Estimating the Probability of Failure When Software Runs Are Dependent: An Empirical Study

The assumption of independence among successive software runs, common to many software reliability models, often is a simplification of the actual behavior. This paper addresses the problem of estimating software reliability when the successive software runs are statistically correlated, that is, when an outcome of a run depends on one or more of its previous runs. First, we propose a generalization of our previous work using higher order Markov chain to model a sequence of dependent software runs. Then, we conduct an empirical study for exploring the phenomenon of dependent software runs using three software applications as case studies. Based on two statistical approaches, we show that the outcomes of software runs (i.e., success or failure) for two of the case studies are dependent on the outcome of one or more previous runs, in which case first or higher order Markov chain models are appropriate. Finally, we estimate the parameters of the appropriate models and discuss the effects of dependent software runs on the estimates of the software reliability.