A Quasi-Bayes Estimate of the Failure Intensity of a Reliability-Growth Model

A non-homogeneous Poisson process has empirically been shown to be useful in tracking the reliability growth of a system as it undergoes development. It is of interest to estimate the failure intensity of this model at the time of failure n. The maximum likelihood estimate is known, but it is desirable to have a Bayesian estimate to allow for input of prior information. Since the ordinary Bayes approach appears to be mathematically intractable, a quasi-Bayes approach is taken. The proposed estimate has the qualitative properties one anticipates from the ordinary Bayes estimate, but it is easy to compute. A numerical example illustrates the Bayesian character of the proposed estimate. A simulation study shows that the proposed estimate, when considered in the classical framework, generally has smaller r.m.s. error than the maximum likelihood estimate.