Empirical Bayesian Software Reliability Model Using Rayleigh Distribution

Abstract

An Empirical Bayesian software reliability model is considered in this paper. It is assumed that the times between failures follow Rayleigh distribution with the parameter in the failure rate function with stochastically decreasing order on successive failure time intervals. The reasoning for the assumption on the parameter is that the intention of the software tester to improve the software quality by the correction of each failure. With the Bayesian approach, the predictive distribution has been arrived at by combining Rayleigh time between failures and gamma prior distribution for the parameter. The expected time between failure measures has been obtained. The posterior distribution of the parameter and its mean has been deduced. For the parameter estimation, Maximum likelihood estimation (MLE) method has been adopted. The proposed model has been applied to two sets of actual software failure data and it has been observed that the predicted failure times as per the proposed model are closer to the actual failure times. The predicted failure times based on Littlewood-Verall (LV) model is also computed. Sum of Square Errors (SSE) criteria has been used for comparing the actual time between failures and predicted time between failures based on proposed model and LV model.