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

Abstract

International audienceThe 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

Estimation and goodness-of-fit tests for imperfect maintenance models: single system vs multi-system

“…We need to know whether a given imperfect maintenance model is adapted or not to a given data set. The authors in Chauvel et al (2016a) developed Goodness-of-Fit (GoF) tests to address this issue. This work has been presented at MIMAR 2016 (see Chauvel et al (2016b)).…”

“…The authors in Chauvel et al (2016a) developed Goodness-of-Fit (GoF) tests to address this issue. This work has been presented at MIMAR 2016 (see Chauvel et al (2016b)). However, they have not considered multi-system data.…”

“…A GoF test is a statistical test of H 0 : "λ ∈ C " versus H 1 : "λ / ∈ C ". Our first idea was to extend one of the classes of tests exposed in Chauvel et al (2016a): the statistics based on the Probability Integral Transform (PIT). Since the intensity is parametric, let…”

“…with uniform distribution, since our systems are independent. Our idea was then to compute the three test statistics, and to perform the test in the same way as in Chauvel et al (2016a). However, as explained later, this procedure performed very poorly compared to the initial one.…”

“…We can also ponder on the fact that the chosen model is adapted or not to the data. One way to address this question is to perform goodness-of-fit (GoF) tests, likewise in Chauvel et al (2016a). In that article, only one system was considered at a time.…”