIONAL EXPECTATION OF ORDER STATISTICS. Reliability: Theory & Applications. 2023, December 4(76): 168-177, DOI: https://doi.org/10.24412/1932-2321-2023-476-168-177

168-177

ANALYSIS OF AN M/M/1/K FEEDBACK WORKING VACATION QUEUE WITH RENEGING

Krishan, Neetu Gupta

The analysis of an M/M/1/N feedback working vacation queueing system with reneging is presented in this paper Customers may become impatient and even disappointed when they see a long line. In the literature on queueing, customer dissatisfaction caused on by unsatisfactory service is referred as feedback. In the case of feedback, customers retry services after receiving unsatisfactory or incomplete. First, we create the equations for the steady-state probabilities using the Markov process method. The steady-state probabilities are then solved by the matrix method. We then provide some system performance measures. We create a cost model using performance analysis. Finally, we give some numerical examples to show how the various model parameters affect the system's behaviour.

Cite: Krishan, Neetu Gupta ANALYSIS OF AN M/M/1/K FEEDBACK WORKING VACATION QUEUE WITH RENEGING. Reliability: Theory & Applications. 2023, December 4(76): 178-188, DOI: https://doi.org/10.24412/1932-2321-2023-476-178-188

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PERFORMANCE CHARACTERIZATION OF TWO-SERVER BATCH SERVICE QUEUE WITH SECOND OPTIONAL SERVICE

Andwilile Abrahamu George, P. Vijaya Laxmi

In this paper, we analyze the performance of a finite capacity two-server Markovian batch service queueing model with second optional service. The servers provide two kinds of services, the first essential service (FES), which is provided to all incoming customers and the second optional service (SOS) to those who demand it after completing FES. The service times of the two servers are identical and are exponentially distributed. Matrix-decomposition method is used to obtain the steady-state probabilities of the model. Numerical results and discussion are presented to demonstrate the impact of the model parameters on the system behavior. Furthermore, the cost model optimization is developed to determine the optimal service rates using the Quasi-Newton method to minimize the expected cost. Finally, the findings of this work show that the blocking probability is monotonically decreases as finite buffer size increases and approaches its minimum value of zero when finite buffer is sufficiently large.

Cite: Andwilile Abrahamu George, P. Vijaya Laxmi PERFORMANCE CHARACTERIZATION OF TWO-SERVER BATCH SERVICE QUEUE WITH SECOND OPTIONAL SERVICE. Reliability: Theory & Applications. 2023, December 4(76): 189-207, DOI: https://doi.org/10.24412/1932-2321-2023-476-189-207

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PROPERTIES OF QUADRASOPHIC FUZZY SET AND ITS APPLICATIONS

G. Aruna, J. Jesintha Rosline

Fuzzy set theory is a distinctive way of approaching ambiguous information. In this artifact, we introduce a new extension of fuzzy set known as Quadrasophic Fuzzy set and its properties. The Quadrasophic Fuzzy set has four parameters. The attributes and operations of the Quadrasophic Fuzzy sets are defined with pertinent examples. The arithmetic aggregator operators with a redefined level of 0.5 are introduced. The theorems of aggregator operators of Quadrasophic Fuzzy sets are explained using mathematical formulations. Suitable results and examples are provided to enlighten the proposed method. The arithmetic aggregator operators of the proposed method have been used in decision- making to get the optimal solution with supplementary statistics. Additionally, the selection of appropriate fertilizer in farming is demonstrated using the operators of the suggested model. A decision-making approach is also used to develop the proposed method in order to identify the ideal solution. An illustration is provided to examine the unique feature of the proposed method to resolve the decision-making problems with a perfect solution.

Cite: G. Aruna, J. Jesintha Rosline PROPERTIES OF QUADRASOPHIC FUZZY SET AND ITS APPLICATIONS. Reliability: Theory & Applications. 2023, December 4(76): 208-220, DOI: https://doi.org/10.24412/1932-2321-2023-476-208-220

208-220

A PENTAGONAL FUZZY-BASED SOLUTION OF MULTIPLE OBJECTIVE LPP

Junaid Basha M, Nandhini S, Nur Aisyah Abdul Fataf

In this paper, the researchers compare proposed approach and Excel solver. In this proposed technique, the researchers converted fuzzy multiple objective linear programming problems (FMOLPP) into multiple objective linear programming problems (MOLPP) with the help of Defuzzified mean of maxima method. Before that, the researchers changed the pentagonal fuzzy numerical valuation to a triangular fuzzy value by using the proposed theorem. Further, the crisp value of MOLPP is solved using standard simplex algorithms. Then the outcomes of the optimal solutions are compared with both the results.

Cite: Junaid Basha M, Nandhini S, Nur Aisyah Abdul Fataf A PENTAGONAL FUZZY-BASED SOLUTION OF MULTIPLE OBJECTIVE LPP. Reliability: Theory & Applications. 2023, December 4(76): 221-228, DOI: https://doi.org/10.24412/1932-2321-2023-476-221-228

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DIFFERENT ESTIMATION METHODS FOR THE PARAMETER OF XGAMMA DISTRIBUTION AND THEIR COMPARISON

Sukanta Pramanik, Sandipan Maiti

The xgamma distribution is vital in reliability/survival analysis and biomedical research. In this article, different estimation methods are proposed for the parameter of this distribution. The distribution is a unique finite mixture of exponential distribution and gamma distribution. Some further properties of the distribution that are not available in the earlier literature are studied. We consider the maximum likelihood estimator, least squares estimator, weighted least squares estimator, percentile estimator, the maximum product spacing estimator, the minimum spacing absolute distance estimator, the minimum spacing absolute log-distance estimator, Cramer von Mises estimator, Anderson Darling estimator, right-tailed Anderson Darling estimator, and compare them using a comprehensive simulation study. For comparison purposes, the estimators’ bias and mean squared error are considered. A real data example is also a part of this work. Some model selection techniques are used to choose the best fitting of the distribution to the data.

Cite: Sukanta Pramanik, Sandipan Maiti DIFFERENT ESTIMATION METHODS FOR THE PARAMETER OF XGAMMA DISTRIBUTION AND THEIR COMPARISON. Reliability: Theory & Applications. 2023, December 4(76): 229-241, DOI: https://doi.org/10.24412/1932-2321-2023-476-229-241

229-241

CONFIDENCE INTERVAL USING MAXIMUM LIKELIHOOD ESTIMATION FOR THE PARAMETERS OF POISSON TYPE LENGTH BIASED EXPONENTIAL CLASS MODEL

Rajesh Singh, Preeti A. Badge, Pritee Singh

In this research paper, Confidence interval using Maximum likelihood estimation is obtained for Poisson type Length biased exponential class for the parameters. Failure intensity, mean time to failure and likelihood function for the parameter is obtained. Confidence interval has been derived for parameters using maximum likelihood estimation. To study the performance of confidence interval, average length and coverage probability are calculated using Monte Carlo simulation technique. From the obtained intervals it is concluded that Confidence interval for the parameter perform better for appropriate choice of execution time and certain values of parameters.

Cite: Rajesh Singh, Preeti A. Badge, Pritee Singh CONFIDENCE INTERVAL USING MAXIMUM LIKELIHOOD ESTIMATION FOR THE PARAMETERS OF POISSON TYPE LENGTH BIASED EXPONENTIAL CLASS MODEL. Reliability: Theory & Applications. 2023, December 4(76): 242-251, DOI: https://doi.org/10.24412/1932-2321-2023-476-242-251

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A TWO NON IDENTICAL UNITS COLD STANDBY SYSTEM WITH CORRELATED FAILURE TIME AND REPAIR MACHINE FAILURE

Alka Chaudhary, Shivali Sharma and Anika Sharma

The paper deals with a system composed of two-non identical units (unit-1 and unit-2). Initially, unit-1 is operative and unit-2 is kept in cold standby. The cold standby unit can't fail in its standby mode. Each unit of the system has two possible modes: Normal (N) and total failure (F). When the unit-1 fails the cold standby (unit-2) becomes operative instantaneously with the help of a perfect and instantaneous switching device. A single repairman is always available with the system to repair a failed unit and failed RM. Unit-1 gets priority in operation and repair over unit-2. However, the RM gets priority in repair over any of the units. The RM machine is good initially and can't fail unless it becomes operative. The system failure occurs when both the units are in total failure mode. The joint distribution of failure and repair times for each unit is taken bivariate exponential distribution. Each repaired unit works as good as new. Using regenerative point technique, various important measures of system effectiveness have been obtained.

Cite: Alka Chaudhary, Shivali Sharma and Anika Sharma A TWO NON IDENTICAL UNITS COLD STANDBY SYSTEM WITH CORRELATED FAILURE TIME AND REPAIR MACHINE FAILURE. Reliability: Theory & Applications. 2023, December 4(76): 252-262, DOI: https://doi.org/10.24412/1932-2321-2023-476-252-262

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DECISION MAKING THROUGH FUZZY LINEAR PROGRAMMING APPROACH

Pandit U. Chopade, Mahesh M. Janolkar, Kirankumar L. Bondar

In this study a real world industrial MPS problem is addressed using the SMF approach. A decision maker, analyst and implementer, all play significant roles in making judgements in an uncertain environment, which is where this difficulty arises in the chocolate manufacturing business. As analysts our goal is to identify a solution with a higher LOS that will enable the decision maker to reach a conclusion. Because all the coefficients including the goals, technical and resource factors are well defined. The MPS problem is taken into consideration. With 24 constraints and 6 variables, this is regarded as one of the sufficiently large problem, which LOV is appropriate for getting satisfactory OR can be determined by a decision maker. To increase the satisfactory income, the decision maker can also advice to the analyst some feasible modification to FI. This collaborative process between the analyst, decision maker and implementer must continue until the best possible solution is found and put into action.

Cite: Pandit U. Chopade, Mahesh M. Janolkar, Kirankumar L. Bondar DECISION MAKING THROUGH FUZZY LINEAR PROGRAMMING APPROACH. Reliability: Theory & Applications. 2023, December 4(76): 263-275, DOI: https://doi.org/10.24412/1932-2321-2023-476-263-275

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DENSITY BY MODULI AND LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES

A. G. K. Ali, A. M. Brono, A. Masha

In this paper, we introduced and studied the concept of lacunary statistical convergence of double sequence with respect to modulus function where the modulus function is an unbounded double sequence. We also introduced the concept of lacunary strong convergence of double sequence via modulus function. We further characterized those lacunary convergence of double sequence for which the lacunary statistically convergent of double sequence with respect to modulus function equals statistically convergent of double sequence with respect to modulus function. Finally, we established some inclusion relations between these two lacunary methods and proved some essential analogue for double sequence.

Cite: A. G. K. Ali, A. M. Brono, A. Masha DENSITY BY MODULI AND LACUNARY STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES. Reliability: Theory & Applications. 2023, December 4(76): 276-287, DOI: https://doi.org/10.24412/1932-2321-2023-476-276-287

276-287

ESTIMATION OF STRESS STRENGTH RELIABILITY USING PRANAV DISTRIBUTION

Ankitha Lukose, Chacko V M

This paper deals with the estimation of stress strength reliability parameter R, which is the probability of Y less than X when X and Y are two independent distribution with different scale parameter and same shape parameter The maximum likelihood method is used to find an estimator for R. We also obtain the asymptotic distribution of the maximum likelihood estimator ofR. Based on this asymptotic distribution, the asymptotic confidence interval can be obtained. We also propose bootstrap confidence interval for the parameter R. Analysis of a simulated data and a real life data have been presented for illustrative purposes.

Cite: Ankitha Lukose, Chacko V M  ESTIMATION OF STRESS STRENGTH RELIABILITY USING PRANAV DISTRIBUTION. Reliability: Theory & Applications. 2023, December 4(76): 288-295, DOI: https://doi.org/10.24412/1932-2321-2023-476-288-295

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FAST AND ROBUST BIVARIATE CONTROL CHARTS FOR INDIVIDUAL OBSERVATIONS

Sajesh T A

There are various circumstances where it is important to simultaneously monitor or control two or more related quality characteristics. Independently tracking these quality characteristics might be quite deceptive. Hotelling's T2 chart, in which the T2 statistics are generated using the classical estimates of location and scatter, is the most well-known multivariate process monitoring and control approach. It is well known that the existence of outliers in a dataset has a significant impact on classical estimators. Any statistic that is computed using the classical estimates will be distorted by even a single outlier. The non-robustness issue is investigated in this study, which also suggests four robust bivariate control charts based on the robust Gnandesikan-Kettenring estimator. This study employs four highly robust scale estimators, with the best breakdown point, namely the Qn estimator, Sn estimator, MAD estimator, and t estimator, in order to robustify the Gnandesikan-Kettenring estimator. Through the use of a Monte Carlo simulation and a real-life data, the performance of the suggested control charts is assessed. The four techniques all outperform the traditional method and provide greater computing efficiency.

