An Adaptive EM Algorithm for the Maximum Likelihood Estimation of Non-Homogeneous Poisson Process Software Reliability Growth Models

Abstract

Non-homogeneous Poisson process (NHPP) software reliability growth models (SRGMa) enable quantitative metrics to guide decisions during the software engineering life cycle, including test resource allocation and release planning. However, many SRGM possess complex mathematical forms that make them difficult to apply. Specifically, traditional procedures solve a system of nonlinear equations to identify the numerical parameters that best characterize failure data. Recently, researchers have developed expectation-maximization (EM) algorithms for NHPP SRGM that exhibit better convergence properties and can therefore find maximum likelihood estimates with greater ease.This paper presents an adaptive EM (AEM) algorithm, which combines an earlier EM algorithm for NHPP SRGM with unconstrained search of the model parameter space. Our performance analysis shows that the AEM outperforms state-of-the-art EM algorithms for NHPP SRGM with very strong statistical significance, which is as much as hundreds of times faster on some data sets. Thus, the approach can fit SRGM very quickly. We also incorporate this high performance adaptive EM algorithm into a heuristic nested model selection procedure to objectively select a model of least complexity that best characterizes the failure data. Results indicate this heuristic approach often identifies the model possessing the best model selection criteria.aAcronyms are not pluralized.