Reliability Evaluation of Multi-State Linear Consecutive-k-out-of-n:G Systems and Its Application to Maintenance Problems

In this study, we focus on the reliability evaluation of the linear consecutive-[Formula: see text]-out-of-[Formula: see text]:G system, where the system is working if and only if at least [Formula: see text] consecutive components work. The multiple state of the system is considered including not only the working and failure state, but also the intermediate state approaching failure, and the reliability evaluation is discussed including the system failure probability, the expected number of failed components and the expected time to the considered intermediate state. We also apply these reliability results to the maintenance problems, and discussed the condition-based maintenance for the system which is based on the state of the system, and give the results of the optimal maintenance interval which minimizes the expected cost rate.