An adaptive EM algorithm for NHPP software reliability models

Abstract

Non-homogeneous Poisson process (NHPP) software reliability growth models (SRGM) enable several quantitative metrics that can be used to guide important decisions during the software engineering life cycle such as testing resource allocation and release planning. However, many of these SRGM possess complex mathematical forms that make them difficult to apply in practice because traditional statistical procedures such as maximum likelihood estimation must solve a system of non-linear equations to identify the numerical parameters that best characterize a set of failure data. Recently, researchers have made significant progress in overcoming this difficulty by developing an expectation-maximization (EM) algorithm that exhibits better convergence properties and can therefore find the maximum likelihood estimates of complex SRGM with greater ease. This EM algorithm, however, assumes that some model parameters are constant and thus the approach is not capable of identifying the set of numerical parameters that maximize the likelihood function. This paper presents an adaptive EM algorithm to identify the maximum likelihood estimates of all parameters of multiple NHPP SRGM with complex mathematical forms. We illustrate our enhanced algorithm through a series of examples. The results show that the algorithm can efficiently identify the set of numerical parameters that globally maximizes the likelihood function. Thus, the adaptive algorithm can significantly simplify the application of complex SRGM.