Cite: Sajesh T A FAST AND ROBUST BIVARIATE CONTROL CHARTS FOR INDIVIDUAL OBSERVATIONS. Reliability: Theory & Applications. 2023, December 4(76): 296-308, DOI: https://doi.org/10.24412/1932-2321-2023-476-296-308

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STATISTICAL MODELS FOR FORECASTING EMERGENCY SITUATIONS OF MAN-CAUSED CHARACTER

Valery Akimov, Ekaterina Ivanova, Yuri Shishkov

The aim of the study is to develop predictive and analytical solutions for technogenic threats for urban areas, the mathematical basis of which is Bayesian classifiers. The result of the work is a formalized description of models for predicting the consequences of a heat supply shutdown; consequences of a power outage; consequences of oil and oil products spills; the consequences of the discharge of liquid technological waste into the hydrosphere; the consequences of the release of hazardous chemicals into the environment.

Cite: Valery Akimov, Ekaterina Ivanova, Yuri Shishkov STATISTICAL MODELS FOR FORECASTING EMERGENCY SITUATIONS OF MAN-CAUSED CHARACTER. Reliability: Theory & Applications. 2023, December 4(76): 309-313, DOI: https://doi.org/10.24412/1932-2321-2023-476-309-313

309-313

CHARACTERIZATION OF CHANDBHAS-P DISTRIBUTION AND ITS APPLICATIONS IN MEDICAL SCIENCE

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

The current research attempts the length biased version of new two-parameter Sujatha distribution, which is referred as ChandBhas-P Distribution (CBPD). Its different structural properties are discussed and the model parameters of this novel distribution are predicted by using the Maximum Likelihood Estimation. The distribution was examined with two real lifetime sets of data. The first set of data is birth weight of new born babies, randomly selected from a hospital at Thrissur, kerala and the second set is the weight of children of age range between three months to four years-collected from a few babysitting centres and play schools across Thrissur, and both are employed in order to discuss the goodness of fit.

Cite: Praseeja C B, Prasanth C B, C Subramanian, Unnikrishnan T CHARACTERIZATION OF CHANDBHAS-P DISTRIBUTION AND ITS APPLICATIONS IN MEDICAL SCIENCE. Reliability: Theory & Applications. 2023, December 4(76): 314-324, DOI: https://doi.org/10.24412/1932-2321-2023-476-314-324

314-324

FORECASTING OF EXTREME RISK USING MARKOV-SWITCHING GARCH MODELS: EVIDENCE FROM GLOBAL ENERGY MARKETS

S. Kavitha, G. Mokesh Rayalu, D. Pachiyappan, P. Manigandan

This paper investigates the Markov-Switching GARCH and Single-Regime (SR) GARCH models for the extreme-risk prediction of the global energy markets. Using daily data from Jan. 2020 to July. 2022, we find the MS-GARCH-types models are appropriate for both developed and emerging energy markets because they efficiently measure the extreme risk of energy commodities in various cases. Meanwhile, the regime-switching model's capture-dynamic structures in the financial markets and this model is only better than single-regime models in terms of long position risk predicting, rather than short position risk forecasting. That is, on the downside risk predicting, it just outperforms the single regime. Through competitive models, this study examines the risk forecast of energy commodities in different conditions. The findings have strong implications for investors and policymakers in selecting the appropriate model to predict the extreme risk of energy commodities when facing asset allocation, portfolio selection, and risk management.

Cite: S. Kavitha, G. Mokesh Rayalu, D. Pachiyappan, P. Manigandan FORECASTING OF EXTREME RISK USING MARKOV-SWITCHING GARCH MODELS: EVIDENCE FROM GLOBAL ENERGY MARKETS. Reliability: Theory & Applications. 2023, December 4(76): 325-337, DOI: https://doi.org/10.24412/1932-2321-2023-476-325-337

325-337

PRICE RISK ANALYSIS USING GARCH FAMILY MODELS: EVIDENCE FROM INDIAN NATIONAL STOCK EXCHANGE FUTURE MARKET

M. Valavan, Mohammed Ahmar Uddin, S. Rita

The prediction of time-varying volatility plays an important role in financial data. In the paper, a comprehensive analysis of the mean return and conditional variance of NSE index is performed to use GARCH, EGARCH and TGARCH models with Normal innovation and Student's t innovation. Conducting a bootstrap simulation study which shows the Model Confidence Set (MCS) captures the superior models across a range of significance levels. The experimental results show that, under various loss functions, the GARCH using Student's t innovation model is the best model for volatility predictions of NSE among the six models.

Cite: M. Valavan, Mohammed Ahmar Uddin, S. Rita PRICE RISK ANALYSIS USING GARCH FAMILY MODELS: EVIDENCE FROM INDIAN NATIONAL STOCK EXCHANGE FUTURE MARKET. Reliability: Theory & Applications. 2023, December 4(76): 338-345, DOI: https://doi.org/10.24412/1932-2321-2023-476-338-345

338-345

IDZ DISTRIBUTION: PROPERTIES AND APPLICATION

Idzhar A. Lakibul

This paper introduces a novel two - parameter continuous distribution. This distribution is derived from the mixture of the Exponential, Weibull and Ailamujia distributions. The derived distribution is named as "Idz distribution". The probability density function of the Idz distribution is derived and some of its plots are presented. It can be observed that the Idz distribution can generate right tailed unimodal, non-monotonic decreasing and exponential shapes. Further, survival and hazard functions of the Idz distribution are derived. It reveals that the hazard function of the Idz distribution can accommodate three types of failure rate behaviors, namely, non-monotonic constant, right tailed unimodal and nonmonotonic decreasing. Moreover, some properties of Idz distribution such as moments, mean, variance, moment generating function, order statistics and maximum likelihood estimates are derived. In addition, the proposed distribution is applied into a Breast Cancer data and compare with the Exponentiated Generalized Inverse Rayleigh distribution, the Ailamujia Inverted Weibull distribution and the New Extended Exponentiated Weibull distribution. Result shows that the Idz distribution gives better estimates as compared with the said distributions for a given dataset.

Cite: Idzhar A. Lakibul  IDZ DISTRIBUTION: PROPERTIES AND APPLICATION. Reliability: Theory & Applications. 2023, December 4(76): 346-354, DOI: https://doi.org/10.24412/1932-2321-2023-476-346-354

346-354

A LITERATURE REVIEW ON DISCRETE-TIME QUEUEING MODELS

Harini R, Indhira K

In this paper, a quantitative research survey is carried out on discrete-time queueing models. In real-life scenarios, the idea of discrete-time queues has taken on a new meaning. This survey mainly focuses on the unfolding of discrete-time queueing models in recent decades, challenges implied on them and their influence in various fields. The ultimate goal of this paper is to provide enough information to all the researchers and analysts who toil in this field and wish to know more about these models. A few open issues and intriguing future research paths has been discussed.

Cite: Harini R, Indhira K A LITERATURE REVIEW ON DISCRETE-TIME QUEUEING MODELS. Reliability: Theory & Applications. 2023, December 4(76): 355-371, DOI: https://doi.org/10.24412/1932-2321-2023-476-355-371

355-371

QUANTILE RESIDUAL ENTROPY FOR SOME LIFE TIME DISTRIBUTIONS

Javid Gani Dar, Mohammad Younus Bhat, Shahid Tamboli, Shaikh Sarfaraj, Aafaq A. Rather, Maryam Mohiuddin, Showkat Ahmad Dar

This study explores the concept of residual entropy as an alternative approach to traditional entropy measures. The field of information theory, built upon Shannon's entropy, has been instrumental in understanding the dynamics of systems. However, existing literature has recognized the limitations of applying traditional entropy measures to systems that have already been in existence for a certain duration. This study delves into the concept of residual entropy, acknowledging the need for a more suitable approach for such systems. Specifically, we investigate the characteristics of residual entropy using a quantile-based framework. By deriving the quantile residual entropy function for various lifetime models, we gain insights into the reordering and ageing phenomena captured by the quantile version of the residual entropy equation. Our findings contribute to an enhanced understanding of residual entropy and provide a novel perspective on analyzing and interpreting the behavior of established systems.

Cite: Javid Gani Dar, Mohammad Younus Bhat, Shahid Tamboli, Shaikh Sarfaraj, Aafaq A. Rather, Maryam Mohiuddin, Showkat Ahmad Dar QUANTILE RESIDUAL ENTROPY FOR SOME LIFE TIME DISTRIBUTIONS. Reliability: Theory & Applications. 2023, December 4(76): 372-381, DOI: https://doi.org/10.24412/1932-2321-2023-476-372-381

372-381

SAMPLING PLANS BASED ON TRUNCATED LIFE TEST FOR LOGISTIC FAMILY OF DISTRIBUTIONS

Sriramachandran G V

In this article, we develops optimal sample size for acceptance number (zero and one) for single and double sampling plans by fixing consumer's risk and test completion time, with the assumption that, the life of the item follows logistic family of distributions (i.e. Logistic Rayleigh distribution/Logistic exponential distribution/Logistic Weibull distribution). The optimal size obtained for single and double sampling plans for logistic family of distributions are compared with baseline distributions and the results are discussed.

Cite: Sriramachandran G V SAMPLING PLANS BASED ON TRUNCATED LIFE TEST FOR LOGISTIC FAMILY OF DISTRIBUTIONS. Reliability: Theory & Applications. 2023, December 4(76): 382-390, DOI: https://doi.org/10.24412/1932-2321-2023-476-382-390

382-390

ECONOMIC ORDER QUANTITY MODEL FOR IMPERFECT ITEMS WITH SHORTAGE BACKORDERING

Priyanka Singh, A. R. Nigwal, U. K. Khedlekar

This study presents the development of an economic order quantity model (EOQ) specifically designed for imperfect quality items. The model takes into consideration three distinct scenarios: (a) Model I trigger a reorder when the inventory level reaches zero; (b) Model II initiates a reorder when the backordered quantity equals the imperfect quantity; (c) Model III initiates a reorder when the shortage persists. To distinguish between perfect and imperfect quality products, a screening process is implemented for each product lot. Upon product delivery from the supplier to the vendor, all received products undergo immediate inspection through the screening process. Following the EOQ ordering policy, the vendor sells imperfect products to customers at a reduced cost at the end of the cycle, rather than returning them to the supplier. To fulfil the remaining demand for high-quality products, the vendor procures such products from a local vendor at a higher price. This study optimizes the duration of positive inventory, selling price, and total profit per unit time. Model I, which exhibits the longest duration of positive inventory, demonstrates greater business stability compared to the other two models. The concavity property is analytically and numerically demonstrated, and a sensitivity analysis is provided to explore the impact of model parameters on outputs.

Cite: Priyanka Singh, A. R. Nigwal, U. K. Khedlekar ECONOMIC ORDER QUANTITY MODEL FOR IMPERFECT ITEMS WITH SHORTAGE BACKORDERING. Reliability: Theory & Applications. 2023, December 4(76): 391-409, DOI: https://doi.org/10.24412/1932-2321-2023-476-391-409

391-409

DESIGNING A HYBRID SINGLE SAMPLING PLAN FOR LIFE-TIME ASSESSMENT USING THE EXPONENTIAL-RAYLEIGH DISTRIBUTION

Radhika A, Nandhini M, Jeslin J

The approach of statistical quality control known as "product control" deals with the steps involved in making judgments on one or more batches of completed goods produced by production processes. One of the main categories of product control is sampling inspection by variables, which includes processes for selecting numerous individual units based on sample measurements for a quality characteristic under investigation. These approaches are predicated on the knowledge of the functional form of the probability distribution and the presumption that the quality feature is measured on a continuous scale. The literature on product control contains inspection techniques that were created with the implicit presumption that the quality characteristic is distributed normally with the associated attributes. In this study, a single variable sampling plan is developed and assessed under the assumption that the quality characteristic will be distributed using an Exponential-Rayleigh distribution. This article discusses the development of reliability sampling plans for intermittent test batches using type-I and type-II censoring data. To build a sampling strategy using the Exponential-Rayleigh distribution, this work offers a two-parameter continuous probability distribution. One of the main categories of acceptance sampling is sampling inspection by variables, which involves processes for making decisions regarding the disposition of numerous individual units based on sample measurements of those units for a quality feature under investigation. Assume that the sample inspection's number of defective items follows the Poisson distribution. The suggested SSP's ideal parameters are determined using a multi-objective genetic algorithm, which is concerned with concurrently minimizing the average number of samples and inspection costs a maximizing the likelihood of the acceptance sampling plan. The Rayleigh distribution is an appropriate model for life-testing studies, and the Exponential Rayleigh Distribution is studied as a model for a lifetime random variable. The paper also analyses the effectiveness of reliable single sampling plans designed using the median lifetime of products. The efficiency of these sampling plans is evaluated in terms of sample size and sampling risks. Poisson probabilities are used to determine the parameters of the sampling plans, to protect both producers and consumers from risks. For manufacturing enterprises to analyze the viability of the sample plan, necessary tables and procedures are constructed with acceptable examples.

