Estimation of Reliability in a Multicomponent Stress- Strength Model Based on Generalized Linear Failure Rate Distribution

Abstract

In this paper, we consider the problem of estimation reliability in multicomponent stress-strength model, when the system consists of $k$-components have strength are given by independently and identically distributed random variables $X_{1},...,X_{k}$ each component experiencing a random stress governed by a random variable $Y$. The reliability such system is obtained when strength and stress variables are given by a generalized linear failure rate distribution. The system is regarded as alive only if at least $s$ out of $k$ $(s<k)$ strength exceed the stress. The multicomponent reliability of the system is given by $R_{s,k}=P[$ at least $s$ of $X_{1},...,X_{k}$ exceed $Y]$. The maximum likelihood estimator $(MLE)$ and Bayes estimator of $R_{s,k}$ are obtained. A simulation study is performed to compare the different estimators of $R_{s,k}$. Real data is used as a practical application of the proposed procedure.