Comparison of Bayes' and minimum variance unbiased estimators of reliability in the extreme value life testing model

The purpose of this study is to consider two different types of estimators for reliability using the extreme value distribution as the life-testing model. First the unbiased minimum variance estimator is derived. Then the Bayes' estimators for the uniform, exponential, and inverted gamma prior distributions are obtained, and these results are extended to a whole class of exponential failure models. Each of the Bayes' estimators is compared with the unbiased minimum variance estimator in a Monte Carlo simulation where it is shown that the Bayes' estimator has smaller squared error loss in each case.

The problem of obtaining estimators with respect to an exponential type loss function is also considered. The difficulties in such an approach are demonstrated.