Cite: Radhika A, Nandhini M, Jeslin J DESIGNING A HYBRID SINGLE SAMPLING PLAN FOR LIFE-TIME ASSESSMENT USING THE EXPONENTIAL-RAYLEIGH DISTRIBUTION. Reliability: Theory & Applications. 2023, December 4(76): 410-418, DOI: https://doi.org/10.24412/1932-2321-2023-476-410-418

410-418

REDESCENDING M-ESTIMATOR BASED LASSO FOR FEATURE SELECTION

R. Muthukrishnan, C. K. James

Aim: Regression analysis is one of the statistical methods which helps to model the data and helps in prediction, a large data set with higher number of variables will often create problem due to its dimensionality and hence create difficulties to gather important information from the data, so it is a need of a method which can simultaneously choose important variables which contains most of the information and hence helps to fit the model. Least absolute shrinkage and selection operator (LASSO) is a popular choice for shrinkage estimation and variable selection. But LASSO uses the conventional least squares technique for feature selection which is very sensitive to outliers. As a result, when the data set is contaminated with bad observations (Outliers), the LASSO technique gives unreliable results, so in this paper the focus is to create a method which can resist to outliers in the data and helps in giving a meaningful result. Method: proposed a new procedure, a LASSO method by adding weights which uses the concept of redescending M-estimator, which can resist outliers in both dependent and independent variables. The observation with greater importance receives a higher weight and less weight to the least important observation. Findings: The efficiency of the proposed method has been studied in the real and simulation environment and compared with other existing procedures with measures like Median Absolute Error (MDAE), False Positive Rate (FPR), False Negative Rate (FNR), Mean Absolute Percentage Error (MAPE). The proposed method with the redescending M-estimator shows a higher resistance to outliers compared to conventional LASSO and other robust existing procedures. Conclusion: The study reveals that the proposed method outperforms other existing procedures in terms of MDAE, FPR, FNR and MAPE, indicating its superior performance in variables selection under outlier contaminated datasets.

Cite: R. Muthukrishnan, C. K. James REDESCENDING M-ESTIMATOR BASED LASSO FOR FEATURE SELECTION. Reliability: Theory & Applications. 2023, December 4(76): 419-428, DOI: https://doi.org/10.24412/1932-2321-2023-476-419-428

419-428

PARAMETER ESTIMATION OF SCALE MUTH DISTRIBUTION(SMD) UNDER TYPE-1 CENSORING USING CLASSICAL AND BAYESIAN APPROACHES

Agni Saroj, Prashant K. Sonker, Shalini Kumari, Rakesh Ranjan, Mukesh Kumar

The lifetime distributions are used to understand and explain the real life circumstances in various fields (medical, engineering, etc.). Many times it is very tough task to complete an experiment with complete data due to lack of time, money or some other factors and get the data in incomplete form. to draw the information from such type of data (incomplete data), we use some censoring techniques. In the field of statistics, there are several censoring techniques available where type-I censoring is most commonly used due to its simplicity. In this article, the scale Muth distribution (SMD) is considered as a lifetime distribution under type-I censoring scheme. The parameter estimation has been done by classical as well as Bayesian approach. Under the classical paradigm, two most popular methods were used maximum likelihood estimation (MLE) and the maximum product of spacing estimation (MPSE). And under the Bayesian paradigm, we used the informative priors for each parameter and obtained the estimates by considering the squared error loss function using an approximation method, Metropolis Hasting (MH) algorithm. The performance of each estimator is evaluated by their mean squared error or simulated risk. Also, a real data set is used to illustrate the real phenomena and to estimate the parameter using above-mentioned techniques under type-I censoring scheme.

Cite: Agni Saroj, Prashant K. Sonker, Shalini Kumari, Rakesh Ranjan, Mukesh Kumar PARAMETER ESTIMATION OF SCALE MUTH DISTRIBUTION(SMD) UNDER TYPE-1 CENSORING USING CLASSICAL AND BAYESIAN APPROACHES. Reliability: Theory & Applications. 2023, December 4(76): 429-445, DOI: https://doi.org/10.24412/1932-2321-2023-476-429-445

429-445

ROBUST MAHALANOBIS DEPTH BASED ON MINIMUM REGULARIZED COVARIANCE DETERMINANT ESTIMATOR FOR HIGHDIMENSIONAL DATA

R Muthukrishnan, Surabhi S Nair

Handling of high-dimensional data is an important issue in robust literature. For analyzing data, location measure plays a vital role in almost all statistical methods. The location parameter of a distribution is used to find the central value. Many computational methods are used to find the measure of location for analyzing data. The data depth procedure is one approach to finding the true representative of the entire data and it is one of the key concepts in multivariate data analysis. Data depth is a term used to describe how deep a particular point is inside the broad multivariate data cloud. Instead of the typical smallest to biggest rank, the sample points can be ordered from the center outward. Mahalanobis depth is one of the popular depth procedures. The traditional approach used to find Mahalanobis depth is based on Mahalanobis distance, it is based on the classical sample mean vector and covariance matrix. So the conventional Mahalanobis depth is sensitive to outliers and may fail when the data is contaminated. To solve this problem, the Minimum Covariance Determinant (MCD) estimators are used instead of classical estimators. However, the MCD estimators cannot be calculated in high dimensional data sets, in which the variable number is higher than the subset size. To calculate Mahalanobis depth values in high dimensional data, propose a new depth function namely the Robust Regularized Mahalanobis Depth (RRMD), which can be calculated in high dimensional data sets. The proposed procedure is based on Minimum Regularized Covariance Determinants (MRCD) estimators, this study shows that the proposed depth function is successful in finding the deepest point in high dimensional data sets with real and simulation studies up to a certain level of contamination.

Cite: R Muthukrishnan, Surabhi S Nair ROBUST MAHALANOBIS DEPTH BASED ON MINIMUM REGULARIZED COVARIANCE DETERMINANT ESTIMATOR FOR HIGHDIMENSIONAL DATA. Reliability: Theory & Applications. 2023, December 4(76): 446-452, DOI: https://doi.org/10.24412/1932-2321-2023-476-446-452

446-452

DISCRETE INVERSE GAMMA DISTRIBUTION BASED LOAD-SHARE MODEL WITH APPLICATION

Rachna Srivastava, Pramendra Singh Pundir

In reliability engineering, the multi-component load-sharing models are being used to amplify system's reliability. This study consists of the k-component load-sharing parallel system model considering each component's failure time distribution as discrete inverse gamma. The classical and Bayesian analysis for this model is performed. The maximum likelihood estimates along with their standard errors for the parameters, system's reliability function, hazard rate function and reversed second rate of failure function are obtained. The asymptotic confidence intervals as well as two bootstrap intervals like bootstrap-p and bootstrap-t confidence intervals are constructed. Further, Bayes estimates along with their posterior standard errors and highest posterior density credible intervals for the parameters and system's reliability characteristics are obtained by using Markov Chain Monte Carlo techniques. A detailed simulation table is formed to demonstrate the effectiveness of the theory developed. Finally, a real data set is used to illustrate the applicability of the model.

Cite: Rachna Srivastava, Pramendra Singh Pundir DISCRETE INVERSE GAMMA DISTRIBUTION BASED LOAD-SHARE MODEL WITH APPLICATION. Reliability: Theory & Applications. 2023, December 4(76): 453-465, DOI: https://doi.org/10.24412/1932-2321-2023-476-453-465

453-465

SURVIVAL ANALYSIS OF A MULTI-STATE SEMI-MARKOV MODEL ON INFECTIOUS DISEASE CONSIDERING VARIOUS LEVELS OF SEVERITY

Sujata Sukhija, Rajeev Kumar

The aim of the paper is to carry out survival analysis of a novel multi-state model on infectious disease considering various levels of severity using semi-Markov processes. Various levels of severity of the disease over time and transitions between these severity levels have been considered. Transition probabilities and expected waiting times are derived. Expressions for mean survival time, expected total time in home isolation, and expected total time in hospital are obtained. The analysis of the proposed model is carried out through numerical computation and plotting several graphs. Important conclusions are drawn. The modelling framework proposed here can be used to model any infectious disease irrespective of disease states. The study will be helpful in designing effective measures to control the infectious disease and selecting the appropriate intervention policies.

Cite: Sujata Sukhija, Rajeev Kumar SURVIVAL ANALYSIS OF A MULTI-STATE SEMI-MARKOV MODEL ON INFECTIOUS DISEASE CONSIDERING VARIOUS LEVELS OF SEVERITY. Reliability: Theory & Applications. 2023, December 4(76): 466-480, DOI: https://doi.org/10.24412/1932-2321-2023-476-466-480

466-480

ON AN IMPATIENT CONSUMER QUEUE WITH SECONDARY SERVICE, MULTIPLE VACATIONS AND SERVER BREAKDOWNS

K. Jyothsna, P. Vijaya Kumar, P. Vijaya Laxmi

This study presents a limited buffer secondary service queue with multiple vacations and server breakdowns. The model under consideration includes two types of impatient policies: balking and reneging. After the completion of the essential primary service, only few consumers choose to proceed with secondary service with a certain probability. During the active period of the server, it is subject to breakdown and the broken down server is immediately sent for repair. Further, the server will go on vacation as soon as there are no waiting consumers in the queue. On returning from a vacation, if the system is still empty the server leaves for another vacation and continues to do so until atleast one consumer is found at a vacation termination epoch. The model is analyzed under steady-state conditions and the explicit expressions of various performance indices are evaluated. A few numerical results illustrate how the model parameters have an effect on the performance metrics.

Cite: K. Jyothsna, P. Vijaya Kumar, P. Vijaya Laxmi ON AN IMPATIENT CONSUMER QUEUE WITH SECONDARY SERVICE, MULTIPLE VACATIONS AND SERVER BREAKDOWNS. Reliability: Theory & Applications. 2023, December 4(76): 481-492, DOI: https://doi.org/10.24412/1932-2321-2023-476-481-492

481-492

MODELING OF RELIABILITY AND SURVIVAL DATA WITH EXPONENTIATED GENERALIZED INVERSE LOMAX DISTRIBUTION

Sule Omeiza Bashiru, Ibrahim Ismaila Itopa

In this paper, a new four-parameter distribution is developed and studied by combining the properties of the exponentiated generalized-G family of distributions and the features of the Inverse Lomax distribution. The newly developed distribution is called the exponentiated generalized inverse Lomax distribution that extends the classical inverse Lomax distribution. The shape of the hazard rate function is very flexible because it possesses increasing, decreasing, and inverted (upside-down) bathtub shapes. Some important characteristics of the exponentiated generalized inverse Lomax distribution are derived, including moments, moment generating function, survival function, hazard function and order statistics. The method of maximum likelihood estimation is used to obtain estimates of the unknown parameters of the new model. The application of the new model is based on two real-life data sets used to show the modeling potential of the proposed distribution. The exponentiated generalized inverse Lomax distribution turns out to be the best by capturing important details in the structure of the data sets considered.

Cite: Sule Omeiza Bashiru, Ibrahim Ismaila Itopa MODELING OF RELIABILITY AND SURVIVAL DATA WITH EXPONENTIATED GENERALIZED INVERSE LOMAX DISTRIBUTION. Reliability: Theory & Applications. 2023, December 4(76): 493-501, DOI: https://doi.org/10.24412/1932-2321-2023-476-493-501

493-501

RELIABILITY ANALYSIS OF THE SHAFT SUBJECTED TO TWISTING MOMENT AND BENDING MOMENT FOR NORMALLY DISTRIBUTED STRENGTH AND STRESS

Md. Yakoob Pasha, M. Tirumala Devi, T. Sumathi Uma Maheswari

Shaft is the rotating component that transmits power from one place to another. The shafts are commonly subject to torsional and bending moments and combinations of these moments. In general, shafts are subjected to a combination of torsional and bending stresses. The design of a shaft is essential, subject to its strength and stress. This paper presents the reliability analysis of the shaft subjected to (a) twisting moment, (b) bending moment and (c) combined twisting and bending moment for which stress and strength follow the normal distribution.

