Modified iterative aggregation procedure for maintenance optimisation of multi-component systems with failure interaction

Abstract

This paper studies maintenance policies for multi-component systems which have failure interaction among their components. Component failure might accelerate deterioration processes or induce instantaneous failures of the remaining components. We formulate this maintenance problem as a Markov decision process (MDP) with an objective of minimising a total discounted maintenance cost. However, the action set and state space in MDP exponentially grow as the number of components increases. This makes traditional approaches computationally intractable. To deal with this curse of dimensionality, a modified iterative aggregation procedure (MIAP) is proposed. We mathematically prove that iterations in MIAP guarantee the convergence and the policy obtained is optimal. Numerical case studies find that failure interaction should not be ignored in a maintenance policy decision making and the proposed MIAP is faster and requires less computational memory size than that of linear programming.