Mathematical Problems in Engineering
Volume 4 (1999), Issue 6, Pages 539-560

The effect of loss functions on empirical Bayes reliability analysis

Vincent A. R. Camara and Chris P. Tsokos

Department of Mathematics, University of South Florida, Tempa 33620-5700, FL, USA

Received 23 February 1998; Revised 9 December 1998

Copyright © 1999 Vincent A. R. Camara and Chris P. Tsokos. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The aim of the present study is to investigate the sensitivity of empirical Bayes estimates of the reliability function with respect to changing of the loss function. In addition to applying some of the basic analytical results on empirical Bayes reliability obtained with the use of the “popular” squared error loss function, we shall derive some expressions corresponding to empirical Bayes reliability estimates obtained with the Higgins–Tsokos, the Harris and our proposed logarithmic loss functions. The concept of efficiency, along with the notion of integrated mean square error, will be used as a criterion to numerically compare our results.

It is shown that empirical Bayes reliability functions are in general sensitive to the choice of the loss function, and that the squared error loss does not always yield the best empirical Bayes reliability estimate.