Cite: Md. Yakoob Pasha, M. Tirumala Devi, T. Sumathi Uma Maheswari RELIABILITY ANALYSIS OF THE SHAFT SUBJECTED TO TWISTING MOMENT AND BENDING MOMENT FOR NORMALLY DISTRIBUTED STRENGTH AND STRESS. Reliability: Theory & Applications. 2023, December 4(76): 502-512, DOI: https://doi.org/10.24412/1932-2321-2023-476-502-512

502-512

GROUP RUNS AND MODIFIED GROUP RUNS CONTROL CHARTS FOR MONITORING LINEAR REGRESSION PROFILES

Onkar Ghadge, Vikas Ghute

Profile monitoring is a critical tool for manufacturing industries to evaluate and maintain quality performance, as well as detect faults. The process of profile monitoring involves observing how variables interact with one another throughout a given period. This enables the understanding of any changes in their functional relationship over time. Generally, control charts are used for monitoring profiles. This paper proposes two new methods to enhance the monitoring of simple and multiple linear regression profiles in Phase II. The proposed methods are based on group runs (GR) and modified group runs (MGR) control charting schemes. The procedure to obtain optimal design parameters for the proposed methods is discussed in detail. The effectiveness of the suggested techniques is assessed through the ARL standard. The study found that the proposed GR and MGR monitoring methods displayed superior performance compared to other available monitoring methods in the literature. A real-life example is illustrated using proposed GR and MGR charting schemes.

Cite: Onkar Ghadge, Vikas Ghute GROUP RUNS AND MODIFIED GROUP RUNS CONTROL CHARTS FOR MONITORING LINEAR REGRESSION PROFILES. Reliability: Theory & Applications. 2023, December 4(76): 513-524, DOI: https://doi.org/10.24412/1932-2321-2023-476-513-524

513-524

ON A CLASS OF LORENTZIAN PARA-KENMOTSU MANIFOLDS ADMITTING QUARTER-SYMMETRIC METRIC CONNECTION

S. Sunitha Devi, K. L. Sai Prasad

In this present paper, a class of Lorentzian almost paracontact metric manifolds known as the LP-Kenmotsu (Lorentzian para-Kenmotsu) is considered that accepts a connection of quarter-symmetric. In this work, it was found that an LP-Kenmotsu manifold is either <p-symmetric or concircular <p-symmetric with respect to quarter-symmetric metric connection if and only if it is symmetric with respect to the Riemannian connection, provided the scalar curvature of Riemannian connection is constant.

Cite: S. Sunitha Devi, K. L. Sai Prasad ON A CLASS OF LORENTZIAN PARA-KENMOTSU MANIFOLDS ADMITTING QUARTER-SYMMETRIC METRIC CONNECTION. Reliability: Theory & Applications. 2023, December 4(76): 525-532, DOI: https://doi.org/10.24412/1932-2321-2023-476-525-532

525-532

EVALUATION OF SAMPLE SIZE AND EFFICIENT FIELD SAMPLING PLAN IN HDP APPLE ORCHARDS

Tabasum Mushtaq, Mushtaq A. Lone, S. A. Mir, Sonali Kedar Powar, Aafaq A. Rather, Adil H. Khan, Faizan Danish

An essential stage in research is choosing an adequate sample size and sampling strategy. In order to obtain the most accurate estimates possible when surveying high density apple orchards, this paper provides the proper procedure for selecting the sample and an effective sampling strategy. For this study, primary information gathered during a two-year period from the SKUAST-Kashmir exotic apple block Plate I was employed. This investigation was conducted using the TCSA of exotic apple trees of the Gala and Fuji types. The sample was obtained using a variety of sampling techniques in order to find the parameters of population. Findings revealed that using proportional allocation of a stratified sample technique, in both the varieties, produces the most efficient population parameter estimates.

Cite: Tabasum Mushtaq, Mushtaq A. Lone, S. A. Mir, Sonali Kedar Powar, Aafaq A. Rather, Adil H. Khan, Faizan Danish EVALUATION OF SAMPLE SIZE AND EFFICIENT FIELD SAMPLING PLAN IN HDP APPLE ORCHARDS. Reliability: Theory & Applications. 2023, December 4(76): 533-538, DOI: https://doi.org/10.24412/1932-2321-2023-476-533-538

533-538

ESTIMATION OF STRESS-STRENGTH RELIABILITY BASED ON KME MODEL

Kavya P., Manoharan M.

In reliability theory the estimation of stress-strength reliability is an important problem. It has many applications in engineering and physics areas. In many practical situations, the assumption of identical strength distributions may not be quite realistic because components of a system are of different structure. Here we establish the estimation of stress-strength reliability of the KM-Exponential (KME) distribution. In this article, we consider the case that the stress-strength variables are independent. KME distribution is parsimonious in parameter and has decreasing failure rate. The stress-strength reliability based on KME model is estabished and using maximum likelihood estimation method, the estimation of the stress-strength reliability is derived and also the asymptotic distribution. Simulation method is used to show the performance of the parameters and the 95% confidence interval is also calculated. With the help of simulated data, we depict the application of the stress-strength reliability of KME distribution.

Cite: Kavya P., Manoharan M. ESTIMATION OF STRESS-STRENGTH RELIABILITY BASED ON KME MODEL. Reliability: Theory & Applications. 2023, December 4(76): 539-546, DOI: https://doi.org/10.24412/1932-2321-2023-476-539-546

539-546

REDUNDANCY OPTIMIZATION FOR A SYSTEM COMPRISING ONE OPERATIVE UNIT AND N HOT STANDBY UNITS

Parveen, Dalip Singh, Anil Kumar Taneja

In many industries and applications, downtime or failure can have serious consequences, such as financial losses, safety hazards, or reputational damage. A hot standby unit can help minimize the impact of such events by providing a backup that can quickly and seamlessly take over in the event of a failure. Further, the question of as to how many hot standby units should be used also needs to be addressed. So, an N+1-Unit-system is investigated wherein N units are on hot standby, whereas one unit is operational and the system is such that the hot standby units can take over seamlessly if the single operative unit fails. The system breaks down completely when all the units fail. It is assumed that the failure rates of all the operational units and the redundant units will vary exponentially. To get different performability measurements, the regenerative point technique has been applied to optimize the value of N.

Cite: Parveen, Dalip Singh, Anil Kumar Taneja  REDUNDANCY OPTIMIZATION FOR A SYSTEM COMPRISING ONE OPERATIVE UNIT AND N HOT STANDBY UNITS. Reliability: Theory & Applications. 2023, December 4(76): 547-562, DOI: https://doi.org/10.24412/1932-2321-2023-476-547-562

547-562

FUZZY CONTROL CHARTS BASED ON RANKING OF PENTAGONAL FUZZY NUMBERS

Mohammad Ahmad, Weihu Cheng, Zhao Xu, Abdul Kalam, Ahteshamul Haq

A Control Chart is a fundamental approach in Statistical Process Control. When uncommon causes of variability are present, sample averages will plot beyond the control boundaries, making the control chart a particularly effective process monitoring approach. Uncertainties are caused by the measuring system, including the gauges operators and ambient circumstances. In this paper, the concept of fuzzy set theory is used for dealing with uncertainty. The control limits are to converted into fuzzy control limits using the membership function. The fuzzy X-R and X-S control chart is developed by using the ranking of the pentagonal fuzzy number system. An illustrative example is done with the discussed technique to make fuzzy X-R and X-R control charts and increase the flexibility of the control limit.

Cite: Mohammad Ahmad, Weihu Cheng, Zhao Xu, Abdul Kalam, Ahteshamul Haq FUZZY CONTROL CHARTS BASED ON RANKING OF PENTAGONAL FUZZY NUMBERS. Reliability: Theory & Applications. 2023, December 4(76): 563-574, DOI: https://doi.org/10.24412/1932-2321-2023-476-563-574

563-574

N-POWER HALF LOGISTIC-G FAMILY: APPLICATIONS TO MEDICAL AND TRAFFIC DATA

Pankaj Kumar, Laxmi Prasad Sapkota, Vijay Kumar

This research article introduces a novel family of distributions achieved through the methodology of the n-power transformation technique. The study focuses on one specific member that is inverse Weibull distribution within this family, which showcases a hazard function exhibiting distinct J, reverse-J, bathtub, or monotonically increasing shapes. The article explores the essential characteristics of this distribution and employs the maximum likelihood estimation (MLE) method to estimate its associated parameters. To evaluate the accuracy of the estimation procedure, a simulation experiment is conducted, revealing a decrease in biases and mean square errors as sample sizes increase, even when working with small samples. Furthermore, the practical application of the proposed distribution is demonstrated by analyzing two real medical and traffic datasets. By employing model selection criteria and conducting goodness-of-fit test statistics, the article establishes that the proposed model surpasses existing models in performance. The application of this research work can be significant in various fields where modeling and analyzing hazard functions or survival data are essential, while also making contributions to probability theory and statistical inferences.

Cite: Pankaj Kumar, Laxmi Prasad Sapkota, Vijay Kumar N-POWER HALF LOGISTIC-G FAMILY: APPLICATIONS TO MEDICAL AND TRAFFIC DATA. Reliability: Theory & Applications. 2023, December 4(76): 575-590, DOI: https://doi.org/10.24412/1932-2321-2023-476-575-590

575-590

POWER KOMAL DISTRIBUTION WITH PROPERTIES AND APPLICATION IN RELIABILITY ENGINEERING

Rama Shanker, Mousumi Ray, Hosenur Rahman Prodhani

The statistical analysis and modeling of reliability data from engineering is really a challenge for statistician because the reliability data from engineering are stochastic in nature. Recently one parameter Komal distribution was introduced in statistics literature for the analysis and modeling of failure time data from engineering. Komal distribution, being one parameter distribution, does not provide good fit to some engineering data due to its theoretical or applied point of view. In this article we propose a two-parameter power Komal distribution, which includes Komal distribution as particular case, for the analysis and modeling of data from reliability engineering. Its statistical properties including behavior of probability density function and cumulative distribution function for varying values of parameters have been presented. The first four raw moments and the variance of the proposed distribution has been derived and given. The expressions for hazard rate function and mean residual life function have been obtained and their behaviors for varying values of parameters have been presented. The stochastic ordering which is very much useful comparing the stochastic nature has also been discussed. Method of maximum likelihood has been discussed for estimating the parameters. Application of the distribution has been investigated using a real lifetime dataset from engineering. The goodness of fit of power Komal distribution has been tested using Akaike Information criterion and Kolmogorov-Smirnov statistic. The goodness of fit of power Komal distribution shows that it gives much closure fit over two-parameter power Garima distribution, Power Shanker distribution and Weibull distribution and one parameter exponential distribution, Shanker distribution, Garima distribution and Komal distribution. As the power Komal distribution gives much better fit over Weibull distribution, which is very much useful for modeling and analysis of data from reliability engineering, the final recommendation is that the power Komal distribution should be preferred over the considered distributions including Weibull for modeling data from reliability engineering.

Cite: Rama Shanker, Mousumi Ray, Hosenur Rahman Prodhani POWER KOMAL DISTRIBUTION WITH PROPERTIES AND APPLICATION IN RELIABILITY ENGINEERING. Reliability: Theory & Applications. 2023, December 4(76): 591-603, DOI: https://doi.org/10.24412/1932-2321-2023-476-591-603

591-603

PROFIT ANALYSIS OF REPAIRABLE COLD STANDBY SYSTEM UNDER REFRESHMENTS

Ajay Kumar, Ashish Sharma

In the generation of science and technology, every company wants to increase the reliability of their products. So, they used the concept of cold standby redundancy, timely repair of the failed unit and providing limited refreshments to the available technician when required. This paper aims to explore the system of two identical units where the primary unit is operative and the secondary unit is in cold standby mode. When the primary unit fails due to any fault then secondary unit starts working immediately. Here, times of failure of unit and technician refreshment request follow the general distribution whereas times of repair of unit and refreshment follow the exponential distributions. Such types of systems are used in industries and education systems to prevent losses. The system's performance is calculated by using concepts of mean time to system failure, availability, busy period of the server, expected number of visits made by the server and profit function using the semi-Markov process and regenerative point technique. Tables are used to explore the performance of the system.

Cite: Ajay Kumar, Ashish Sharma PROFIT ANALYSIS OF REPAIRABLE COLD STANDBY SYSTEM UNDER REFRESHMENTS. Reliability: Theory & Applications. 2023, December 4(76): 604-612, DOI: https://doi.org/10.24412/1932-2321-2023-476-604-612

604-612

POWER WEIBULL QUANTILE FUNCTION AND IT'S RELIABILITY ANALYSIS

Jeena Joseph, Sonitta Tony

In this article, we propose a new class of distributions defined by a quantile function, which is the sum of the quantile functions of the Power and Weibull distributions. Various distributional properties and reliability characteristics of the class are discussed. To examine the usefulness of the model, the model is applied to a real life datasets. Parameters are estimated using maximum likelihood estimation technique.

