^{a}, Anders Reenberg Andersen, Bo Friis Nielsen and Murat Kulahci

^{a}jfan@dtu.dk

We present empirical results for the size limit of multi-component Condition-Based Maintenance (CBM) problems modelled as Markov Decision Processes (MDP), when solving the problem to optimality. Due to recent technological advances for monitoring equipment deterioration, CBM has become accessible to a larger part of industry. Frequently updated information about the condition of the monitored system makes MDP a natural candidate for optimization of CBM, and it is a commonly used approach for single-component systems (Alaswad and Xiang (2017)). Though a number of MDP algorithms exist for computing globally optimal policies (Puterman (2005)), the required computational effort increases rapidly with the number of components, thus making these exact methods applicable only to a certain extent. For this reason approximating methods, simulation, and heuristic search over a specific class of maintenance policies are the approaches most commonly used in multi-component maintenance optimization (Nicolai and Dekker (2008)). In spite of the aforementioned limitation of its solution algorithms, MDP is a quite versatile modelling framework for CBM in general. Therefore, we believe it is worth investigating the maximum number of components, for which it is computationally feasible to obtain a globally optimal policy. We do this by applying a variety of established algorithms to solve a generic infinite horizon MDP model of a multi-component system, and compare them w.r.t. speed and memory usage. For generality, we assume a system with non-identical components, and consequently we cannot use symmetries to reduce the state or action space of the MDP. In return, we also assume non-decreasing degradation of components, which leads to sparse transition matrices in the MDP, thus reducing the computational burden. We solve the MDP for a varying number of components and varying number of degradation levels between asgood- as-new and failure. Future research includes extension of the model to include partial observability, as this is a complication often present in real-world predictive maintenance settings. Exact solutions for these problems are considerably harder to obtain.