Estimation of Multicomponent Stress-strength Reliability under Inverse Topp-Leone Distribution

Abstract

In this article, the reliability inference for a multicomponent stress-strength (MSS) model, when both stress and strength random variables follow inverse Topp-Leone distributions, was studied. The maximum likelihood and uniformly minimum variance unbiased estimates for the reliability of MSS model were obtained explicitly. The exact Bayes estimate of MSS reliability was derived the under squared error loss function. Also, the Bayes estimate was obtained using the Monte Carlo Markov Chain method for comparison with the aforementioned exact estimate. The asymptotic confidence interval was determined under the expected Fisher information matrix. Furthermore, the highest probability density credible interval was established through using Gibbs sampling method. Monte Carlo simulations were implemented to compare the different proposed methods. Finally, a real life example was presented in support of the suggested procedures.