Cite: Jeena Joseph, Sonitta Tony POWER WEIBULL QUANTILE FUNCTION AND IT'S RELIABILITY ANALYSIS. Reliability: Theory & Applications. 2023, December 4(76): 613-624, DOI: https://doi.org/10.24412/1932-2321-2023-476-613-624

613-624

GENERALISED EXPONENTIAL RATIO-CUM-PRODUCT ESTIMATOR FOR ESTIMATING POPULATION VARIANCE IN SIMPLE RANDOM SAMPLING

Rafia Jan, T. R. Jan, Faizan Danish

This study presents a comprehensive investigation into the estimation of population variance for a study variable using Simple Random Sampling, with the incorporation of two auxiliary variables. To address the challenges of variance estimation in complex scenarios, a novel approach termed the "Proposed Generalized Exponential Ratio-cum-Product Estimator" is introduced. This innovative estimator belongs to a class of estimators that rely on exponential functions of the auxiliary variables, providing enhanced precision and efficiency in variance estimation. To thoroughly assess the performance of the proposed estimators, the research develops equations for both Mean Square Errors and Biases, unveiling their statistical properties. The study systematically explores the conditions under which these estimators demonstrate superior efficiency compared to traditional alternative estimators, thereby enabling researchers to identify contexts where their utilization is most beneficial. The empirical aspect of the research constitutes a significant contribution to the study's validity. Through empirical analysis, the proposed estimators are directly compared against the conventional Unbiased Sample Variance Estimator, showcasing their clear superiority in terms of efficiency. Furthermore, Mean Square Errors and Percent Relative Efficiency are calculated for all estimators and subjected to theoretical and empirical comparisons with existing estimation methods. These findings corroborate the advantageous attributes of the proposed estimator in real-world scenarios, reinforcing its practicality and reliability in various research domains. Beyond methodological developments, this study also delves into the real-world implications and applications of the proposed estimators. It highlights the potential benefits of utilizing these estimators in situations where study variables exhibit intricate relationships with auxiliary variables, offering valuable insights into multifaceted data sets and multidimensional factors. Additionally, a comprehensive sensitivity analysis is undertaken to assess the robustness of the proposed estimators under varying assumptions and sampling schemes. The researchers' meticulous evaluation enhances the credibility of the proposed estimators and ensures their adaptability across diverse practical scenarios. Overall, this study's significance extends beyond statistical theory, presenting valuable practical implications for researchers and practitioners across different fields. Improved population variance estimation leads to enhanced decision-making, optimal resource allocation, and deeper insights into underlying phenomena. By introducing the proposed estimator and thoroughly examining its performance through rigorous theoretical and empirical analyses, this research lays a solid foundation for more robust and efficient variance estimation techniques. The insights gained from this study can reshape statistical practices, paving the way for advancements in diverse scientific disciplines and inspiring further knowledge exploration.

Cite: Rafia Jan, T. R. Jan, Faizan Danish GENERALISED EXPONENTIAL RATIO-CUM-PRODUCT ESTIMATOR FOR ESTIMATING POPULATION VARIANCE IN SIMPLE RANDOM SAMPLING. Reliability: Theory & Applications. 2023, December 4(76): 625-631, DOI: https://doi.org/10.24412/1932-2321-2023-476-625-631

625-631

EXPONENTIAL-PARETO MIXTURE DISTRIBUTION

Irina Peshkova

In this paper we introduce the Exponential-Pareto mixture distribution. This distribution is associated as mixture of light and heavy-tailed data which arise in a wide class applications including risk analysis. Characteristic function, failure rate function, mean excess, conditional excess distribution are derived. It is proved that the limiting distribution of maxima among n values of rv's with Exponential-Pareto distribution has Frechet-type form. The maximal likelihood estimation of parameters is discussed. The upper bound of uniform distance between Exponential-Pareto mixture and Pareto distributions is derived.

Cite: Irina Peshkova EXPONENTIAL-PARETO MIXTURE DISTRIBUTION. Reliability: Theory & Applications. 2023, December 4(76): 632-645, DOI: https://doi.org/10.24412/1932-2321-2023-476-632-645

632-645

RELIABILITY ASSESSMENTS USING STOCHASTIC DEGRADATION PROCESS FOR CURRENT TIME ANALYSIS CUMULATIVE DAMAGE MODELS

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

The reliability study of such incredibly reliable items is inappropriate for the use of failure time data analysis and testing methodologies. More trustworthy information can be obtained from degradation data than from standard censored failure-time data, especially in cases where few or no failures are anticipated. The market for lighting has given a lot of attention to high-power white light emitting diodes (HPWLEDs). But as one of the more dependable electronic goods, it may not be expected to fail in either a traditional or even an accelerated life test. DDDM, or data-driven degradation methodology, is used in this research. Using data on lumen maintenance gathered from the IES LM-80-08 lumen maintenance test standard and based on the general degradation path model, the dependability of HPWLED was predicted. Testing such devices in typical working situations, and occasionally even under worse conditions, is difficult enough without trying to collect an adequate amount of time-to-failure data. Modern items are made with superb quality and high reliability in mind. Some safety-critical parts and systems are even made to last for an incredibly long time in order to prevent the disastrous effects of probable breakdowns. A cumulative damage model based on stochastic degradation processes has been developed in this paper. A suitable numerical representation is used to support the analytical findings. As a result, the degradation analysis approach has been developed to address dependability modeling issues using data on product degradation gleaned from historical records or degradation testing.

Cite: G. Sathya Priyanka, S. Rita, M. Iyappan RELIABILITY ASSESSMENTS USING STOCHASTIC DEGRADATION PROCESS FOR CURRENT TIME ANALYSIS CUMULATIVE DAMAGE MODELS. Reliability: Theory & Applications. 2023, December 4(76): 646-656, DOI: https://doi.org/10.24412/1932-2321-2023-476-646-656

646-656

SOFTWARE QUALITY ANALYSIS BASED ON SELECTIVE PARAMETERS USING ENHANCED ENSEMBLE MODEL

Rakhi Singh, Mamta Bansal, Surabhi Pandey

Software Quality Analysis refers to the process of evaluating and assessing the quality of software products or applications. It involves analyzing various aspects of the software to determine its level of quality, identify potential issues or defects, and make informed decisions to expand the software's overall quality. There are investigated different software quality models based on machine learning algorithms. Nevertheless, the explored approaches have an inconsistent understanding of the software product quality and high complexity. This research presents an enhanced ensemble model (EEM) that involves Support Vector Machine (SVM), K-Nearest Neighbor (KNN), and Extreme Learning Machine (ELM) to assess the optimal outcomes. This model performance is computed based on multiple selective parameters namely functional suitability and maintainability of the software and compared along with several algorithms namely Decision Tree, Random Forest, AdaBoost, and Naive Bayes. The outcome of this ensemble model demonstrates that it offers highly accurate results for software validation, verification, and overall product development process to analyze the functional suitability as well as software maintainability. The measured accuracy on Decision Tree, Random Forest, Naive Bayes, AdaBoost, and EEM is found 92.08%, 93.35%, 94.50%, 95.60%, and 99.14%, respectively.

Cite: Rakhi Singh, Mamta Bansal, Surabhi Pandey SOFTWARE QUALITY ANALYSIS BASED ON SELECTIVE PARAMETERS USING ENHANCED ENSEMBLE MODEL. Reliability: Theory & Applications. 2023, December 4(76): 657-669, DOI: https://doi.org/10.24412/1932-2321-2023-476-657-669

657-669

OPTIMIZATION OF SYSTEM PARAMETERS OF 2: 3 GOOD SERIAL SYSTEM USING DEEP LEARNING

Shakuntla Singla, Shilpa Rani, Umar Muhammad Modibbo, Irfan Ali

In this paper, Optimization of System Parameters of 2:3 Good Serial System controlled with the help of a controlling unit Using Deep Learning Optimization with packing unit in series with priority in repair and single server which never fails is carried out. There are three units of different capacities working in parallel in which if three/two units are working then the system is working at full/reduced capacity. Working of these online parallel and offline units is managed by the controlling unit, which also manages the preventive maintenance of all type of units, together with a 24/7 repair facility is modeled for reliability performance measurements. Taking exponential failure and repair rates of units and facilities a steady state transition diagram (depicting transition rates and states) is drawn using Markov process. The system parameters are modelled using Regenerative Point graphical Technique (RPGT) and optimized using Deep learning methods such as Adam, SGD, RMS prop. The results of the optimization may be used to validate and challenge existing models and assumptions about the systems.

Cite: Shakuntla Singla, Shilpa Rani, Umar Muhammad Modibbo, Irfan Ali OPTIMIZATION OF SYSTEM PARAMETERS OF 2: 3 GOOD SERIAL SYSTEM USING DEEP LEARNING. Reliability: Theory & Applications. 2023, December 4(76): 670-679, DOI: https://doi.org/10.24412/1932-2321-2023-476-670-679

670-679

RAP AND AVAILABILITY ANALYSIS OF MANUFACTURING SYSTEM: SMO AND PSO

Sarita Devi, Nakul Vashishth, Deepika Garg

In today's scenario manufacturing industries are highly complex and prone to failure. That's why redundancy allocation problem (RAP) and time dependent availability analysis plays a major role for the successful life cycle of a manufacturing industry. RAP is a Np-hard problem which is very difficult to solve by traditional methods. Therefore in this paper, RAP for the Manufacturing system is solved by Spider monkey optimization. SMO is recent meta-heuristic technique. Till now it is not used to solve RAP. Further results are compared with the Particle swarm optimization algorithm and comparison validates the better performance of SMO in this problem. As mentioned above, for avoiding the complete breakdown of the manufacturing system time- dependent availability is analyzed in this study. Firstly failure and repair data is collected from the manufacturing system then with the help of this information transition diagram is developed. Further equations are developed from transition diagram by using Markov birth death process then equations are solved with the use of Runge-Kutta method. This methodology is implemented in MATLAB.

Cite: Sarita Devi, Nakul Vashishth, Deepika Garg RAP AND AVAILABILITY ANALYSIS OF MANUFACTURING SYSTEM: SMO AND PSO. Reliability: Theory & Applications. 2023, December 4(76): 680-691, DOI: https://doi.org/10.24412/1932-2321-2023-476-680-691

680-691

INTEGRATING TESTING COVERAGE, EFFORT AND CHANGE POINT IN A SOFTWARE RELIABILITY GROWTH MODEL: A COMPREHENSIVE ANALYSIS

Sudeep Kumar, Anu G Aggarwal

Software reliability growth models (SRGMs) are essential for forecasting and controlling the reliability of software systems. In present article, we propose an enhanced SRGM that incorporates three important factors: testing coverage, testing effort, and change point detection. We introduce a novel testing coverage function that captures the delayed S-shaped behaviour commonly observed in software reliability growth. Weibull distribution is utilized to model the testing effort. Finally, we address the impact of change points in software reliability. To assess how well our suggested model works, we conducted experiments using real-world software failure data provide by Tandem computers. The results demonstrate that our model outperforms existing SRGMs by providing more accurate predictions and a better understanding of the interplay between testing coverage, testing effort, and change points.

Cite: Sudeep Kumar, Anu G Aggarwal INTEGRATING TESTING COVERAGE, EFFORT AND CHANGE POINT IN A SOFTWARE RELIABILITY GROWTH MODEL: A COMPREHENSIVE ANALYSIS. Reliability: Theory & Applications. 2023, December 4(76): 692-700, DOI: https://doi.org/10.24412/1932-2321-2023-476-692-700

692-700

PREDICTION OF RELIABILITY CHARACTERISTICS OF THRESHER PLANT BASIS ON GENERAL AND COPULA DISTRIBUTION

Urvashi, Shikha Bansal

In the agriculture field industry, farming tools play an important role. Any type of machinery's performance is influenced by factors including dependability, accessibility, and operating conditions. Different types of modern machinery are being used in today's modern world, so the farming system has become very easy. Thresher plants are essential equipment in the agriculture field industry, and these plants have many uses. A transition diagram for the system is used to develop a mathematical model of the thresher plant. Partial differential equations are created associated with the help of a transition diagram and solved using Laplace transforms and the supplementary variables approach to assessing the system's reliability. The copula approach was used to design the experiment, and the same methodology was used to assess the outcomes. The main aim of the present article is to evaluate the reliability factors, Profit, and sensitive analysis of a threshers plant. It is also possible to compute the dependability factor with the aid of general distributions and compare it to that copula distribution.

