A study of the effect of the loss function on Bayes estimates of failure intensity, MTBF, and reliability

Abstract

The number of failures in a fixed time T is assumed to follow the Poisson distribution, and the failure intensity (reciprocal MTBF) is assumed to have a gamma prior distribution. This model has recently been employed on actual USAF failure data, and the parameters in the various comparisons of this study typify these data. Bayes estimates of failure intensity, MTBF, and reliability are compared for five classes of loss functions. Included in the study are two new classes of loss functions which appear to have useful applications and a third, well-known loss function whose usefulness seems not to have been exploited. Mathematical properties on the new loss function are given in addition to comparing them to the other loss functions. The “popular” squared error loss function is shown to be a poor approximation to other loss functions for the most part, even when it is used to approximate other symmetric loss functions. Numerical comparisons are made to show the widely different decisions that may be reached if different loss functions are used and to aid researchers in selecting a loss function to meet experimental objectives.