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.

中文翻译：

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广义拐点S形软件可靠性增长模型

本文提出了新的广义拐点S型软件可靠性增长模型。这是一个非常灵活的有限失效泊松过程，具有两个显着特征：1) 包括作为特殊情况的流行拐点 S 形模型、Goel 广义非齐次泊松过程和 Goel-Okumoto 模型以及 2) 与后面的这些模型不同，允许用于对每个故障函数的非单调故障率进行建模。讨论了广义拐点 S 形模型的特性，并提供了直观的论据来证明其结构的合理性。公式化了模型参数的最大似然估计并总结了它们的特性。特别关注最大似然估计的不存在问题。还解决了估计软件产品的最佳发布时间的问题。基于真实的软件可靠性数据集，通过四个应用示例证明了所提出模型的可负担性和灵活性。获得的结果表明，广义拐点 S 形模型提供的输出可能与嵌套在其中的模型所提供的输出显着不同。作为附带结果，开发的示例还表明，在有限失效泊松过程的情况下，最大似然估计的不存在问题不能被视为奇怪，并且其发生不一定与模型复杂性有关。获得的结果表明，广义拐点 S 形模型提供的输出可能与嵌套在其中的模型所提供的输出显着不同。作为附带结果，开发的示例还表明，在有限失效泊松过程的情况下，最大似然估计的不存在问题不能被视为奇怪，并且其发生不一定与模型复杂性有关。获得的结果表明，广义拐点 S 形模型提供的输出可能与嵌套在其中的模型所提供的输出显着不同。作为附带结果，开发的示例还表明，在有限失效泊松过程的情况下，最大似然估计的不存在问题不能被视为奇怪，并且其发生不一定与模型复杂性有关。