Cite: Urvashi, Shikha Bansal PREDICTION OF RELIABILITY CHARACTERISTICS OF THRESHER PLANT BASIS ON GENERAL AND COPULA DISTRIBUTION. Reliability: Theory & Applications. 2023, December 4(76): 701-715, DOI: https://doi.org/10.24412/1932-2321-2023-476-701-715

701-715

APPLICATION OF MACHINE LEARNING ALGORITHMS IN THE PROBLEMS OF IMPROVING MODE RELIABILITY OF MODERN POWER SYSTEMS

Viktor Kurbatsky, Huseyngulu Guliyev, Nikita Tomin, Famil Ibrahimov, Nijat Huseynov

In order to increase the regime reliability of energy systems, the experience of applying machine learning algorithms and models for various issues of operative-dispatching and counter-accident management was reviewed. It is indicated that an effective solution to this problem is the use of machine learning algorithms and models that are able to learn to predict and control the operating modes of the power system, taking into account many changing influencing factors. The experience of using machine learning technology in the tasks of operational dispatch and emergency control of EPS is presented, which clearly shows the prospects of such studies for subsequent practical implementation in the work of various automated control systems for electric power networks of power systems. Until recently, models based on neural network structures have remained the most popular among machine approaches in predictive problems. The advantages of using this structure are shown, first of all, by the fact that the neural network structure makes it possible to obtain models with good approximating abilities. A comparative analysis of the effectiveness of various models in predicting electricity consumption is given. The issues of voltage and reactive power regulation in the electrical network of power systems using an artificial neural network are considered and the effectiveness of this approach is shown. A model and algorithm for estimating voltage stability in power system nodes under various influencing factors is proposed, as well as results are presented that confirm the reliability of the results obtained.

Cite: Viktor Kurbatsky, Huseyngulu Guliyev, Nikita Tomin, Famil Ibrahimov, Nijat Huseynov APPLICATION OF MACHINE LEARNING ALGORITHMS IN THE PROBLEMS OF IMPROVING MODE RELIABILITY OF MODERN POWER SYSTEMS. Reliability: Theory & Applications. 2023, December 4(76): 716-728, DOI: https://doi.org/10.24412/1932-2321-2023-476-716-728

716-728

OPTIMIZATION OF PRIORITY SERVICE WITH EFFICIENT COORDINATION OF ADMISSION CONTROL, EMERGENCY VACATION OF AN UNRELIABLE SERVER

G. Ayyappan, S. Nithya

In this paper, we establish a single server retrial queueing system with two types of customers, admission control, balking, emergency vacation, differentiate breakdown, and restoration. There are two distinct factors which must be considered when classifying priority and ordinary customers. The non-preemptive priority discipline proposed by this concept. Ordinary and priority customers arrive in accordance with Poisson processes. For both priority and ordinary customers, the server continuously offers a single service that is distributed arbitrarily. In this study, we compute the Laplace transforms of the time-dependent probabilities of system states using a probability generating function and the supplementary variable technique. The sensitivity analysis of system descriptions is assisted by study of numerical findings.

Cite: G. Ayyappan, S. Nithya OPTIMIZATION OF PRIORITY SERVICE WITH EFFICIENT COORDINATION OF ADMISSION CONTROL, EMERGENCY VACATION OF AN UNRELIABLE SERVER. Reliability: Theory & Applications. 2023, December 4(76): 729-743, DOI: https://doi.org/10.24412/1932-2321-2023-476-729-743

729-743

PERFORMANCE ANALYSIS OF BULK ARRIVAL GENERAL SERVICE QUEUE WITH FEEDBACK, IMPATIENT CUSTOMERS AND SECOND OPTIONAL SERVICE

P. Vijaya Laxm, Hasan A. Qrewi, E. Girija Bhavani

This paper analyzes the steady state behavior of batch arrival non-Markovian service queue with feedback, balking, reneging, and second optional service (SOS). The steady-state probabilities are computed using the probability generating function. After completing the first essential service (FES), if a customer is unsatisfied with it, he may choose to rejoin the system (feedback), opt for the SOS, or depart from the system with specific probabilities. Once a customer arrives, he decides immediately to join the queue or refuses to join (balking). Furthermore, after joining the queue if a customer does not get service within a specific time, may become impatient, and decide to leave the line without getting any service (reneging). Reneging time follows exponential distribution while service time (FES and SOS) follow general distribution. Also, the cost model was presented to determine the optimal service rates to minimize the expected cost. Finally, various performance measures and numerical illustrations are provided.

Cite: P. Vijaya Laxm, Hasan A. Qrewi, E. Girija Bhavani PERFORMANCE ANALYSIS OF BULK ARRIVAL GENERAL SERVICE QUEUE WITH FEEDBACK, IMPATIENT CUSTOMERS AND SECOND OPTIONAL SERVICE. Reliability: Theory & Applications. 2023, December 4(76): 744-759, DOI: https://doi.org/10.24412/1932-2321-2023-476-744-759

744-759

RELIABILITY MODELLING OF A PARALLEL-COLD STANDBY SYSTEM WITH REPAIR PRIORITY

Puran Rathi, Anuradha, S.C. Malik

This paper deals with the reliability modelling of a parallel cold standby system of four units. The units operate in two phases; phase-I and phase-II. In phase-I, two identical units (called main units) work in parallel and the other two identical units (called duplicate units) have been taken as spare in cold standby. The units of phase-I and of the phase-II are not identical. The priority to repair the units of phase-I has been given over the repair of the units of the phase-II. However, no priority is given for operation of the units of both phases. There is a single repair facility which tackles all types of faults whenever occurred in the system. After repair each unit works as new and the switches devices are considered as perfect. The repair time of the units follows arbitrary probability distribution while the failure time of the units is assumed as constant. The behaviour of mean sojourn time (MST), transition probabilities, mean time to system failures (MTSF), availability, expected number of repairs for both phase-I and phase-II units, expected number of visits of the server, busy period of the server and finally the profit function are obtained in steady state by making use of well-known semi-Markov process (SMP) and Regenerative Point Technique (RPT) for arbitrary values of the parameters in steady state. Novelty and Application: A four-unit system is configured in two phases namely; phase-I and phase-II under some novel assumptions with a practical visualization in metallic bush manufacturing industries.

Cite: Puran Rathi, Anuradha, S.C. Malik RELIABILITY MODELLING OF A PARALLEL-COLD STANDBY SYSTEM WITH REPAIR PRIORITY. Reliability: Theory & Applications. 2023, December 4(76): 760-770, DOI: https://doi.org/10.24412/1932-2321-2023-476-760-770

760-770

ANALYSIS OF M, MAP/PH\, PH2/1 NON-PREEMPTIVE PRIORITY QUEUEING MODEL WITH DELAYED WORKING VACATIONS, IMMEDIATE FEEDBACK, IMPATIENT CUSTOMER, DIFFERENTIATE BREAKDOWN AND PHASE TYPE REPAIR

G. Ayyappan, N. Arulmozhi

The arrival of high priority customers is governed by the Poisson process while that of low priority customers is governed by the Markovian Arrival Process, and the service times are determined by a distinct Phase-type distribution. When the service is finished and the system is empty, the server stays idle for a random period (delay time). If a customer arrives within the delayed period, the server resumes normal service to the customer immediately. Otherwise, at the end of the delayed period, the server will take a working vacation and will instantly provide slow service to customers (high priority customers only). The Matrix analytic method is used to investigate the system. We also discussed the steady-state vector and busy period for our concept. The estimated and visually displayed performance measures of the system.

Cite: G. Ayyappan, N. Arulmozhi ANALYSIS OF M, MAP/PH\, PH2/1 NON-PREEMPTIVE PRIORITY QUEUEING MODEL WITH DELAYED WORKING VACATIONS, IMMEDIATE FEEDBACK, IMPATIENT CUSTOMER, DIFFERENTIATE BREAKDOWN AND PHASE TYPE REPAIR. Reliability: Theory & Applications. 2023, December 4(76): 771-790, DOI: https://doi.org/10.24412/1932-2321-2023-476-771-790

771-790

ANALYSIS OF MAP/ PH1, PH2, PH3/1 QUEUEING-INVENTORY SYSTEM WITH TWO COMMODITIES

S. Meena, N. Arulmozhi, G. Ayyappan, K. Jeganathan

In this work, a single server implements a two-commodity inventory queueing system. We assume that both commodities have a finite capacity. Customers arrive by a Markovian Arrival Process, there is a need for a single item, and either or both types of commodities are required, and this requirement is modeled using certain probabilities. The lead times are exponentially distributed, and the service times have a PH distribution. We use matrix analytical techniques to investigate the queueing inventory system and adopt an (s, S)-type replenishment policy that is dependent on the type of commodity. In the steady state, the joint and individual probability distribution of the Esystem, inventory level, and server status is obtained. A few significant performance measures are attained. Our mathematical concept is then illustrated with a few numerical examples.

Cite: S. Meena, N. Arulmozhi, G. Ayyappan, K. Jeganathan ANALYSIS OF MAP/ PH1, PH2, PH3/1 QUEUEING-INVENTORY SYSTEM WITH TWO COMMODITIES. Reliability: Theory & Applications. 2023, December 4(76): 791-805, DOI: https://doi.org/10.24412/1932-2321-2023-476-791-805

791-805

EXPLORING THE ADAPTABILITY OF THE UNIT INVERSE WEIBULL DISTRIBUTION FOR MODELING DATA ON THE UNIT INTERVAL

Shameera T, BlNDU P.P

This paper derives a new lifetime distribution called the unit inverse Weibull distribution (UIWD) from inverse weibull distribution. Various statistical properties such as the survival function, hazard rate function, revised hazard rate function, cumulative hazard rate function, moments, and quartiles have been discussed. Additionally, we have explored other properties like skewness, kurtosis, order statistics, and the quantile function. Various methods of estimation, including maximum likelihood, moments, percentiles, and the Cramer-Von Mises, have been discussed. Simulation studies were conducted to assess the accuracy and precision of the parameters. Comparative analyses were performed to highlight the effectiveness and utility of the proposed model in comparison to other existing models, using two real-life applications. Finally, real life data analysis reveals that derived distribution can provide a better fit than several well-known distributions.

Cite: Shameera T, BlNDU P.P EXPLORING THE ADAPTABILITY OF THE UNIT INVERSE WEIBULL DISTRIBUTION FOR MODELING DATA ON THE UNIT INTERVAL. Reliability: Theory & Applications. 2023, December 4(76): 806-820, DOI: https://doi.org/10.24412/1932-2321-2023-476-806-820

806-820

On MIXTURE OF BURR XII AND NAKAGAMI DISTRIBUTIONS: PROPERTIES AND APPLICATIONS

Hemani Sharma, Parmil Kumar

The Burr XII and Nakagami distributions hold significant importance in both lifetime distribution and wealth distribution analyses. The Burr XII distribution serves as a valuable tool for understanding the distribution of wealth and wages within specific societies, while the Nakagami distribution finds its application in the realm of communication engineering. The incorporation of finite mixture distributions, aimed at accounting for unobserved variations, has gained substantial traction, particularly in the estimation of dynamic discrete choice models. This research delves into the fundamental characteristics of the mixture Burr XII and Nakagami distributions. The study introduces parameter estimation techniques and explores various aspects, including the cumulative distribution function, hazard rate, failure rate, inverse hazard function, odd function, cumulative hazard function, rth moment, moment generating function, characteristic function, moments, mean and variance, Renyi and Beta entropies, mean deviation from mean, and mean time between failures (MTBF). The paper also addresses the estimation of the mixing parameter through a Bayesian approach. To illustrate the effectiveness of the proposed model, two real-life datasets are examined.

Cite: Hemani Sharma, Parmil Kumar On MIXTURE OF BURR XII AND NAKAGAMI DISTRIBUTIONS: PROPERTIES AND APPLICATIONS. Reliability: Theory & Applications. 2023, December 4(76): 821-841, DOI: https://doi.org/10.24412/1932-2321-2023-476-821-841

821-841

STARTING MODE OF SYNCHRONOUS MACHINES WITH MASSIVE ROTORS

Laman Hasanova, Nurali Yusifbayli

It is known that in synchronous machines with massive rotors, it is required to take into account the change in the equivalent rotor of active resistance depending on the frequency of the current in the rotor at starting of these machines. A three-phase mathematical model of these machines has been compiled, the equations of which are written in axes rotating at the speed of the machine rotor. Study of the start-up modes of these machines and operation in synchronous mode with a load surge (dynamic mode) has been carried out on this model. The studies have allowed for making the following conclusions. When starting synchronous machines with massive rotors, it is most preferable to take into account the change in the equivalent resistance in the form of a linear sliding function. It was found out that in the synchronous mode of operation of these machines, including in stable dynamic modes, there is no need to take into account changes in the rotor resistance-sliding, since the sliding in these modes oscillatory damps around zero, thereby not affecting changes in the value of the equivalent resistance. Therefore, in these modes it is recommended to consider the value of this resistance constant and definite at slip equal to zero.

