Bayes estimation of hazard and acceleration in accelerated testing

In accelerated life testing, the time transformation function θ(t) is often unknown, even if that function is assumed to be linear. If θ(t) is known, data in the accelerated condition can be adjusted to provide information about the failure time distribution in the use condition. If θ(t) is unknown, the usual estimation procedures require data from the use condition as well as data from the acceleration condition. In this work it is assumed that the uncertainty about θ can be modeled by a prior distribution, chosen from the truncated Pareto family of distributions, and that the uncertainty in λ, the failure rate, can be modeled by a prior distribution from the gamma family. Under these assumptions, the posterior distributions and their first two moments are provided for both λ and θ. Thus, this complete Bayes approach to accelerated life testing with the assumed model allows the adjustment of data taken in the accelerated condition to provide the user with the important estimates in the use condition. The results are illustrated by examples