Performance Optimized Expectation Conditional Maximization Algorithms for Nonhomogeneous Poisson Process Software Reliability Models

Nonhomogeneous Poisson process (NHPP) and software reliability growth models (SRGM) are a popular approach to estimate useful metrics such as the number of faults remaining, failure rate, and reliability, which is defined as the probability of failure free operation in a specified environment for a specified period of time. We propose performance-optimized expectation conditional maximization (ECM) algorithms for NHPP SRGM. In contrast to the expectation maximization (EM) algorithm, the ECM algorithm reduces the maximum-likelihood estimation process to multiple simpler conditional maximization (CM)-steps. The advantage of these CM-steps is that they only need to consider one variable at a time, enabling implicit solutions to update rules when a closed form equation is not available for a model parameter. We compare the performance of our ECM algorithms to previous EM and ECM algorithms on many datasets from the research literature. Our results indicate that our ECM algorithms achieve two orders of magnitude speed up over the EM and ECM algorithms of [1] when their experimental methodology is considered and three orders of magnitude when knowledge of the maximum-likelihood estimation is removed, whereas our approach is as much as 60 times faster than the EM algorithms of [2]. We subsequently propose a two-stage algorithm to further accelerate performance.