Cite: Laman Hasanova, Nurali Yusifbayli STARTING MODE OF SYNCHRONOUS MACHINES WITH MASSIVE ROTORS. Reliability: Theory & Applications. 2023, December 4(76): 842-849, DOI: https://doi.org/10.24412/1932-2321-2023-476-842-849

842-849

DESIGNING OF PHASE II ARL-UNBIASED 52-CHART WITH IMPROVED PERFORMANCE USING REPETITIVE SAMPLING

Sonam Jaiswal, Nirpeksh Kumar

In this paper, we consider a two-sided Phase II S2-chart with probability limits because the surveillance of both an increase and decrease in the process variance plays a decisive role in a continuous quality improvement program. We propose a two-sided average run length unbiased S2-chart under the repetitive sampling with probability limits for a fixed in-control average run length and average sample size to eliminate the average run length biasedness. It is well established that the Shewhart-type charts are less sensitive to detect small to moderate changes in the process parameters. Therefore, a repetitive sampling scheme is taken into consideration to improve the S2-chart's ability to detect changes in the process variance. Under the repetitive sampling methodology, the detection ability of the chart is improved by using more than one samples if the first sample does not provide sufficient evidence to decide whether the process is in-control or out-of-control. The proposed chart is compared with the existing charts, such as the equal tailed standard Shewhart S2-chart and unequal tailed S2-chart under repetitive sampling. Results show that the proposed chart is more efficient than the existing chart. Finally, an illustration has been provided in the favor of the proposed chart with the help of a published dataset.

Cite: Sonam Jaiswal, Nirpeksh Kumar DESIGNING OF PHASE II ARL-UNBIASED 52-CHART WITH IMPROVED PERFORMANCE USING REPETITIVE SAMPLING. Reliability: Theory & Applications. 2023, December 4(76): 850-860, DOI: https://doi.org/10.24412/1932-2321-2023-476-850-860

850-860

EVALUATION OF PERFORMANCE MEASURES FOR RELIABLE AND SECURE PHISHING DETECTION SYSTEM

Pratikkumar A Barot, Sunil A Patel, H B Jethva

Phishing is an illegal act and security breach which acquires a user's confidential information without consent. Anti-phishing techniques used to detect and prevent such malicious acts to provide data safety to the end user. Researchers proposed an anti-phishing solution with the help of techniques like the blacklist record, heuristic function, visual similarity, and machine learning algorithm. In recent times many researchers proposed machine learning techniques for phishing detection and achieve more than 90% accuracy. However, there is reliability issue in the accuracy measures used by the researchers. In real life, the phishing dataset is unbalanced. Most of the researchers ignore this data quality during their research work design. In the case of unbalanced data, traditional accuracy measure does not give proper performance evaluation. It shows biased performance evaluations. In this paper, we experimented with an unbalanced dataset of phishing detection and did detailed result analysis to highlight the reliability issue of traditional performance evaluation measures for unbalanced data classification. We experiment with four classification algorithms and found that more than 90% of accuracy does not entitle any classifier as secure and safe if the dataset is unbalanced. Our work highlights the data factors and algorithmic limitations that compromise the system security and data safety.

Cite: Pratikkumar A Barot, Sunil A Patel, H B Jethva EVALUATION OF PERFORMANCE MEASURES FOR RELIABLE AND SECURE PHISHING DETECTION SYSTEM. Reliability: Theory & Applications. 2023, December 4(76): 861-870, DOI: https://doi.org/10.24412/1932-2321-2023-476-861-870

861-870

DEVELOPING A NEW HUNTSBERGER TYPE SHRINKAGE ESTIMATOR FOR THE ENTROPY OF EXPONENTIAL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS

Priyanka Sahni, Rajeev Kumar

The aim of the paper is to develop a new Huntsberger type shrinkage estimator for the entropy function of the exponential distribution. The present paper proposes a Huntsberger type shrinkage estimator for the entropy function of the exponential distribution. This Huntsberger type shrinkage entropy estimator is based on test statistic, which eliminates arbitrariness of choice of shrinkage factor. For the developed estimator risk expressions under LINEX loss function and squared error loss function have been calculated. To assess the efficacy of the proposed estimator, numerical computations are performed, and graphical analysis is carried out for risk and relative risks for the proposed estimator. It is also compared with the existing best estimator for distinct degrees of asymmetry and different levels of significance. Based on the criteria of relative risk, it is found that the proposed Huntsberger type shrinkage estimator is better than the existing estimator for the entropy function of the exponential distribution for smaller values of level of significance and degrees of freedom. 

Cite: Priyanka Sahni, Rajeev Kumar DEVELOPING A NEW HUNTSBERGER TYPE SHRINKAGE ESTIMATOR FOR THE ENTROPY OF EXPONENTIAL DISTRIBUTION UNDER DIFFERENT LOSS FUNCTIONS. Reliability: Theory & Applications. 2023, December 4(76): 871-881, DOI: https://doi.org/10.24412/1932-2321-2023-476-871-881

871-881

THE SABUR DISTRIBUTION: PROPERTIES AND APPLICATION RELATED TO ENGINEERING DATA

Aijaz Ahmad, Afaq Ahmad, Aafaq A. Rather

This paper introduces a novel probability distribution called the Sabur distribution (SD), characterized by two parameters. It offers a comprehensive analysis of this distribution, encompassing various properties such as moments, moment-generating functions, deviations from the mean and median, mode and median, Bonferroni and Lorenz curves, Renyi entropy, order statistics, hazard rate functions, and mean residual functions. Furthermore, the paper delves into the graphical representation of the probability density function, cumulative distribution function and hazard rate function to provide a visual understanding of their behavior. The distribution's parameters are estimated using the well-known method of maximum likelihood estimation. The paper also showcases the practical applicability of the Sabur distribution through real-world examples, underscoring its performance and relevance in various scenarios.

Cite: Aijaz Ahmad, Afaq Ahmad, Aafaq A. Rather THE SABUR DISTRIBUTION: PROPERTIES AND APPLICATION RELATED TO ENGINEERING DATA. Reliability: Theory & Applications. 2023, December 4(76): 882-892, DOI: https://doi.org/10.24412/1932-2321-2023-476-882-892

882-892

COST & PROFIT ANALYSIS OF TWO-DIMENSIONAL STATE M/M/2 QUEUING MODEL WITH CORRELATED SERVERS, MULTIPLE VACATION, BALKING AND CATASTROPHES

Sharvan Kumar, Indra

The present study obtains the time-dependent solution of a two-dimensional state Markovian queuing model with infinite capacity, correlated servers, multiple vacation, balking and catastrophes. Inter arrival times follow an exponential distribution with parameters A and service times follow Bivariate exponential distribution BVE (p, p, v) where p is the service time parameter and v is the correlation parameter. Both the servers go on vacation with probability one when there are no units in the system and the servers keeps on taking a sequence of vacations of random length each time the system becomes empty, till it finds at least one unit in the system to start each busy period referred as multiple vacation. The unit finds a long queue and decides not to join it; may be considered as balking. All the units are ejected from the system when catastrophes occur and the system becomes temporarily unavailable. The system reactivates when new units arrive. Occurrence of catastrophes follow Poisson distribution with rate £,. Laplace transform approach has been used to find the time-dependent solution. By using differential-difference equations, the recursive expressions for probabilities of exactly i arrivals and j departures by time t are obtained. The probabilities of this model are consistent to the results of "Pegden & Rosenshine". The model estimates the total expected cost, total expected profit and obtained the optimal values by varying time t for cost and profit. These important key measures give a greater understanding of the model behaviour. Numerical analysis and graphical representations have been done by using Maple software.

Cite: Sharvan Kumar, Indra COST & PROFIT ANALYSIS OF TWO-DIMENSIONAL STATE M/M/2 QUEUING MODEL WITH CORRELATED SERVERS, MULTIPLE VACATION, BALKING AND CATASTROPHES. Reliability: Theory & Applications. 2023, December 4(76): 893-908, DOI: https://doi.org/10.24412/1932-2321-2023-476-893-908

893-908

INNOVATIVE METHODS OF ENSURING THE FUNCTIONAL SAFETY OF TRAIN CONTROL SYSTEMS

I.B. Shubinsky, E.N. Rozenberg, H. Schabe

The paper examines the specificity of the modern intelligent control systems. The Big Data technology and Data Science algorithms open up great potential in train traffic management based on hazard prevention. An example is given of high reliability and acceptable accuracy of hazardous railway infrastructure failure prediction using methods based on artificial intelligence. A great deal of attention is given to economical methods of ensuring the required levels of functional safety of train control systems. For that purpose, the efficiency of the digital twin-based method was evaluated. It is shown that, under certain conditions, this method allows significantly reducing the cost of a control system while achieving an acceptably high level of functional safety. The method of virtual second channels is based on the same principle of using information redundancy rather than hardware redundancy. The paper presents and analyses the method of virtual second channels in respect to an axle counter-based train control system. It is established that it is possible to ensure a safety integrity level of an entire control system with a virtual second channel at least as high as SIL3. The above methods ensure, on the one hand, a reduction of the amount of equipment and significantly lower cost of the systems and, on the other hand, requires the creation of additional software and substantiation of the acceptability of the achieved level of functional safety. This matter is within the competence of the developer of the control system.

Cite: I.B. Shubinsky, E.N. Rozenberg, H. Schabe INNOVATIVE METHODS OF ENSURING THE FUNCTIONAL SAFETY OF TRAIN CONTROL SYSTEMS . Reliability: Theory & Applications. 2023, December 4(76): 909-920, DOI: https://doi.org/10.24412/1932-2321-2023-476-909-920

909-920

A FUZZY INNOVATIVE ORDERING PLAN USING STOCK DEPENDENT HOLDING COST OF INSPECTION WITH SHORTAGES IN TIME RELIABILITY DEMAND USING TFN

Sivan V, Thirugnanasambandam K, Sivasankar N, Sanidari

The considerations in this paper are, the demand is consistent with time deterioration, the holding cost is dependent based on the quantity of stock available in the system, and the ordering cost is linear and time-dependent. This system should be considered in terms of fuzziness. It is assumed that the shortages are permitted partially, the order is inspected, defective items are identified, by using penalty cost, the defective items should be minimized. Under the classical model and fuzzy environment, the mathematical equation is arrived at to find the optimal solution of total relevant cost with optimal order quantity and time using triangular fuzzy numbers. Defuzzification has been accomplished through the use of the signed distance method of integration. The solutions have been arrived and the model numerical problem of three levels of values (lower, medium and upper) in parametric changes has been verified. Using Sensitivity analysis, the solution is used to validate the changes in different parameter values of the system. To demonstrate the convexity of the TRC function over time, it has used a three-dimensional mesh graph.

Cite: Sivan V, Thirugnanasambandam K, Sivasankar N, Sanidari A FUZZY INNOVATIVE ORDERING PLAN USING STOCK DEPENDENT HOLDING COST OF INSPECTION WITH SHORTAGES IN TIME RELIABILITY DEMAND USING TFN. Reliability: Theory & Applications. 2023, December 4(76): 921-939, DOI: https://doi.org/10.24412/1932-2321-2023-476-921-939

921-939

STOCHASTIC ANALYSIS OF JUICE PLANT SUBJECT TO REPAIR FACILITY

Amit Kumar, Pinki Kumari

The performance of a juice plant is analyzed by using the base state and the regenerative point graphical technique. The juice plant under consideration consists of three distinct units. It is considered that units A and B may be in a complete failed state through partial failure mode but unit C is in only partially failed state. If one of the units A or B or C partially fails then the system works in a reduced state. When any unit is completely failed then the system is in failed state and no unit can fail further when the system is in a failed state. A technician is always available to repair the failed unit. In this paper, the failure time and repair time follow general distributions. Tables are used to describe the reliability measures such as mean time to system failure, availability and profit values of juice plant.

