Non Informative Priors for the Stress-Strength Reliability in the Generalized Augmented Inverse Gaussian Distribution

Abstract

In this paper the Bayesian and classical estimation of augmented strength reliability under Augmentation Strategy Plan (ASP) have been considered. The Augmentation Strategy Plan (ASP) is suggested for enhancing the strength of failed equipment. The Bayes estimation is carried out by assuming the model parameters are random variable and having non-informative type of priors (uniform and Jeffery's priors) under two different loss functions, viz. squared error loss function (SELF) and Linex loss function (LLF). We assume that the Inverse Gaussian stress (Y) is subjected to equipment having Inverse Gaussian strength (X) and are independent to each other. A comparative study between ML and Bayesian estimators have been carried out on the basis of mean square errors (MSE) and absolute biases. The Markov Chain Monte Carlo method of approximations has been applied to draw posterior expectations under both the loss functions. The MSE and absolute biases are calculated with 1000 replications.