Estimation of multicomponent stress-strength reliability following Weibull distribution based on upper record values

Abstract

Stress-strength models are of special importance in reliability literature and engineering applications. This paper deals with the estimation problem of a stress-strength model incorporating multi-component system. The system is regarded as alive only if at least ${\mathcal{S}} $ out of $k $ $({\mathcal{S}} \lt k) $ strength components exceed the stress. The reliability of such system is obtained when strength and stress variables have Weibull distributions. Maximum likelihood estimator of ${R_{{\mathcal{S}},k}} $ and asymptotic confidence intervals are obtained based on upper record values. Bayesian estimator under squared error and linear exponential loss functions using gamma prior distributions and the corresponding credible intervals are obtained. Due to the lack of explicit forms for the Bayes estimates, the Markov Chain Monte Carlo (MCMC) method is employed. A simulation study is implemented to assess the performance of estimates. A real-life example is presented to show how the proposed model may be utilized in breaking strength of jute fibre data.

Keywords

• weibull distribution
• multicomponent stress–strength reliability
• upper record values
• asymptotic confidence interval
• markov chain monte carlo