Delay time-based inspection and replacement optimization under Semi-Markov decision process

Condition-based replacement and spare part scheduling is essential to increase system reliability and reduce failure probabilities. The majority of current studies assume there are enough replacement parts to replace failed units, while neglecting delays caused by a shortage of spare components. The delay-time model generally employs two-stage failure processes, the first of which begins with a healthy condition and progresses to an unhealthy state, followed by a failure state. The failure process is described using a semi-Markov model, where the sojourn time in each stage follows the Erlang distribution. The state of the system is detected at some discrete equidistant epochs, and an order action is triggered once the accumulated deterioration reaches the pre-specified limit. The system is then put on hold until the spare part arrives. The goal is to reduce the operational cost by optimizing the inspection interval, and then using a semi-Markov decision process to calculate system performance indices. Finally, under the delay-time model, a numerical example is provided to demonstrate the effectiveness of the proposed optimization model.