A Markovian decision model for optimizing a maintenance system with Coxian repair times and non-observable phases

In this paper we analyze a manufacturing system with two different servers. The times to failure follow an exponential distribution and the machines repair times follow a phase type distribution with Cox configuration. We consider two models: a full information model and a partial information model, which differ themselves by the possibility of observing or not the phases of the phase type distribution. The first one is modelled by a continuous time Markov decision process, and the second one by a decision Markov process with partial information, as defined by Hordijk & Loeve.