Performance evaluation of multi-state degraded systems with minimal repairs and imperfect preventive maintenance

In this paper, we develop a model for evaluating the availability, the production rate and the reliability function of multi-state degraded systems subjected to minimal repairs and imperfect preventive maintenance. The status of the system is considered to degrade with use. These degradations may lead to decrease in the system efficiency. It is assumed that the system can consecutively degrade into several discrete states, which are characterized by different performance rates, ranging from perfect functioning to complete failure. The latter is observed when the degradation level reaches a certain critical threshold such as the system efficiency may decrease to an unacceptable limit. In addition, the system can fail randomly from any operational or acceptable state and can be repaired. This repair action brings the system to its previous operational state without affecting its failure rate (i.e., minimal repair). The used preventive maintenance policy suggests that if the system reaches the last acceptable degraded state, it is brought back to one of the states with higher efficiency. Considering customer demand as constant, the system is modeled as a continuous-time Markov process to assess its instantaneous and stationary performance measures. A numerical example is given to illustrate the proposed model.