A generalised partially observable Markov decision process updated by decision trees for maintenance optimisation

This paper proposes a generalised partially observable Markov decision process (POMDP) combining decision analysis and dynamic programming. The model is applied to a maintenance optimisation problem, even though the scope of its utility is far beyond that particular class of problems and it is relevant to any POMDP. The proposed model allows easy mathematical modelling for optimising complex sequences of decisions that are to be undertaken during each stage. We provide a step-by-step derivation of the mathematical equations for three of the most important types of sequences of decisions to be carried out during each stage of a POMDP and which are used in practice for maintenance optimisation, namely, maintenance action, inspection-maintenance action and inspection-inspection-maintenance action. In a later section, we indicate how to extend the proposed model so that it takes into account epistemic uncertainty that veils the exact value of the probabilistic input parameters of our model.