Using proxy failure times with the Jelinski-Moranda software reliability model

We introduce the concept of proxy failure times for situations where system test data only consists of the fraction of test cases that fail for a set of execution scenarios. We show how proxy failure times can be simulated if external information about the user frequency of the test cases is available. We develop statistical inference procedures for fitting the Jelinski-Moranda model (Z. Jelinski and P. Moranda, 1996). In particular, we present a graphical diagnostic for testing goodness of fit and show how it suggests appropriate transformations of the failure times that would improve the fit. Influential observations are also identified by the diagnostic and moreover, it provides regression estimators of the model parameters as a quick alternative to the maximum likelihood estimators. Formulas for likelihood based confidence intervals for the model parameters are provided. The simulation of proxy failure times and the statistical inference procedures for the Jelinski-Moranda model are illustrated with an example