Optimal condition‐based maintenance policy for systems with mutually dependent competing failure

Joint optimization of maintenance and spares inventory policy for a series-parallel system considering dependent failure processes

The two dependent competing risks are soft failure due to aging degradation and fragmentation caused by shocks and hard failure due to spring breakage caused by the same shock process. Considering the complexity of the product itself and the instability of the working environment, this study proposed a generalized reliability model for systems experiencing dependent competing failure processes (DCFPs) of degradation and random shocks, which considered two kinds of DCFP: (1) shock process could affect soft failure thresholds; (2) degradation process could affect hard failure thresholds. In case (1), we considered the effect that a cumulative number of shocks above a certain magnitude could have on the change in the soft failure threshold. In case (2), we considered not only the shock process's impact on the soft failure threshold but also the total degradation (including continuous degradation and sudden degradation caused by shock) on the hard failure threshold. The model captures the features that the shocks experienced by the system affect the degradation process, accelerating the system degradation and causing soft failures; the degradation process of the system affects the shock process, making the system more susceptible to failure from external shocks. Finally, an example using micro‐electro‐mechanical systems devices illustrates the effectiveness of the proposed approach with sensitivity analysis.

In many applications, units from the same population exhibit heterogeneity that they degrade with different rates due to random factors. This article studies how this heterogeneity in degradation influences condition-based maintenance (CBM) policy. Many CBM polices are developed based on gamma process because it is popularly used to characterise monotone degradation processes. In this study, we also model the unit’s degradation by gamma process. To account for the heterogeneity among units’ degradation, we incorporate a random effect parameter in the gamma process. Then the optimal policy for CBM is obtained through Markov decision process. We show that when heterogeneity exists, the transition probability of degradation state depends on both unit’s age and observed degradation level. And consequently, the optimal maintenance policy is a monotone control limit policy. We conduct extensive numerical experiments to validate and demonstrate our findings in depth.

Many systems experience dependent competing failure processes (DCFP) resulting due to degradation processes and random shocks. In some complex systems, the threshold of random shocks will descend because of the degradation processes. According to previous researches, two cases of shock threshold descent will be considered. The first case is the hard failure threshold decent to a lower value when derogation exceeds the critical degradation value. The second case is the hard failure threshold decent continuously with the increasing degradation. In mutually DCFP system, the two cases of hard failure threshold decent will exist simultaneously, so they compete with each other. In this paper, a case of laser lithography machine will be introduced to verify the theory derivation. The Monte Carlo sampling method will be used to sample and simulate the case data to obtain the reliability of the system. The result showed that when shock threshold descent, the reliability of the system drops significantly.

Optimal maintenance policy for multicomponent systems with periodic and opportunistic inspections and preventive replacements

Modeling dependent competing failure processes with degradation-shock dependence

A generalized system reliability model based on survival signature and multiple competing failure processes

This study proposes a general maintenance policy for a system whose deterioration process is in a Gamma process. Such systems under scheduled inspection will be modeled by a multi-state Markov system with time-dependent transition probabilities. Such a policy is mainly to determine, at each inspection time nd, the optimal maintenance action from multiple candidates under the conditions that: (1) the transition probabilities and the risks of each maintenance action are updated at each nd, (2) both the times spent on inspection and maintenance are ignored, etc. Finally, a numerical example is presented through simulation to illustrate how such a policy can be carried out.

Condition-based maintenance (CBM) is proved to be effective in reducing the long-run operational cost for a system subject to degradation failure. Most existing research on CBM focuses on single-unit systems where the whole system is treated as a black box. However, a system usually consists of a number of components and each component has its failure behavior. When degradation of the components is observable, CBM can be applied to the component level to improve the maintenance efficiency. This paper aims to study the optimal inspection/replacement CBM strategy for a multi-unit system. Degradation of each component is assumed to follow a Wiener process and periodic inspection is considered. We cast the problem into a Markov decision framework and derive the optimal maintenance decisions that minimize the maintenance cost. To better illustrate the optimal maintenance strategy, we start from a 1-out-of-2: G system and show that the optimal maintenance policy is a two-dimensional control limit policy. The argument used in the 1-out-of-2: G system can be readily extended to general cases in a similar way. The value iteration algorithm is used to find the optimal control limits, and the optimal inspection interval is subsequently determined through a one-dimensional search. A numerical study and a comprehensive sensitivity analysis are provided to illustrate the optimal maintenance strategy.

