Multicomponent stress-strength reliability estimation for the standard two-sided power distribution

Abstract

A system of $k$ components that functions as long as at least $s$ components survive is termed as $s$-out-of-$k$:G system, where G refers to "good". In this study, we consider the $s$-out-of-$k$:G system when $X_{1}, X_{2},\cdots, X_{k}$ are independent and identically distributed strength components and each component is exposed to common random stress $Y$ when the underlying distributions all belong to the standard two-sided power distribution. The system is regarded as surviving only if at least $s$ out of $k$ $1<s<k$ strengths exceed the stress. The reliability of such a system is the surviving probability and is estimated by using the maximum likelihood and Bayesian approaches. Parametric and nonparametric bootstrap confidence intervals for the maximum likelihood estimates and the highest posterior density confidence intervals for Bayes estimates by using the Markov Chain Monte Carlo technique are obtained. A real data set is also analyzed to illustrate the performances of the estimators.

Keywords

• Bayesian estimation
• maximum likelihood estimation
• reliability
• stress-strength model
• two-sided power distribution

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