Abstract: Much work on the statistical analysis of accelerated life tests have been done, generally under the following two assumptions: （1） that the failure distribution of the items is known; （2） that there is a known functional ralationship between the parameters of the failure distribution and the applied stress. These assumptions are not reasonable in many practical situations. Proschan and Singpurwalla proposed a Bayesian solution without requiring the above two assumptions. The author of this paper, however, does not agree with their choice of prior distribution. In addition, their adjustment of the original data at certain places is too arbitrary to be acceptable. This paper intends to rectify these points so as to make the implementation easier and more reasonable.