Phase-Type Software Reliability Models (Mathematical Decision Making under Uncertainty)
Hiroyuki Okamura, Yasuhiro Watanabe, Tadashi Dohi · Kyoto University Research Information Repository (Kyoto University) · 2002
Software reliability models (SRMs) are classified into time domain models and counting process models.The time domain model is the stochastic model based on the sequence of inter-failure times.Jelinski and Moranda model [4] and Schick and Wolverton model [13] are the most classical models belonging to this class.On the other hand, the counting process models have gained popularity for describing the stochastic behavior of the number of software failures observed in the testing phase.The most well-known and tractable models are non-homogeneous Poisson process (NHPP) models.Goel and Okumoto [3], Yamada, Ohba and Osaki [15], Musa and Okumoto [9] develop representative NHPP models.These SRMs are based on the different debugging scenarios, and can catch qualitatively typical (but not general) reliability growth phenomena observed in the testing phase of software products.It should be noted, however, that the SRMs based on past observations may not be always useful in the software testing process.Because one cannot catch the global trend of the software failure occurrence phenomena in the initial testing phase.In other words, aunified modeling framework comprising some typical reliability growth patterns should be developed for robust software reliability assessment.Langberg and Singpurwalla [7] show that several SRMs can be comprehensively viewed by adopting aBayesian point of view.Miller [8] extends the Langberg and Singpurwalla's idea and considers an exponential order statistics model.Raftery [12], Kuo and Yang [5] investigate the modeling framework based on the generalized order statistics (GOS), and discuss several parameter estimation methods from the standpoint of both Bayesian and non-Bayesian statistics.In the GOS modeling framework, the SRMs can be characterized by only the fault detection time distribution.This article proposes phase-type SRMs based on the GOS of software failure data.To unify some existing SRMs, the phase-type distribution [10], which represents the software fault detection time distribution, is used to represent the GOS of software failure data.Also, we provide aunified estimation method for model parameters in the phase-type SRMs.The usual estimation method, such as the maximum likelihood estimation (MLE) based on the Newton's method, does not function well in many