Abstract: Nowadays, the mechanical equipment is become more and more complex with high requirement of accuracy and complexity. The failure modes of systems are more and more diverse. The classical models considering only one single failure mode is incapable of describing the failure evolution and developing efficient maintenance strategies for systems. In this paper, we consider a K-out-of-N system with identical components.Both load sharing and common cause failure effects are investigated. The system may fail when the operating component number is less than K, or, due to the common cause. The common cause failure is a two-stage process, where the system can experience a defective state and the defectiveness is revealed and repaired, and then no common cause failure will occur. Otherwise, the defective state can turn into the failure state if no maintenance action is implemented in time. The sojourn time in the perfect working state and the defectiveness state all follow general distributions. An imperfect inspection policy is implemented to reveal the hidden failure of the system. If a system failure occurs and it is revealed by the inspection, maintenance is implemented immediately which can restore the system to the as-good-as-new state. Otherwise, if the failure is unrevealed due to the inspection error, it will be in the failure state until the failure is inspected. If no failure occurs, the system will continue to operate. We also assume that the inspection and maintenance times are non-negligible. The instantaneous availability and the steady availability of the system are derived. The inspection interval of the system is also optimized. A numerical example is presented to show the applicability of the proposed model. It can provide theoretical reference for the decision-maker when developing efficient maintenance strategies.
We utilize probability theory to model the system reliability indexes. The renewal theory is implemented in formulating the stochastic optimization model where the objective is to minimize the inspection and maintenance cost of the system in the infinite time horizon. The decision parameter is the inspection period and the availability is the constraint. The stochastic optimization problem is solved numerically.
Theoretically,the expressions of instantaneous availability and the steady availability are given. The cost rate in the infinite time horizon is derived. Numerically, an example is given to show the variety of the system reliability quantities with respect to different system parameters. It is shown that the system availability decreases with respect to the inspection interval and the inspection error rate. When the inspection is not frequent or when the efficiency is low, system defectiveness may be hidden without any correction and turns into a system failure with larger probability, which may decrease the system availability in average. In addition, the sensitivity of the system reliability with respect to K is examined, and as expected, the reliability function decreases the K, which is the smallest number of required operating component for the system functionality. With respect to the inspection and maintenance cost rate in the infinite time horizon, the optimal inspection interval is presented. It seems that the cost rate in the infinite time horizon is a convex function with respect to the inspection interval.
In this work, both load sharing and common cause failure effects are investigated for a K-out-of-N repairable system. An imperfect inspection policy is implemented to reveal the hidden failure of the system. The instantaneous availability, the steady availability and the maintenance cost rate in the long-run are derived. Numerical examples are presented to illustrate this study. The optimum of the maintenance cost with respect to the imperfect inspection period subject to the availability constraint is discussed. It can provide theoretical references for the decision-maker.This work could be further extended in the following three aspects. First, we have considered the failure rates of components are constant. It is more interesting and challenging to relax this assumption by allowing general time-dependent failure rates of components. Secondly, we have considered only a constant inspection error rate, under which the inspection may fail to reveal the system defectiveness. In the future work, we can also consider the inspection may misidentify the system as in the defectiveness state, where its true state is good. Thirdly, we have assumed that the system is periodically inspected to facilitate the modelling, the corresponding calculation and analysis. Non-periodical inspection policies can be studied, where the inspection time based on the system health condition or the prediction lifetimes, etc. We plan to investigate these issues in the future work.

Key words: common cause failure, load sharing, imperfect inspection, maintenance optimization

摘要： 随着仪器设备的大型化、精密型和复杂化,传统的单一故障模型很难精确地描述系统。针对可修的表决系统,考虑了负载分担和共因失效两种失效模式,提出了不完美的故障检测策略,并对模型进行了可靠性和维修性分析,求得了系统的瞬时可用度、稳态可用度和平均维修费用。最后通过数值案例给出了同时考虑可用度和维修费用的最优检测策略,能够为设备管理者提供决策依据。

关键词: 共因失效, 负载分担, 不完美检测, 维修优化