The robustness of the semi-Markov and delay time single-component inspection models to the Markov assumption

The context of planned preventive maintenance lends itself readily to probabilistic modelling. Indeed, many of the published theoretical models to be found in the literature adopt a Markov approach, where states are usually ‘operating’, ‘operating at one of several levels of deterioration’, and ‘failed’. However, most of these models assume the required Markovian property and do not address the issue of testing the assumption, or the related task of estimating parameters. It is possible that data are inadequate to test the assumption, or that the Markov property is believed to be not strictly valid, but acceptable as an approximation. In this paper we consider within a specific inspection–maintenance context the robustness of a Markov-based model when the Markov assumption is not valid. This is achieved by comparing the output of an exact delay time model of an inspection–maintenance problem with that of a semi-Markov approximation. The importance of establishing the validity of the Markov property in the modelling application is highlighted. If the plant behaviour is seen to be nearly Markov, in the case considered the semi-Markov model gives a good approximation to the exact model. Conversely if the Markov assumption is not a good approximation, the semi-Markov model can lead to inappropriate advice.