Determination of Pareto frontier in multi-objective maintenance optimization

The objective of a maintenance policy generally is the global maintenance cost minimization that involves not only the direct costs for both the maintenance actions and the spare parts, but also those ones due to the system stop for preventive maintenance and the downtime for failure. For some operating systems, the failure event can be dangerous so that they are asked to operate assuring a very high reliability level between two consecutive fixed stops. The present paper attempts to individuate the set of elements on which performing maintenance actions so that the system can assure the required reliability level until the next fixed stop for maintenance, minimizing both the global maintenance cost and the total maintenance time. In order to solve the previous constrained multi-objective optimization problem, an effective approach is proposed to obtain the best solutions (that is the Pareto optimal frontier) among which the decision maker will choose the more suitable one. As well known, describing the whole Pareto optimal frontier generally is a troublesome task. The paper proposes an algorithm able to rapidly overcome this problem and its effectiveness is shown by an application to a case study regarding a complex series-parallel system.     

基于PIWOA的绿色闭环供应链网络多目标模糊优化设计

针对闭环供应链网络优化设计问题,建立了一种基于Me测度的闭环供应链网络多目标优化设计模型,以此降低供应链网络设计中不确定性因素在求解时的影响。首先,针对多层级闭环供应链网络,建立以成本最小、CO₂排放量最小以及社会效益最大为目标的优化函数,并采用Me测度和三角模糊数对模型及相关约束进行模糊处理,得到不确定性闭环供应链网络优化模型;其次,在原有鲸鱼算法的基础上,引入变异收敛因子,增强其搜索能力,并将Pareto引入改进后的鲸鱼算法求解所建模型;最后,通过数值实例和仿真分析验证算法在搜索能力、时间以及优化目标函数值等方面具有较强的优势和性能。     

冲击环境下租赁设备预防维护策略优化研究

从租赁设备的工作环境出发,提出了一种基于冲击模型的故障建模方法,综合考虑改善因子与预防维护成本的制约关系以及租赁条件下的故障惩罚机制,建立了一种面向租赁设备的等周期预防维护策略,并以最小化期望总成本率为决策目标得到租赁设备的优化维护计划。算例分析显示,该策略符合一般租赁设备维护的实际情况,能为服务制造商提供有效的维护解决方案。     

Optimization of imperfect preventive maintenance for multi-state systems

The paper generalizes a preventive maintenance optimization problem to multi-state systems, which have a range of performance levels. Multi-state system reliability is defined as the ability to satisfy given demand. The reliability of system elements is characterized by their hazard functions. The possible preventive maintenance actions are characterized by their ability to affect the effective age of equipment. An algorithm is developed which obtains the sequence of maintenance actions providing system functioning with the desired level of reliability during its lifetime by minimum maintenance cost.To evaluate multi-state system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Basic GA procedures adapted to the given problem are presented. Examples of the determination of optimal preventive maintenance plans are demonstrated.     

Failure modeling and optimizing preventive maintenance strategy during two-dimensional extended warranty contracts

Offering extended warranty (EW) contracts for products such as automobiles is a good source of revenue for manufactures, insurers and third party companies. However, difficulties in the modeling of product’s failure process and assessing corrective and preventive maintenance actions’ effects on the reliability of product enforce the service providers to propose limited EW contracts with simple “minimal repair at failures” servicing strategy. In this paper for a product sold with a two-dimensional warranty, we model the failure process of product, the effect of imperfect preventive maintenance (PM) and corresponding servicing cost in terms of product’s age and usage. Then, we propose a mathematical optimization model to derive optimal number and degrees of preventive repairs to minimize the EW provider’s servicing cost. We also provide some guidelines to help the EW provider to design flexible EW contracts and determine their corresponding optimal maintenance strategies. To reproduce an illustrative numerical example, we use the failure history of a commercial vehicle produced in a plant in Iran. The provided results reveal that considering proper preventive maintenance strategy during the EW period may effectively reduces the cost of EW servicing.     

A new multi-objective optimization model for preventive maintenance and replacement scheduling of multi-component systems

In this article, a new multi-objective optimization model is developed to determine the optimal preventive maintenance and replacement schedules in a repairable and maintainable multi-component system. In this model, the planning horizon is divided into discrete and equally-sized periods in which three possible actions must be planned for each component, namely maintenance, replacement, or do nothing. The objective is to determine a plan of actions for each component in the system while minimizing the total cost and maximizing overall system reliability simultaneously over the planning horizon. Because of the complexity, combinatorial and highly nonlinear structure of the mathematical model, two metaheuristic solution methods, generational genetic algorithm, and a simulated annealing are applied to tackle the problem. The Pareto optimal solutions that provide good tradeoffs between the total cost and the overall reliability of the system can be obtained by the solution approach. Such a modeling approach should be useful for maintenance planners and engineers tasked with the problem of developing recommended maintenance plans for complex systems of components.     

