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

Abstract

Let us consider repairable systems subject to failures and maintenances. Observations can come from only one system or from several identical and independent systems. The maintenance is supposed to be imperfect. This is an intermediate situation between the case where a maintenance renews the system, called As Good As New, and the case when the sole effect of maintenance is to get the system working again, called As Bad As Old. Imperfect maintenance models have a parameter that can be interpreted as the maintenance efficiency. Other parameters lie in the baseline hazard rate of the first failure time. All these parameters can be estimated through maximisation of the log-likelihood, which takes into account the single system or multisystem nature of the data. The first aim of this paper is to compare the quality of parameter estimation in the single and multi-system cases. The second aim is to compare the quality of goodness-of-fit tests in this framework. Moreover, new goodness-of-fit tests are introduced in the multi-system case.