Practically, many repairable systems are subject to neglected failures, i.e. if some failures can be repaired promptly they will not affect system availability. This paper investigates the availability and optimal maintenance policy for inspected Markov systems with down time threshold. Based on practical applications, a down time threshold is introduced. If a down time of the system is less than a given threshold, then the system may be considered as operating during the down time, i.e. the down time could be neglected. Otherwise, if a down time is longer than the given threshold, then the system is considered as operating from the beginning of the system failure until the down time exceeding the threshold, i.e. the down time could be delayed. Incorporating the down time threshold, the instantaneous and steady-state availabilities of the system are derived. Furthermore, a maintenance model is formulated to find the optimal inspection interval, T^*, which minimizes the long-run average cost rate. A numerical example for ventilator system is presented to demonstrate the application of the developed approach.

实际上，许多可修复的系统都可以忽略不计的故障，即，如果可以立即修复某些故障，它们将不会影响系统可用性。本文研究了具有停机时间阈值的经过检查的Markov系统的可用性和最佳维护策略。根据实际应用，介绍了停机时间阈值。如果系统的停机时间小于给定的阈值，则该系统可以被视为在停机时间期间运行，即可以忽略停机时间。否则，如果停机时间长于给定的阈值，则系统将从系统故障的开始一直到停机时间超过阈值，即停机时间可能被延迟。结合停机时间阈值，得出系统的瞬时和稳态可用性。此外，制定维护模型以找到最佳检查间隔，T ^*，这使长期平均成本率最小化。给出了通风机系统的数值示例，以演示所开发方法的应用。