This article deals with the problem of reliability in a multicomponent stress-strength (MSS) model when both stress and strength variables are from exponentiated Teissier (ET) distributions. The reliability of the system is determined using both classical and Bayesian methods, based on two scenarios where the common scale parameter is unknown or known. In the first scenario, where the common scale parameter is unknown, the maximum likelihood estimation (MLE) and the approximate Bayes estimation are derived. In the second scenario, where the scale parameter is known, the MLE, the uniformly minimum variance unbiased estimator (UMVUE) and the exact Bayes estimation are obtained. In the both scenarios, the asymptotic confidence interval and the highest probability density credible interval are established. Furthermore, two other asymptotic confidence intervals are computed based on the Logit and Arcsin transformations. Monte Carlo simulations are implemented to compare the different proposed methods. Finally, one real example is presented in support of suggested procedures.
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.
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