A rule-based approach for establishing states in a Markov process applied to maintenance modelling

Abstract

The deterioration of technical systems can often be classified into discrete states, and the transitions between these states can be modelled using a Markov process. Instead of using an exponential distribution, it may be more realistic to assume that a general probability distribution describes the sojourn time in one of these states. The resultant model is a semi-Markov process, which may be difficult to treat analytically. This paper therefore presents an approach where the sojourn times in these states are gamma distributed and where the gamma distribution is transformed into a Markov process with a sequence of states that have exponentially distributed sojourn times. This means that the gamma distribution is approximated by a Markov process, which simplifies maintenance modelling. The approach presented is based on a simple rule such that it can easily be implemented in a maintenance model. It is shown that the approach yields good results compared with available alternatives.