Level Diagrams analysis of Pareto Front for multiobjective system redundancy allocation

Reliability-based and risk-informed design, operation, maintenance and regulation lead to multiobjective (multicriteria) optimization problems. In this context, the Pareto Front and Set found in a multiobjective optimality search provide a family of solutions among which the decision maker has to look for the best choice according to his or her preferences. Efficient visualization techniques for Pareto Front and Set analyses are needed for helping decision makers in the selection task.In this paper, we consider the multiobjective optimization of system redundancy allocation and use the recently introduced Level Diagrams technique for graphically representing the resulting Pareto Front and Set. Each objective and decision variable is represented on separate diagrams where the points of the Pareto Front and Set are positioned according to their proximity to ideally optimal points, as measured by a metric of normalized objective values. All diagrams are synchronized across all objectives and decision variables. On the basis of the analysis of the Level Diagrams, we introduce a procedure for reducing the number of solutions in the Pareto Front; from the reduced set of solutions, the decision maker can more easily identify his or her preferred solution.     

考虑预防维修时间及相关性的多部件系统维护策略

针对动车组关键系统维修过程中涉及部件数量多、维修时间长、维修费用高的特点，提出了预防维修时间、故障相关性、经济相关性3重因素影响下的多部件系统机会维护策略。首先对多部件建立部件故障率模型。在此基础上，考虑预防维修时间，将部件层预防维修成本分为独立时间成本和依赖时间成本，对经济相关性进行建模，再以系统维修费用率最小为优化目标建立系统层维护模型，并应用遗传算法求解。最后通过算例表明，相较于考虑单一因素的维修策略，所提维修策略可降低系统维修成本10%及以上，验证了考虑维修时间和部件联合相关性的必要性和有效性。     

考虑环境因素的包装机械动力机衰退演化规则及多目标决策

目的 为了提高包装机械动力机的使用寿命。方法 考虑到包装机械动力机工作外界环境因素的影响以及自身内部衰退规律,引入环境因子和调整因子,在综合内外因素衰退演化规则的基础上,建立以稳态可用度和平均成本率为目标的多目标优化决策模型,并且分析不同环境工况对预防维护时间间隔的影响,再根据最优预防维护时间间隔进行动态预防维护策略研究。结果 研究数值算例表明,衰退演化规则是合理的,且恶劣的环境会加速机械动力机的衰退,急剧缩短预防维护时间间隔。结论 考虑环境因素的影响对机械动力机维护具有实际意义,为其提供良好的工作环境,对提高其稳态可用度和降低维护平均成本率是非常重要的。     

Joint optimization of maintenance,buffers and machines in manufacturing lines

This article considers a series manufacturing line composed of several machines separated by intermediate buffers of finite capacity. The goal is to find the optimal number of preventive maintenance actions performed on each machine, the optimal selection of machines and the optimal buffer allocation plan that minimize the total system cost, while providing the desired system throughput level. The mean times between failures of all machines are assumed to increase when applying periodic preventive maintenance. To estimate the production line throughput, a decomposition method is used. The decision variables in the formulated optimal design problem are buffer levels, types of machines and times between preventive maintenance actions. Three heuristic approaches are developed to solve the formulated combinatorial optimization problem. The first heuristic consists of a genetic algorithm, the second is based on the nonlinear threshold accepting metaheuristic and the third is an ant colony system. The proposed heuristics are compared and their efficiency is shown through several numerical examples. It is found that the nonlinear threshold accepting algorithm outperforms the genetic algorithm and ant colony system, while the genetic algorithm provides better results than the ant colony system for longer manufacturing lines.     

基于机会维修策略的预防性维修优化模型研究

为了利用系统内故障部件维修的机会,考虑部件之间在维修方面存在的相关性情况,提出了将机会维修信息融入系统预防性维修的优化模型．该模型在比较按机会预防性维修和按计划预防性维修期望效益的基础上,以系统内故障时机为优化变量、部件维修费用率最小化为目标进行系统预防性维修优化,使确定部件在不同的故障来源时机可提前预防性维修的阈值．最后通过算例,表明不同故障的机会维修阈值对部件预防性维修效果的影响差异,为系统预防性维修决策提供有力的支持．     

Optimum policies for a system with general imperfect maintenance

This study considers periodic preventive maintenance policies, which maximizes the availability of a repairable system with major repair at failure. Three types of preventive maintenance are performed, namely: imperfect preventive maintenance (IPM), perfect preventive maintenance (PPM) and failed preventive maintenance (FPM). The probability that preventive maintenance is perfect depends on the number of imperfect maintenances conducted since the previous renewal cycle, and the probability that preventive maintenance remains imperfect is not increasing. The optimum preventive maintenance time that maximizes availability is derived. Various special cases are considered. A numerical example is given.     

Optimization for condition-based maintenance with semi-Markov decision process

The semi-Markov decision model is a powerful tool in analyzing sequential decision processes with random decision epochs. In this paper, we have built the semi-Markov decision process (SMDP) for the maintenance policy optimization of condition-based preventive maintenance problems, and have presented the approach for joint optimization of inspection rate and maintenance policy. Through numerical examples, the improvement of this method is compared with the scheme, which optimizes only over the inspection rate. We also find that under a special case when the deterioration rate at each failure stage is the same, the optimal policy obtained by SMDP algorithm is a dynamic threshold-type scheme with threshold value depending on the inspection rate.     

