BAYESIAN RELIABILITY APPROACH TO THE POWER LAW PROCESS WITH SENSITIVITY ANALYSIS TO PRIOR SELECTION

Abstract

The intensity function is the key entity to the power law process, also known as the Weibull process or nonhomogeneous Poisson process. It gives the rate of change of the reliability of a system as a function of time. We illustrate that a Bayesian analysis is applicable to the power law process through the intensity function. First, we show using real data, that one of the two parameters in the intensity function behaves as a random variable. With a sequence of estimates of the subject parameter we proceeded to identify the probability distribution that characterizes its behavior. Using the commonly used squared-error loss function we obtain a Bayesian reliability estimate of the power law process. Also a simulation procedure shows the superiority of the Bayesian estimate with respect to the maximum likelihood estimate and the better performance of the proposed estimate with respect to its maximum likelihood counterpart. As well, it was found that the Bayesian estimate is sensitive to a prior selection.