Maintenance optimization for a Markovian deteriorating system with population heterogeneity

We develop a partially observable Markov decision process model to incorporate population heterogeneity when scheduling replacements for a deteriorating system. The single-component system deteriorates over a finite set of condition states according to a Markov chain. The population of spare components that is available for replacements is composed of multiple component types that cannot be distinguished by their exterior appearance but deteriorate according to different transition probability matrices. This situation may arise, for example, because of variations in the production process of components. We provide a set of conditions for which we characterize the structure of the optimal policy that minimizes the total expected discounted operating and replacement cost over an infinite horizon. In a numerical experiment, we benchmark the optimal policy against a heuristic policy that neglects population heterogeneity