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In this article, Bayes estimation of system’s augmented strength reliability is studied under squared-error loss function (SELF) and LINEX loss function (LLF) for the generalized case of augmentation strategy plan (ASP). ASP is helpful in enhancing the strength reliability of weaker system/equipment. It is assumed that the stress (usual) and augmented strength follow a gamma distribution with common shape [Formula: see text] and scale [Formula: see text] parameters. A simulation study is performed for the comparisons of Bayes estimators of augmented strength reliability for non-informative types of prior (uniform and Jeffrey’s priors) with maximum likelihood estimators on the basis of their mean square errors and the absolute biases by simulating 1,000 Monte Carlo samples. The proposed methods are compared by analysing real and simulated datasets for illustration purpose.

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.

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