Bayesian Reliability Analysis of Exponential Distribution Model under a New Loss Function

Abstract

Loss function is an important content in Bayes statistical inference. The task of this article is to study the reliability analysis of the exponential model based on a new proposed symmetric loss function. The new proposed loss function is established on the basis of the LINEX asymmetric loss function. Firstly, the Bayes estimation of the parameter is derived under the prior distribution of the parameter based on non-information Quasi prior distribution, and then the admissibility of the estimators are also discussed. Furthermore, this paper puts forward a novel testing procedure to evaluate the lifetime performance of exponential products based on the new derived Bayes estimator. Finally, Monte Carlo statistical simulation and an applicable example are used to illustrate that the new proposed Bayes estimators and testing procedure are effective and feasible.