On estimation of augmented strength reliability parameters under non-informative priors: A non-identical case

Abstract

In this article we consider the Bayesian and Maximum Likelihood (ML) estimation of augmented strength of a system for the generalized case of the proposed Augmentation Strategy Plan (ASP). ASP has interesting applications in stress strength reliability. The Bayes estimation is performed by assuming non-informative (uniform and Jeffreys) types of priors under two different loss functions i.e. squared error loss function (SELF) and LINEX loss function (LLF) for better comprehension purpose. It is assumed that the strength ( $X$ ) and the imposed stress ( $Y$ ) follow independent and non-identical two parameter gamma distributions. The MCMC simulation techniques are employed to study the comparison between the ML and Bayes estimators of augmented strength reliability on the basis of their mean square errors (mse) and absolute biases. The proposed estimators are validated by Monte Carlo simulated as well as real data sets.