Bayesian Computation for Nonhomogeneous Poisson Processes in Software Reliability

Abstract

A unified approach to the nonhomogeneous Poisson process in software reliability models is given. This approach models the epochs of failures according to a general order statistics model or to a record value statistics model. Their corresponding point processes can be related to the nonhomogeneous Poisson processes, for example, the Goel—Okumoto, the Musa—Okumoto, the Duane, and the Cox—Lewis processes. Bayesian inference for the nonhomogeneous Poisson processes is studied. The Gibbs sampling approach, sometimes with data augmentation and with the Metropolis algorithm, is used to compute the Bayes estimates of credible sets, mean time between failures, and the current system reliability. Model selection based on a predictive likelihood is studied. A numerical example with a real software failure data set is given.

Key Words:

• General order statistics
• Gibbs sampling
• Intensity function
• Metropolis algorithm
• Model determination
• Record value statistics