Estimation of Reliability in Multicomponent Set-up when Stress and Strength are Non-identical

Abstract

Abstract In the multicomponent stress–strength reliability literary work, though assumption of identical stress and strengths components may not be universally true but have been commonly considered. Herein, we consider a multicomponent stress–strength model having k identical strength components, say $$X_i,~i=1,2,...,k$$ X i , i = 1 , 2 , . . . , k , which are exposed to a common random stress Y, so that $$Y, X_i,~i=1,2,...,k$$ Y , X i , i = 1 , 2 , . . . , k are independent. Two different generalized cases of estimation are considered; namely, (i) when the strength components follow the proportional hazard rate model and stress component follows the proportional reversed hazard rate model and (ii) when the strength components follow the proportional reversed hazard rate model and stress component follow the proportional hazard rate model. In each case, maximum likelihood and Bayesian approach using Markov Chain Monte Carlo method has been utilized to estimate the reliability of the system. Asymptotic confidence intervals are also constructed for the reliability functions in both the cases. Monte Carlo simulation study is exercised to compare the performance of the aforementioned estimators. A real data example is also explored to examine the utility of the paper.

Keywords

• Proportional hazard rate and reversed hazard rate models
• Maximum likelihood estimation
• Asymptotic confidence interval
• Bayes estimation
• Multicomponent reliability