The lognormal distribution of software failure rates: application to software reliability growth modeling

Abstract

There are many models of software reliability growth, but none of them is able to model the varied patterns observed in practice. A previous paper (R.E. Mullen, 1998), suggested that since event rates in software systems are generated by multiplicative processes, the distribution of rates of events, including failure rates, is lognormal. It also showed that many previously published empirical failure rate distributions are well fit by the lognormal. The theoretical roots and experimental confirmation of the lognormal distribution of failure rates in software systems provide a unique and potentially fruitful basis for constructing a new software reliability model. The paper derives a Lognormal Execution Time Software Reliability Growth Model, a member of the family of Doubly Stochastic Exponential Order Statistic Models, by developing a numerical approximation for the Laplace transform of the lognormal. The model is used to analyze two series of failure data as an example of its use. The likelihood of that data arising from the lognormal and log-Poisson models is computed and shown to be highly favorable to the lognormal in one case and slightly favorable in the other. A preliminary comparison of the lognormal, the LPET, and the BET models using ten "Musa" data sets further demonstrates the ability of the lognormal model to fit a wide variety of reliability growth scenarios. Of particular novelty is the use of a software failure rate model which has both plausible theoretical justification and solid support from prior studies of software failure rate distributions. Also novel is the application of the Laplace Transform of the Lognormal to the problem of software reliability growth.