Condition-based maintenance optimization based on matrix algebra

We develop a matrix algebra approach for optimizing condition-based maintenance with a planning time for gradually deteriorating, continuously monitored equipment. This avoids the calculation times of simulation and the approximations of more direct approaches. We consider a model in which maintenance after failure should be planned as well, resulting in downtime, and a model with emergency repairs upon failure. Numerical examples are provided to compare the optimal policies of the two models and their performances under different parameter settings.