Bayesian Estimation of Stress Strength Reliability from Inverse Chen Distribution with Application on Failure Time Data

Abstract

In this article, we develop Bayesian estimation procedure for estimating the stress strength reliability R = P [X > Y ] when X (strength) and Y (stress) are the inverse Chen random variables. First, we study some statistical properties of the inverse Chen distribution such as quantiles, mode, stochastic ordering, entropy measure, order statistics and stress strength reliability. Then, we estimate the stress strength parameters and R using maximum likelihood and Bayesian estimations. A symmetric (squared error loss) and an asymmetric (entropy loss) loss functions are considered for Bayesian estimation under the assumption of gamma prior. Since, joint posterior distribution of the model parameters and R involve multiple integrations and have complex form. So, we do not get analytical solution without using any numerical techniques. Therefore, we propose to use Lindley’s approximation and Markov chain Monte Carlo techniques for Bayesian computation. A simulation study is carried out for the proposed Bayes estimators of unknown parameters and compared with the maximum likelihood estimator on the basis of mean squared error. Finally, an empirical illustration based on failure time data is presented to demonstrate the applicability of inverse Chen stress strength model.