A Fine-grained parametric bootstrap approach for NHPP-based software reliability modeling

In software reliability, practitioners demand to estimate software reliability measures accurately from software fault-count data, for making the release decision and project management. To achieve these objectives, software fault-count processes are often described using software reliability models (SRMs) based on stochastic counting processes like non-homogeneous Poisson processes (NHPPs), and statistical point estimation of model parameters is carried out. Substituting the point estimates of model parameters into several software reliability measures, one gets the point estimates of desired reliability measures. However, since such point estimators tend to have high variances, the resulting release decision and project management plans are not reliable under uncertainty. Then, interval estimation of software reliability measures is expected to realize more robust decision making, but is quite difficult to obtain the analytical confidence regions. Bootstrap is a statistical method that generates realizations of statistical estimators by resampling fault-count data. It allows us to evaluate the statistical properties of software reliability measures under uncertainty. In this paper, we propose a fine-grained parametric bootstrap method for NHPP-based SRMs, where a thinning-like resampling algorithm is employed instead of intuitive resampling algorithms which generate the bootstrap data with ties problem. We compare our thinning-like resampling algorithm with the existing ones in both Monte Carlo simulation and empirical study. It can be shown that the model parameters and their associated software reliability measures estimated by our fine-grained parametric bootstrap method are more accurate and robust than the other bootstrap algorithms.