Bayesian Estimation of the Failure Rate Using Extension of Jeffreys? Prior Information with Three Loss Functions

The Weibull distribution is widely used in Reliability and life data analysis due to its versatility. We Consider the Constant Shape Bi-Weibull distribution which has been extensively used in the testing and reliability studies of the strength of materials. Studies have been done vigorously in the literature to determine the best method in estimating its Failure Rate. In this paper, we examine the performance of Maximum Likelihood Estimator (MLE) and Bayesian Estimator using Extension of Jeffreys Prior Information with three Loss functions, namely, the Linear Exponential (LINEX) Loss, General Entropy Loss, and Square Error Loss for estimating the Constant Shape Bi-Weibull Failure time distribution. The results show that Bayesian Estimator using Extension of Jeffreys Prior under Linear Exponential (LINEX) Loss function in most cases gives the smallest Mean Square Error and Absolute Bias for Failure Rate FR (t) for the given values of Extension of Jeffreys Prior. An illustrative example is also provided to explain the concepts.