Dynamic Programming for Optimal Maintenance of Systems with Degradation and Traumatic Event Failures

<ns3:p>Background Systems operating in industrial environments are often exposed to two concurrent failure mechanisms: gradual degradation and sudden traumatic events. Maintenance decisions must account for these competing risks while controlling inspection, replacement, and failure costs. This study develops a quantitative framework to determine an economically efficient maintenance strategy under such conditions. Methods A discrete-state model is formulated with three operational conditions: Good, Degraded, and Failed. Transitions between states are driven by the system’s degradation trajectory and the occurrence of traumatic failures. A long-term expected cost model is established, incorporating inspection costs, preventive replacement costs, and failure-related losses. Dynamic programming is used to identify the policy that minimizes the expected cost per unit time. The optimisation evaluates how inspection intervals, degradation rates, and traumatic event probabilities influence replacement decisions. Results The optimisation results indicate that the cost-effective policy depends strongly on the interaction between degradation progression and the frequency of traumatic events. Higher rates of traumatic events lead to earlier preventive replacement, while intermediate degradation rates make the inspection interval the primary driver of cost reduction. The model delineates the parameter regions in which periodic inspection is justified and quantifies the cost effects of different maintenance schedules. Conclusions The proposed dynamic programming approach provides a structured method for selecting inspection and replacement strategies in systems subject to multiple failure mechanisms. The results offer decision-support guidance for maintenance planning, particularly in environments where degradation and traumatic events jointly affect system reliability and operating costs.</ns3:p>