On Bayesian Estimation of Generalized Augmented Inverse Gaussian Strength Reliability of a System under Different Loss Functions

This article deals with the problem of Bayes and Maximum Likelihood Estimation (MLE) of generalized augmented strength reliability of the equipment under Augmentation Strategy Plan (ASP), where ASP is suggested for enhancing the strength of weaker / early failed equipment under three possible cases. It is assumed that the Inverse Gaussian stress (Y) is subjected to equipment having Inverse Gaussian strength (X) and are independent to each other. Assuming informative (gamma and inverted gamma) types of priors, the Bayes estimates of augmented strength reliability have been computed and compared with that of MLE on the basis of mean square errors (mse) and absolute biases. The posterior means under Squared Error Loss Function (SELF) as well as Linex Loss Function (LLF) are approximated by using Markov Chain Monte Carlo (MCMC). The mse and absolute biases are calculated with 1000 replications of the whole simulation process.