A phase-type maintenance model considering condition-based inspections and maintenance delays

This paper proposes a maintenance model for systems subject to discrete-state deterioration processes. The deterioration of the system is described by the phase-type (PH) expansion of a multi-state Markov model, where the sojourn times at different states follow general distributions. In contrast to the periodic inspections and exponentially distributed repairs in most works, this study considers condition-based inspections and significant delays from planning a maintenance task until its actual implementation. These delays are usually due to logistic reasons and are considered close to deterministic. This allows the decision-makers to evaluate more flexible inspection strategies and move towards more cost-effective solutions. A case study about road bridge maintenance is presented to demonstrate the modelling process and the value of introducing PH distributions and condition-based inspections. With the proposed model, a less conservative maintenance strategy with fewer inspections and postponed repairs can be derived, bringing significant cost reductions.