Burr Distributions and Software Reliability Modeling

摘要

It is well known that software reliability models (SRMs) based on non-homogeneous Poisson process possesses a simple structure having only one parameter called mean value function, but their goodness-of-fit and predictive performances strongly depend on a fault-detection time distribution in the mean value function. In past, the representative absolutely continuous distribution functions with positive support, such as exponential, gamma, Pareto, normal (lognormal and truncated normal), logistic (log logistic, truncated logistic), extreme (Weibull, Gompertz) distributions, are widely used. On one hand, SRMs can be unified by more generalized fault-detection time classes which include several distributions as special cases, where the typical examples are generalized exponential, generalized gamma, generalized Weibull, phase-type, Marshall-Olkin distributions. In this article we introduce the Burr family which consists of 12 probability distributions for the fault-detection time, and investigate the both of goodness-of-fit and predictive performances with actual software fault count data sets.