Using a proportional hazards model to analyze software reliability

Abstract

Proportional hazards models (PHMs) are proposed for the analysis of software reliability. PHMs facilitate the merging of two research directions that have to a large extent developed independently-defect modeling based on software static analyses and reliability growth modeling based on dynamic assumptions about the software failure process. Determinants of software reliability include a composite measure of software complexity, software development volatility as measured by non-defect changes, and cumulative testing effort. A PHM is developed using execution time-between-failure data for a collection of subsystems from two software projects. The PHM analysis yields non-parametric estimates of the baseline hazard functions for each of the projects and parametric estimates of the determinants of software reliability. Weibull curves are shown to provide a good fit to the non-parametric estimates of the baseline hazard functions. These curves are used to extrapolate the non-parametric estimates for times between failure to infinity in order to compute the mean time between failures. Failure curves are generated for each of the subsystems as a function of the cumulative project execution times and summed over the subsystems to obtain project failures vs. cumulative project execution times. These estimated project failure curves track the empirical project failure curves quite well. Project failure curves estimated for the case when no non-defect changes are made show that in excess of 50% of failures can be attributed to non-defect changes.