Bayesian reliability analysis based on the Weibull model under weighted General Entropy loss function
Fuad S. Alduais
Abstract
In this work, we develop a General Entropy loss function (GE) to estimate the reliability function of the Weibull distribution based on complete data. We do this by merging a weight into GE to produce a new loss function called weighted General Entropy loss function (WGE). We then use WGE to derive the reliability function of the Weibull distribution. Consequently, we discuss the loss functions for three different types of loss function, including squared error (SE), GE, and WGE. By using WGE, the proposed method Bayesian (BWGE) and the approximate Bayesian estimation (BLWGE) are examined and compared with other methods including maximum likelihood estimation, Bayesian estimation, and approximate Bayesian estimation under SE and GE by using Monte Carlo simulation. It is found that the proposed methods of the BWGE and the BLWGE present the best performance in estimating reliability according to the smallest values of mean square error (MSE).