Classical and Bayesian estimation of reliability in a multicomponent stress–strength model based on a general class of inverse exponentiated distributions

Abstract

A s-out-of-k : G system consists of k components functions if and only if at least s components functions. In this paper, we consider the s-out-of-k : G system when this system is exposed a common random stress and the underlying distributions belong to the family of inverse exponentiated distributions. The estimates of this sytem reliability are investigated by using classical and Bayesian approaches. The uniformly minimum variance unbiased and exact Bayes estimates of the reliability of system are obtained analytically when the common second parameter is known. The Bayes estimates for the reliability of system have been developed by using Lindley’s approximation and the Markov Chain Monte Carlo method due to the lack of explicit forms when the all parameters are unknown. The asymptotic confidence interval and coverage probabilities are derived based on the Fisher’s information matrix. The highest probability density credible interval is constructed by using the Markov Chain Monte Carlo method. The comparison of the derived estimates are carried out by using Monte Carlo simulations. Real data set is also analysed for an illustration of the findings.