Parametric Bootstrap Goodness-of-Fit Tests for Imperfect Maintenance Models

Abstract

The simultaneous modeling of ageing and maintenance efficiency of repairable systems is a major issue in reliability. Many imperfect maintenance models have been proposed. To analyze a dataset, it is necessary to check whether these models are adapted or not. In this paper, we propose a general methodology for testing the goodness of fit of any kind of imperfect maintenance model. Two families of tests are presented, based respectively on martingale residuals and probability integral transforms. The quantiles of the test statistics distributions under the null hypothesis are computed with parametric bootstrap methods. An extensive simulation study is provided, from which we recommend the use of two tests in practice, one from each family. Finally, the tests are applied to several real datasets.