Imprecise probabilistic inference for software run reliability growth models.

Abstract

This paper presents the application of an inferential statistical approach which combines imprecise Bayesian methods with likelihood inference, to a standard software run reliability growth model. The main idea of the approach is to divide the set of model parameters into two subsets related to fundamentally different aspects of the overall model, and to combine an imprecise Bayesian method related to one of the subsets of the model parameters with maximum likelihood estimation for the other subset. In accordance with the first subset and statistical data, the imprecise Bayesian model is constructed, which provides lower and upper predictive probability distributions depending on the second subset of parameters. These further parameters are then estimated by a maximum likelihood method. This method is applied to a basic software run reliability growth model and it is shown to perform better than a standard model. Several aspects related to the method are discussed, including its advantages, its wider applicability and the possibility to include relevant expert judgements.