Estimation of reliability of multicomponent stress-strength of a bathtub shape or increasing failure rate function

Purpose: The purpose of this paper is to deal with the Bayesian and non-Bayesian estimation methods of multicomponent stress-strength reliability by assuming the Chen distribution. Design/methodology/approach: The reliability of a multicomponent stress-strength system is obtained by the maximum likelihood (MLE) and Bayesian methods and the results are compared by using MCMC technique for both small and large samples. Findings: The simulation study shows that Bayes estimates based on γ prior with absence of prior information performs little better than the MLE with regard to both biases and mean squared errors. The Bayes credible intervals for reliability are also shorter length with competitive coverage percentages than the condence intervals. Further, the coverage probability is quite close to the nominal value in all sets of parameters when both sample sizes n and m increases. Originality/value: The lifetime distributions used in reliability analysis as exponential, γ, lognormal and Weibull only exhibit monotonically increasing, decreasing or constant hazard rates. However, in many applications in reliability and survival analysis, the most realistic hazard rate is bathtub-shaped found in the Chen distribution. Therefore, the authors have studied the multicomponent stress-strength reliability under the Chen distribution by comparing the MLE and Bayes estimators.