Cite: Amit Kumar, Pinki Kumari STOCHASTIC ANALYSIS OF JUICE PLANT SUBJECT TO REPAIR FACILITY. Reliability: Theory & Applications. 2023, December 4(76): 940-947, DOI: https://doi.org/10.24412/1932-2321-2023-476-940-947

940-947

STOCHASTIC MODEL ON EARLY-STAGE BREAST CANCER WITH TWO TYPES OF TREATMENTS

Suman, Rajeev Kumar

The aim of the paper is to study effectiveness of the different treatments of early-stage breast cancer through analysis of a stochastic model. The early-stage breast cancer is a term used to describe breast cancer that is detected at an early stage of development, typically before it has spread to other parts of the body. Early detection of breast cancer is critical as it greatly increases the chances of successful treatment and saves lives. At early-stage breast cancer of the patient, two types of treatment namely, tamoxifen and tamoxifen combined with radiation therapy are commonly used. As it is essential to consider innovative and cost-effective strategies for early detection and treatment. Investigations through analysis of the stochastic model on early-stage breast cancer with these two types of treatments may help the stakeholders. Keeping this in view, in the present paper, a stochastic model is developed for the early-stage breast cancer considering two treatment types, namely tamoxifen and tamoxifen combined with radiation therapy. The model is analyzed by Markov process and regenerative point technique. Mean sojourn time refers to the average amount of time spent by a patient in a particular state before transitioning to another state and mean survival time refers to the average time a patient survives after diagnosis of breast cancer. Mean sojourn time and mean survival time have been calculated. Sensitivity analysis is a technique to understand how changes in input variables or parameters affect the output or outcome of a model and it helps assess the robustness, reliability, and stability of a model by quantifying the impact of variations in input factors. The paper also includes sensitivity and relative sensitivity analyses of the model which explore the impact of different parameters on the survivability of the patient. The MATLAB software has been used for numerical computing and plotting various graphs. The investigation through our analysis of the stochastic model shows that the mean survival time lessens with the rise in the rates of transition and mean survival time from the treatment, tamoxifen plus radiation is higher than the treatment, tamoxifen only. It is concluded that tamoxifen plus radiation is more effective and useful than only tamoxifen for treatment of early-stage breast cancer.

Cite: Suman, Rajeev Kumar STOCHASTIC MODEL ON EARLY-STAGE BREAST CANCER WITH TWO TYPES OF TREATMENTS. Reliability: Theory & Applications. 2023, December 4(76): 948-963, DOI: https://doi.org/10.24412/1932-2321-2023-476-948-963

948-963

SYNTHETIC RELIABILITY MODELING AND PERFORMANCE ENHANCEMENT FOR MULTI-UNIT SERIAL SYSTEMS: UNVEILING INSIGHTS VIA GUMBEL-HOUGARD FAMILY COPULA APPROACH

Ismail Muhammad Musa, Ibrahim Yusuf

This paper presents a comprehensive study of a series-parallel system comprising four interconnected subsystems: subsystem-1, subsystem-2, subsystem-3, and subsystem-4. Subsystem-1 stands as a single unit, subsystem-2 consists of three identical units in active parallel, subsystem-3 involves two identical units in series, while subsystem-4 incorporates two identical units in parallel. The system operates under good conditions, considering various failure rates and repair rates. The investigation employs Laplace transforms and Supplementary variable techniques to analyze the system's performance. Key reliability parameters, including Availability, Reliability, Mean Time to Failure (MTTF), Sensitivity, and Cost, are evaluated for specific values of failure and repair rates. The paper delves into the intricate analysis of a multi-unit series system, focusing on its reliability and performance evaluation. The study employs the Gumbel-Hougard Family Copula approach, a sophisticated and robust methodology to capture the interdependencies among system units. By utilizing this advanced technique, the paper provides a comprehensive understanding of the system's behavior under varying operating conditions. Various reliability and performance metrics, including Availability, Mean Time to Failure (MTTF), and Component Importance Measures, are thoroughly examined, offering valuable insights for optimizing the system's reliability and performance. The results are presented in a clear and visually appealing manner, utilizing tables and figures to aid in the comprehension of the findings.

Cite: Ismail Muhammad Musa, Ibrahim Yusuf SYNTHETIC RELIABILITY MODELING AND PERFORMANCE ENHANCEMENT FOR MULTI-UNIT SERIAL SYSTEMS: UNVEILING INSIGHTS VIA GUMBEL-HOUGARD FAMILY COPULA APPROACH. Reliability: Theory & Applications. 2023, December 4(76): 964-979, DOI: https://doi.org/10.24412/1932-2321-2023-476-964-979

964-979

A BAYESIAN PREDICTION FOR THE TOTAL FERTILITY RATE OF AFGHANISTAN USING THE AUTO-REGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) MODEL

Sayed Rahmi Khuda Haqbin and Athar Ali Khan

In this article, a simple methodology to predict the total fertility rate of Afghanistan via a Bayesian statistical analysis method has been applied. R- statistical analysis tool is used for data analysis. To forecast, the "bayesforecast" package is needed. It is a substitute package in Rfor the "forecast" package in the traditional (frequentest) statistical method. The Bayesian data analysis using the specific case of the general auto-regressive integrated moving average model (ARIMA) is processed as follows; As the first step, the stationarity of the given data-set is assessed, the time series has been made stationary by taking differences. After fitting several models, as the most appropriate fitted model, the ARIMA (1, 2,1) model has been fitted to the data. The accuracy of the fitted model is examined, and thereafter, the developed model is analyzed. The posterior computation is done, using the Markov Chain Monte Carlo (MCMC) simulation method. The method ultimately focuses on drawing relevant inferences including the 16 years prediction, and the results are; in general, found to be satisfactory.

Cite: Sayed Rahmi Khuda Haqbin and Athar Ali Khan A BAYESIAN PREDICTION FOR THE TOTAL FERTILITY RATE OF AFGHANISTAN USING THE AUTO-REGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) MODEL. Reliability: Theory & Applications. 2023, December 4(76): 980-997, DOI: https://doi.org/10.24412/1932-2321-2023-476-980-997

980-997

EXPONENTIATED DISCRETE HYPO EXPONENTIAL DISTRIBUTION AND ITS GENERALIZATIONS

Krishnakumari.K, Dais George

Generalizations of standard probability distributions is a thought-provoking concept in statistical literature and was inspired by many researchers in recent days. This is because the addition of parameters may increase the flexibility of the new models. Now a days various generalization techniques are available in literature. In this work, we proposed a generalization of discrete hypo exponential distribution and studied its various properties. A real data analysis is carried out and check the flexibility of the new model by comparing it with other standard distributions. Two generalizations of the proposed distribution are introduced.

Cite: Krishnakumari.K, Dais George EXPONENTIATED DISCRETE HYPO EXPONENTIAL DISTRIBUTION AND ITS GENERALIZATIONS. Reliability: Theory & Applications. 2023, December 4(76): 998-1010, DOI: https://doi.org/10.24412/1932-2321-2023-476-998-1010

998-1010

AN INNOVATIVE APPROACH FOR RELIABILITY MODELING OF HVDC CONVERTER STATION

Aditya Tiwary, R. S. Mandloi

Assessment of reliability indices is important when availability and unavailability of the system or systems or components or group of components are to be assessed. There are various reliability indexes which are very important for overall performance of any complex engineering system. Reliability block diagram modeling is required to be formulated for evaluating different essential and important reliability parameters of any complex engineering system. In view of above, in this paper, reliability block diagram modeling of HVDC converter station is represented and formulated. The schematic diagram of the HVDC converter station is available in literature and based on that schematic diagram the modeling of HVDC converter station is formulated in this paper. After the reliability block diagram modeling of HVDC converter station, the mean time to failure (MTTF) of each and every components of HVDC converter station are also evaluated and represented in the result and discussion section. The reliability of each and every component of the HVDC converter station is evaluated and expressed in result section. Assessment of unavailability is also obtained and shown in result section.

Cite: Aditya Tiwary, R. S. Mandloi AN INNOVATIVE APPROACH FOR RELIABILITY MODELING OF HVDC CONVERTER STATION. Reliability: Theory & Applications. 2023, December 4(76): 1011-1018, DOI: https://doi.org/10.24412/1932-2321-2023-476-1011-1018

1011-1018

TIME DEPENDENT BEHAVIOUR OF A SINGLE SERVER QUEUEING SYSTEM WITH DIFFERENTIATED WORKING VACATIONS SUBJECT TO SYSTEM DISASTER

V Karthick, V Suvitha

This study investigates the time dependent behaviour of the single server queue with differentiated working vacations. The model also takes into account the possibility of a disaster happening during busy periods and working vacations, with the repair procedure starting right away. The time-dependent probabilities of system size are described in terms of modified Bessel functions in the paper using explicit equations that were generated using generating functions. Numeric instances have been added to support the theoretical findings even more.

Cite: V Karthick, V Suvitha TIME DEPENDENT BEHAVIOUR OF A SINGLE SERVER QUEUEING SYSTEM WITH DIFFERENTIATED WORKING VACATIONS SUBJECT TO SYSTEM DISASTER. Reliability: Theory & Applications. 2023, December 4(76): 1019-1031, DOI: https://doi.org/10.24412/1932-2321-2023-476-1019-1031

1019-1031

ON THE PROPERTIES AND APPLICATIONS OF TOPP-LEONE GOMPERTZ INVERSE RAYLEIGH DISTRIBUTION

Sule Omeiza Bashiru, O.Y. Halid

In this study, we introduce a new four-parameter continuous probability distribution known as the Topp-Loene Gompertz Inverse Rayleigh (TLGoIRa) distribution. This novel model extends the Gompertz Inverse Rayleigh distribution. We present various mathematical properties of the distribution, including moments, moment generating functions, quantile functions, survival functions, hazard functions, reversed hazard functions, and odd functions. We also derive the distribution of order statistics, yielding both the maximum and minimum order statistics. This process of parameter estimation using the maximum likelihood estimation method is discussed. Furthermore, we present two real-life applications that illustrate the effectiveness and robustness of the TLGoIRa distribution when compared to several considered lifetime models. Our analysis reveals that the TLGoIRa distribution demonstrates superior robustness in comparison to the competing lifetime models. Additionally, the study highlights the distribution's efficacy in fitting biomedical datasets.

Cite: Sule Omeiza, Bashirub O.Y., Halid Anyigba, Kogi State, ON THE PROPERTIES AND APPLICATIONS OF TOPP-LEONE GOMPERTZ INVERSE RAYLEIGH DISTRIBUTION. Reliability: Theory & Applications. 2023, December 4(76): 1032-1045, DOI: https://doi.org/10.24412/1932-2321-2023-476-1032-1045

1032-1045

SOME APPLICATIONS OF TRANSMUTED LOG-UNIFORM DISTRIBUTION

Ashin K Shaji, Rani Sebastian

As a generalization of the Log Uniform distribution, Transmuted Log - Uniform distribution is introduced and its properties are studied. We obtained graphical representations of its pdf, cdf, hazard rate function and survival function. We have derived statistical properties such as moments, mean deviations, and the quantile function for the Transmuted Log-Uniform distribution. We also obtained the order statistics of the new distribution. Method of maximum likelihood is used for estimating the parameters. Estimation of stress strength parameters is also done. We applied the Transmuted Log-Uniform distribution to a real data set and compared it with Transmuted Weibull distribution and Transmuted Quasi-Akash distribution. It was found that the Transmuted Log-Uniform distribution was a better fit than the Transmuted Weibull distribution and Transmuted Quasi-Akash distribution 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: Ashin K Shaji, Rani Sebastian SOME APPLICATIONS OF TRANSMUTED LOG-UNIFORM DISTRIBUTION. Reliability: Theory & Applications. 2023, December 4(76): 1046-1055, DOI: https://doi.org/10.24412/1932-2321-2023-476-1046-1055

1046-1055

MEASUREMENTS OF BRIDGE STRUCTURES USING NON-DESTRUCTIVE TESTING METHODS AND THEIR STABILITY IN WIND GUSTS

Alena Rotaru

As bridge structures become older and older, they are subject to wear and tear due to ageing, weather conditions or environmental effects, as well as due to surprise structural modifications substantially affecting the condition of the structures. Therefore, the condition assessment of bridge structures is a must for the safety and absence of risk. The condition assessment of bridge structures is also necessary for the maintenance and repair of existing structures having been in service for more than 30 years, in order to avoid breakdowns and save human lives. This paper states the condition assessment performed with the use of various nondestructive test methods.

Cite: Alena Rotaru MEASUREMENTS OF BRIDGE STRUCTURES USING NON-DESTRUCTIVE TESTING METHODS AND THEIR STABILITY IN WIND GUSTS. Reliability: Theory & Applications. 2023, December 4(76): 1056-1066, DOI: https://doi.org/10.24412/1932-2321-2023-476-1056-1066

1056-1066

STATISTICAL MODELS FOR FORECASTING NATURAL EMERGENCIES

Valery Akimov, Maxim Bedilo, Olga Derendiaeva

The article considers predictive-analytical solutions for natural hazards for urbanized areas, the mathematical basis of which is Bayesian classifiers. The result of the work is a formalized description of models for predicting forest fires, the consequences of earthquakes and floods resulting from floods.

Cite: Valery Akimov, Maxim Bedilo, Olga Derendiaeva STATISTICAL MODELS FOR FORECASTING NATURAL EMERGENCIES. Reliability: Theory & Applications. 2023, December 4(76): 1067-1072, DOI: https://doi.org/10.24412/1932-2321-2023-476-1067-1072

1067-1072