Maximum-Likelihood Estimation of Parameters of NHPP Software Reliability Models Using Expectation Conditional Maximization Algorithm

Since its introduction in 1977, the expectation maximization (EM) algorithm has been one of the most important and widely used estimation method in estimating parameters of distributions in the presence of incomplete information. In this paper, a variant of the EM algorithm, the expectation conditional maximization (ECM) algorithm, is introduced for the first time and it provides a promising alternative in estimating the parameters of nonhomogeneous poisson (NHPP) software reliability growth models (SRGM). This algorithm circumvents the difficult M-step of the EM algorithm by replacing it by a series of conditional maximization steps. The utility of the ECM approach is demonstrated in the estimation of parameters of several well-known models for both time domain and time interval software failure data. Numerical examples with real-data indicate that the ECM algorithm performs well in estimating parameters of NHPP SRGM with complex mean value functions and can produce a faster rate of convergence.

I. Introduction

Computers play a pervasive role in many spheres of human activity and is strongly coupled with the meteoric rise of the software industry, producing innovative applications and driving societal transformation globally. Therefore, much effort has been devoted to achieve optimum software quality and reliability, commonly defined as the probability of failure-free operation of a computer program in a specific environment for a specified period of time.