Abstract: As the quality of software systems improves, the demand for the reliability of software systems increases. Due to the complexity of software systems and the uncertainty inherent in their operating environments, it is challenging for researchers to obtain accurate estimates of software reliability. Software reliability models based on the non-homogeneous Poisson process (NHPP) can incorporate the uncertainty of the operating environment into the assessment of software reliability. By quantifying the uncertainty in the environment, a numerical solution method for reliability models based on NHPP and the generalized polynomial chaos framework is proposed, which takes into account the impact of uncertainty in the software testing environment to complete the software reliability assessment. On the premise of quantifying environmental uncertainty, a unified generalized polynomial chaos framework solution for ordinary differential equations is provided by analyzing the state and distribution form of input parameters. To verify the performance of the above method, three traditional solutions of software reliability models based on different fault detection rates are used as controls, and a series of common statistical indicators is used to show the performance of numerical solutions for different models. The results show that the performance of this numerical solution method can be comparable to the results of the analytical solutions of the three classic models. At the same time, this numerical solution method can quickly obtain model results, reducing the requirements of the model itself, providing an efficient and practical analysis tool for the field of software quality assurance, and has good value for promotion.

Key words: reliability, fault detection rate, generalized polynomial chaos, non-homogeneous Poisson process (NHPP)

摘要： 随着软件系统质量的提高，用户对软件系统可靠性的需求增加。由于软件系统复杂，加之运行环境中含有不确定性，研究人员较难获取精确的软件可靠性估计。基于非齐次泊松过程（NHPP）的软件可靠性模型可将运行环境中的不确定性纳入软件可靠性评估。将环境中的不确定性量化，提出了基于NHPP及广义多项式混沌框架的可靠性模型数值解法，将软件测试环境的不确定性的影响纳入考虑，以完成软件可靠性评估。在量化环境中不确定性的前提下，拟通过分析输入参数状态及分布形式，给出统一广义多项式混沌框架求解常微分方程数值解。为验证上述方法的性能，将三个基于不同的故障检测率的软件可靠性模型的传统解法作为对照，用系列常用统计指标来给出面向不同模型数值求解的表现。结果表明，该数值解法的表现可与三个经典模型解析解的结果媲美。同时，该数值解法能够快速获得模型结果，降低了模型本身的要求，为软件质量保障领域提供了一种高效且实用的分析工具，有较好的推广价值。

关键词: 可靠性, 故障检测率, 广义多项式混沌, 非齐次泊松过程（NHPP）