This study proposes a sequential Condition-Based Maintenance (CBM) policy for intelligent monitored system based on cost and reliability prioritisation. It is assumed that system's reliability could be continuously monitored, whenever it reaches the threshold R, and scheduled maintenance activity is performed to restore the system. This maintenance policy differs from other policies in taking into consideration of influences from the frequency of maintenance activities and operating time on system's failure rate function subject to a deterioration process. Meanwhile, this CBM policy firstly considers the variant operational cost and variant minimal repair cost by the effects of system's corresponding condition, which helps to construct more practical maintenance model. Finally, a numerical example is presented to test this proposed sequential predictive maintenance policy and the simulation results show its efficiency.

Condition based maintenance optimization for multi-component systems using proportional hazards model

This paper models a real-time warm standby system that has to accomplish a specified amount of task by a hard deadline. The system is subject to corrective replacements (CRs) upon failure of its operating element. It can also be renewed according to a predetermined schedule through preventive replacements (PRs). To facilitate an effective recovery of system operation after replacements, periodic backups are performed so that warm standby elements, upon being activated, can take over the mission task from the last backup point instead of from scratch. This paper presents a novel integrated model that considers effects of periodic backups, CRs and PRs in analyzing and optimizing real-time warm standby systems. Mission success probability and expected mission completion time are evaluated. Impacts of different mission and element parameters on mission success probability, optimal backup and PR policies, and optimal element activation sequence are investigated. It is shown that in warm standby systems with periodic backups and tight deadlines, PRs can improve the mission success probability even when they take the same time as CRs. When the maximum allowed mission time exceeds a certain level, PRs become ineffective and the optimal policy can involve only periodic backups.

In condition-based maintenance (CBM) with periodic inspection, the system is preventively replaced if failure risk, which is calculated based on the information obtained from inspection, exceeds a pre-determined threshold. The determination of optimal replacement threshold is often based on the minimisation of average maintenance costs per unit time due to preventive and failure replacements over a long time horizon. It is often assumed that inspections are performed at equal time intervals with no cost. However, in practice, inspections require labour, specific test devices, and sometimes suspension of operations and, thus, it is reasonable to inspect less frequently during the time the system is in its early age and/or in a healthier state and to perform inspections more frequently as time passes and/or as the system degrades. In other words, an age-based inspection scheme. This paper proposes a novel two-phase approach for the determination of an optimal replacement threshold and an optimal age-based inspection scheme for CBM such that the total long-run average costs of replacements and inspections are minimised. First, it takes into account failure and preventive replacement costs to determine the optimal replacement threshold assuming that inspections are performed at equal time intervals with no cost. This assumption is, subsequently, relaxed and its consequences on total average cost are evaluated using a proposed iterative procedure based on A* search algorithm to obtain the optimal age-based inspection scheme. The proposed approach is illustrated through a numerical example.

Condition-based maintenance using the inverse Gaussian degradation model

Different type of maintenance problems have been investigated during the past decades. With the growth in complexity of modern systems, the cost of purchasing new systems becomes higher ever than before. Surprisingly, very little attention in the literature has been paid to the failure replacement in these preventive maintenance models. However, in practice most systems incur increasingly expensive down time costs when the systems suffer the unexpected failures. The major changes to the standard maintenance model in this research are the addition of a failure replacement cost for a failed system and the reliability limit for which system has to be replaced. The overall objective of this research is to propose an efficient algorithm to obtain the optimal maintenance policy. The optimal preventive maintenance policy is investigated with incorporating the costs of minimal repair, imperfect preventive maintenance, failure replacement and preventive replacement. The specific maintenance actions for a repairable system are when to perform an imperfect preventive maintenance or to replace the system while the system is in the operating condition. In another case, the specific maintenance actions for a repairable system are whether to replace the system, or to perform a minimal repair when the system fails. The number of imperfect preventive maintenance and the control limits of the optimal maintenance policy are calculated under the expected average cost rate criterion.