Balancing Downtime and Maintenance Costs for Multi-Component Systems with Economic and Structural Dependencies

In the maintenance of multi-component systems, failures can cause downtime costs because immediate maintenance may not be possible. This leads to the need to balance these downtime costs with periodic maintenance costs while ensuring that the system operates with the requisite reliability, given its structural and economic dependencies. Specifically, we formulate a Markov Decision Process model with two novel features. First, the system can have any reliability structure, including structures in which it operates even if some components have failed. Toward this end, the corresponding reliability function is obtained from a binary decision diagram, which significantly increases the range of practical maintenance problems that can be addressed. Second, expected downtime costs are derived from the reliability function for every possible state transition. A modified policy-iteration algorithm is then used to determine the optimal policy to minimise the discounted total costs that consist of maintenance and downtime costs. By varying the unit cost of system downtime, a range of Pareto-optimal policies is derived. Furthermore, we also derive suggestions for changing structural dependencies so that the resulting maintenance costs would be lower.

Keywords: Multi-component system, Markov decision Process, Downtime, Economic and structural dependencies.