Parameter Estimation of Shifted Mixture Models for Software Reliability Assessment

Abstract This paper proposes a novel approach for predicting software reliability using shifted mixtures of Weibull, lognormal and Gompertz distributions. By integrating these three distributions with shift parameters, we aim to model the complex, multi-phase failure processes observed in software systems more accurately than traditional models. One way to get accurate solutions in software reliability assessments is to adopt the challenges of parameter estimation of proposed shifted models that arise due to the numerous parameters involved in the models. We employ expectation–maximization (EM), particle swarm optimization (PSO) and differential evolution (DE) algorithms, which provide not only a granular view of failure mechanisms but also guide effective maintenance and reliability enhancement strategies. A comparative analysis of proposed models using an actual failure data set is presented. Numerical experiments illustrate the performance of proposed approach and use some goodness of fit tests to determine the best-fitting shifted mixture model. We show that the method can automatically select the better mixture model for the data set, and validate the performance indices for the software reliability prediction.