Inferences on Non-Identical Stress and Generalized Augmented Strength Reliability Parameters Under Informative Priors

Abstract

In this paper, an attempt has been made to estimate the augmented strength reliability of a system for the generalized case of Augmentation Strategy Plan (ASP) by assuming that the strength [Formula: see text] and common stress [Formula: see text] are independently but not identically distributed as gamma distribution with parameters [Formula: see text] and [Formula: see text], respectively. ASP deals with two important challenges (i) early failures in a newly manufactured system while first and subsequent use and (ii) frequent failures of used system. ASP has a significant role in enhancing the strength of a weaker (or poor) system for failure-free journey to achieve its mission life. The maximum likelihood (ML) and Bayes estimation of augmented strength reliability are considered. In Bayesian context, the informative types of priors (Gamma and Inverted gamma) are chosen under symmetric and asymmetric loss functions for better comprehension purpose. A comparison between the ML and Bayes estimators of the augmented strength reliability is carried out on the basis of their mean square errors (mse’s) and absolute biases by simulating Monte-Carlo samples from posterior distribution through Metropolis–Hasting approximation. Real life data sets are also considered for illustration purpose.