The Generalized Inflection S-Shaped Software Reliability Growth Model

In this paper, the new generalized inflection S-shaped software reliability growth model is proposed. It is a very flexible finite failure Poisson process that possesses two distinguishing features: 1) includes as special cases the popular inflection S-shaped model, Goel generalized nonhomogenous Poisson process, and Goel–Okumoto model and 2) differently than these latter models, allows for modeling nonmonotonic failure rate per fault functions. The properties of the generalized inflection S-shaped model are discussed and intuitive arguments are provided to justify its structure. Maximum-likelihood estimators of model parameters are formulated and their properties are summarized. A special attention is devoted to the nonexistence issue of maximum-likelihood estimates. The problem of estimating the optimal release time of a software product is also addressed. Affordability and flexibility of the proposed model are demonstrated via four applicative examples, based on real sets of software reliability data. Attained results show that the generalized inflection S-shaped model provides outputs that may significantly differ from those provided by the models nested within it. As a side result, the developed examples also show that the nonexistence issue of maximum-likelihood estimates, in the case of finite failure Poisson processes, cannot be considered an oddity and that its occurrence is not necessarily related to model complexity.