An adaptive degradation‐based maintenance model taking into account both imperfect adjustments and AGAN replacements

This paper presents an adaptive maintenance model for equipment that can be adjusted (minor preventive maintenance, imperfect state) or replaced (major preventive maintenance, as good as new) at specific scheduled times based on degradation measurements. An initial reliability law that uses a degradation‐based model is built from the collection of hitting times of a failure threshold. Inspections are performed to update the reliability, the remaining useful life, and the optimum time for preventive maintenance. The case of both as good as new replacements and imperfect adjustments is considered. The proposed maintenance model is based on the optimization of the long‐term expected cost per unit of time. The model is then tested on a numerical case study to assess its effectiveness. This results in an improvement for the occurrences of maintenance tasks that minimizes the mean cost per unit of time as well as an optimized number of adjustments that can be considered before replacing an item. The practical application is a decision aid support to answer the 2 following questions: Should we intervene now or wait for the next inspection? For each intervention, should we adjust or replace the item of equipment? The originality is the presence of 2 criteria that help the maintainer to decide to postpone or not the preventive replacement time depending on the measured degradation and to decide whether the item should be adjusted or replaced.     

Considerations in the use of optimal preventive maintenance policies

Designing products which require maintenance always involves compromises between reliability and maintainability. Both scheduled and preventive maintenance (PM) should be considered in the design phases of a product so that the design can include features to ease the maintenance task. In addition, many design decisions based on Failure Modes and Effects Criticality Analysis (FMECA), Pareto criticality rankings, etc., could and should be strongly influenced by the potential for using preventive maintenance. A component that has a major negative impact on system reliability (because of its life distribution) could become much less consequential if appropriate PM policies are implemented. This paper describes the use of an easy-to-implement analysis procedure to assist a designer or systems analyst in making the reliability/maintainability tradeoff.     

生产调度与维护集成的多目标Lorenz非劣遗传优化

研究了一种单机环境下集成生产和维护的双目标优化调度问题。机床的故障间隔时间和平均维修时间服从指数分布,同时结合加工序列相关准备时间。预防性维护活动不能与作业加工同时进行,但与准备时间不相冲突。调度目标是同时最小化作业总计完成时间和机床不可得性。在问题建模的基础上,构造了一种基于Lorenz非劣关系的分类遗传算法(表示为L-NSGA-Ⅱ),详细设计了算法的核心部分。最后,通过大量计算实验,将L-NSGA-II算法与NSGA-II算法进行了比较分析,说明了L-NSGA-II算法的有效性。     

Simultaneous scheduling of production and maintenance tasks in the job shop

This paper deals with the job shop problem of simultaneous scheduling of production operations and preventive maintenance tasks. To solve this problem, we develop an elitist multi-objective genetic algorithm that provides a set of Pareto optimal solutions minimising the makespan and the total maintenance cost. A deep study was made to choose the best encoding, operators, and the different probabilities. Some lower bounds of the adopted criteria are developed. The computational experiments carried out on a set of published instances validate the efficiency of the proposed algorithm.     

基于寿命周期成本分析的产品延伸保修决策优化模型

随着用户对产品寿命周期成本的日益重视,延伸保修已成为生产商新的关注点。延伸保修对产品维修使用费用以及市场竞争力有很大影响,为得到产品延伸保修决策优化方案以降低寿命周期成本,在考虑预防性维修策略的基础上,分析了生产商延伸保修定价策略,构建出一种以用户在产品使用寿命期内单位时间总维修成本最小为目标的延伸保修决策优化模型,并提出了求解模型的网格搜索(grid search)算法。通过引入算例,借助Matlab仿真软件实现网格搜索算法,在保证生产商利益的基础上,有效的降低了产品单位时间总维修成本,延长了产品使用寿命周期长度,由此得到了用户最优延伸保修决策方案,验证了模型和算法的合理性和有效性。     

基于NSGA-II的城市桥梁系统震后可恢复性分析与优化

城市桥梁是经济和社会发展的重要基础设施,特别是重要桥梁以及由其构成的网络在灾难发生后如何快速恢复,对社会安定和地区发展十分重要。近年来抗震韧性倍受关注,如何考虑结构可恢复性并将韧性纳入桥梁系统抗震性能综合评估和优化,还存在很多问题尚待研究。该文定量分析桥梁震后恢复过程、剩余功能和修复时间与韧性指标间的联系,建立城市桥梁系统性能评估方法。由桥梁不同损伤状态计算不同恢复过程的剩余功能、修复时间、可恢复性和震后经济损失;对震后恢复过程的功能函数模型给出建议,量化不同震后恢复策略的影响;将韧性纳入城市桥梁系统抗震性能框架中,提出城市桥梁系统震后可恢复性评估框架,对风险高低不同采用不同的修复过程;对震后经济损失、可恢复性和震前修/改造成本采用多目标优化算法NSGA-II求解震前提升韧性优化策略,用于抗震加固措施的选取。通过案例给出了方法流程,也为城市桥梁系统地震韧性提升提供了新思路。