软件可靠性增长模型的不确定性量化研究

数量激增的软件系统被开发出来为用户提供了极大便利性，但也给系统开发带来了极大的不确定性.故障调试过程中的故障检测率FDR（Fault Detection Rate）是不规律变化的，且通常被描述为白色噪音.白色噪音具有马儿可夫性，但是在实践中，噪音出现非马尔可夫性是普通现象，而噪音呈现马尔可夫性仅仅是例外.在许多真实情况下，白色噪声的理想化假设是不足的：真正的不规则因素总是非马尔可夫相关性的.我们提出了一个新的模型来量化调试过程相关的环境不确定性因素.基于广泛应用于软件故障检测过程的非齐次泊松过程（Non-Homogeneous Poisson Process，简称NHPP）模型，我们将环境的不确定性考虑为任意分布和时间相关性的噪声.通过与一些现有模型的比较，新的框架表现出更接近实际观测数据的特征.除了常用的关注故障数的平均值，我们提供了公式来计算其累积密度函数（CDF）和概率密度函数（PDF），来获得调试过程的完整统计信息.

Characterizing Uncertainty of Software Reliability Growth Model

Increasing software systems have been developed to provide great flexibility to customers but also introduce great uncertainty to software development. The fault detection rate (FDR) within the fault detection process shows an irregular fluctuation and is usually modeled as a white noise. White noise is Markovian, but Non-Markov is the rule, Markov is the exception. In many cases the white noise idealization is insufficient:Real fluctuations are always correlated noise (non-Markovian noise). We propose a novel model to quantify the uncertainties associated with the debugging process. Based on the Non-Homogeneous Poisson Process (NHPP) model for software fault detection process, we consider the environmental uncertainties collectively as a noise of arbitrary distribution and correlation structure. Through a number of comparisons with existing methods, the new model exhibits a closer fitting to observation data. In addition to conventional focus on the mean value of detected-fault number, we provide a formula to compute its cumulative density function (CDF) and probabilistic density function (PDF), which encapsulate full statistical information of the debugging process.