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Building Phase-Type Software Reliability Models

This paper presents a unified framework for software reliability modeling with non-homogeneous Poisson processes, where each software fault-detection time obeys the phase-type distribution and the initial number of inherent faults is given by a Poisson distributed random variable. However, it is worth noting that the resulting software reliability models, called phase-type software reliability models, generalize the existing models but may involve a number of model parameters in the phase-type software reliability model, so that the usual maximum likelihood estimation based on the Newton's method or quasi-Newton's method does not often function well. In this paper, we develop EM (expectation-maximization) algorithms for the phase-type software reliability models with two types of fault data: fault-detection time data and grouped data with arbitrary time intervals. In numerical examples, we compare the EM algorithms with the quasi-Newton's method and illustrate the effectiveness on our unified model and parameter estimation method