软件可靠性测试的数学模型研究

In order to evaluate the software reliability effectively, this project focuses on studying the mathematical foundation of software reliability testing, including: the connection between the software removal process and reliability, the distribution of the software defects in the testing process, and the evolution of the reliability under the changing environment. By building up mathematical models and studying these models, the dynamic behaviors and the general law of the software under test can be undertood, which will assist the evaluation of the software reliability. Besides, new mathematical method or theory may be proposed in the research of the emerging problems in software testing. More precisely, we can consider the following issues in our project: .1) The difference of the testing process if new defects may be introduced in the defect removal process;.2) The stability and the convergence rate of the testing process;.3) When the defect removal time can not be neglected and the observed failure process follows Phase Type type, how will the testing process behave?.4) Research the sudden change behavior in the software testing process.

为了有效的评估软件系统的可靠性问题，本项目着重研究软件可靠性测试的数学基础，包括：揭示软件缺陷的发生、剔除与软件可靠性的内在联系、软件缺陷在测试过程中的分布规律、以及软件在环境变化和自身演化下可靠性的变化规律等。通过建立有效的数学模型以及对这些数学模型的深入研究，一方面，了解软件在测试过程中的动态表现和一般规律，为软件可靠性的正确评估打下数学基础；另一方面，对研究过程中出现的新问题，研究新的数学方法和理论。具体的有：1）考虑"剔除缺陷时会带来新的缺陷"这个因素，软件测试过程的结构发生的变化；2）考虑软件测试过程稳定性的问题，并分析过程收敛的速度问题；3）在缺陷剔除时间不可忽略时，分析非标准Phase Type型到达过程的新性质；4）研究相应软件测试过程的结构及其突变等。

我们建立了五个软件可靠性测试模型，分别讨论了相关的性质，部分的给出了算法，并得到一项国家专利。我们的工作涵盖了申请书中的主要方面。