Multi-component stress-strength model for Weibull distribution in progressively censored samples

Kohansal Akram (), Shoaee Shirin () and Nadarajah Saralees ()
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Kohansal Akram: Department of Statistics, Imam Khomeini International University, Qazvin, Iran
Shoaee Shirin: Department of Actuarial Science, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran
Nadarajah Saralees: School of Mathematics, University of Manchester, Manchester, United Kingdom

Statistics & Risk Modeling, 2022, vol. 39, issue 1-2, 1-21

Abstract: One of the important issues is risk assessment and calculation in complex and multi-component systems. In this paper, the estimation of multi-component stress-strength reliability for the Weibull distribution under the progressive Type-II censored samples is studied. We assume that both stress and strength are two independent Weibull distributions with different parameters. First, assuming the same shape parameter, the maximum likelihood estimation (MLE), different approximations of Bayes estimators (Lindley’s approximation and Markov chain Monte Carlo method) and different confidence intervals (asymptotic and highest posterior density) are obtained. In the case when the shape parameter is known, the MLE, uniformly minimum variance unbiased estimator (UMVUE), exact Bayes estimator and different confidence intervals (asymptotic and highest posterior density) are considered. Finally, in the general case, the statistical inferences on multi-component stress-strength reliability are derived. To compare the performances of different methods, Monte Carlo simulations are performed. Moreover, one data set for illustrative purposes is analyzed.

Keywords: Multi-component stress-strength; progressive Type-II censored sample; Weibull distribution; Lindley approximation; MCMC method (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1515/strm-2020-0030

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