ON THE CHOICE OF PRIOR FOR THE BAYES ESTIMATION IN ACCELERATED LIFE TESTING

In accelerated life testing, the rime to failure of an item is observed under a high stress level and the problem is to estimate the acceleration parameter. The usual estimation procedure requires data from use condition or the normal stress level as well as data from the acceleration condition. When we consider two data sets, the hazard rate under the normal stress level acts like a nuisance parameter. and the acceleration parameter is the parameter of interest. Thus the efficient estimation of the acceleration parameter can be obtained by appropriately eliminating the nuisance parameter. In this paper we use a Bayes set up to eliminate the nuisance parameter and measure the information contained in the nuisance parameter. Since the choice of the prior on the nuisance parameter is not unique, we give a methodology for measuring the information which gives more insight for the appropriate choice of the prior. Noninformative, reference and conjugate priors are considered and the corresponding information measures are compared. Finally, Bayes estimates and credible regions are obtained.