Estimation of reliability for multi-component stress–strength model based on modified Weibull distribution

• Published in: Statistical papers (Berlin, Germany) Vol. 62; no. 6; pp. 2763 - 2797
• Main Authors: Kotb, M. S., Raqab, M. Z.
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01-12-2021; Springer Nature B.V
• Subjects: Approximation; Component reliability; Confidence intervals; Datasets; Economic Theory/Quantitative Economics/Mathematical Methods; Economics; Estimates; Failure; Failure analysis; Failure times; Finance; Insurance; Management; Markov analysis; Markov chains; Mathematics; Mathematics and Statistics; Maximum likelihood estimators; Monte Carlo simulation; Operations Research/Decision Theory; Probability Theory and Stochastic Processes; Random variables; Regular Article; Software; Statistics; Statistics for Business; Weibull distribution; Maximum likelihood estimator; Bayes estimator; Bootstrap confidence interval; Stress–strength model; 62G30; 62F10; 62F12; Markov chain Monte Carlo simulation; 62F15; Confidence interval
• ISSN: 0932-5026; 1613-9798
• DOI: 10.1007/s00362-020-01213-0

This paper is devoted to estimating the reliability of a multi-component stress–strength model in an
s
-out-
m
(
s
≤
m
) system under progressively type-II censored modified Weibull data. This type of systems functions only if at least
s
out of
m
strengths exceed the stress. Maximum likelihood and Bayes estimators of the stress–strength reliability based on conjugate prior are obtained. The associated confidence and credible intervals are also developed. The Lindley’s approximation and Markov chain Monte Carlo methods are used to compute approximate Bayes estimates. Two real data sets representing the excessive drought of Shasta Reservoir in California, USA and failure times of software model are analyzed for illustrative purposes. Further, Monte Carlo simulations are performed to compare the so developed estimates.