Optimal non-periodic inspection scheme for a multi-component repairable system using A1 search algorithm

This paper proposes an approach for finding an optimal non-periodic inspection scheme on a finite time horizon for a multi-component repairable system. The system consists of several components, each of which is subjected to soft failure. Soft failures of each component do not cause the system to stop functioning, but increase the system operating costs and are detected only if inspection is performed. Thus, the system is inspected at the scheduled inspection instances and if any of its components is found to have failed, the failed component is minimally repaired. The system’s expected total cost associated with a given inspection scheme includes inspection costs, repair costs, and the penalty costs that are incurred due to the time delay between the actual occurrence of a soft failure of the components and its detection at an inspection. The objective is to determine the optimal inspection scheme which minimizes system’s expected total cost.In the proposed approach, the system’s expected total cost is first formulated in terms of inspection scheme. Then, A¹ search algorithm, with a proposed heuristic cost function for calculating lower bounds, is employed to search through alternative inspection schemes to determine the optimal one. The proposed approach is illustrated through a numerical example.     

Optimal inspection interval for a k-out-of-n system with non-identical components

In this paper, we develop a continuous-time discrete-state model for periodic inspection of a k-out-of-n cold-standby system with non-identical components. A perfect switching system detects the components’ failures, and the failed component(s) are repaired during the next inspection interval, and then added to the standby queue. The system can be in different states depending on the combination of working components and the order of the components on the standby queue at the beginning of an inspection interval. We present a matrix-based approach to determine the system states and calculate the system-states transition probabilities and the transition matrix. We calculate the expected total cost of the inspection intervals by determining the system state at the beginning and end of each inspection interval and calculating the inspection cost matrix. The expected total inspection cost consists of the system downtime cost, components repair cost, system repair cost, and system inspection costs. Finally, we minimize the system’s expected total cost by determining the system’s optimal inspection interval. The results show that determining the optimal inspection interval decreases the system's total inspection interval cost up to 60 % in comparison with the cases when the inspection interval is selected arbitrarily.     

Optimal completed work dependent loading of components in cold standby systems

This paper considers the modelling and optimization of 1-out-of-N: G cold standby (CS) systems with non-repairable components functioning at different levels of productivity or load. The productivity heterogeneity leads to difference in component failure behaviour as well as in operational and replacement costs. Thus, the choice of load or productivity of components can greatly affect the system reliability and mission cost. To make the optimal choice of component loading, we first suggest a method for analysing the reliability and expected mission cost of 1-out-of-N: G non-repairable CS systems with heterogeneous components. The optimal dynamic load distribution problem is then formulated and solved, in which the component loading is chosen depending on the amount of work completed prior to the component activation. The optimal loading is aimed at minimizing the expected mission cost, while meeting a certain system reliability constraint. Examples are given to demonstrate the proposed methodology and the improvement in the optimal design solution through introducing the component productivity’s dependence on the completed work.     

Optimal periodic and random inspections with first,last and overtime policies

It has been assumed for a standby unit that periodic inspection is performed more easily to detect failures, but such a strict periodic mode would be impractical if the unit is executing some procedures without stops. From the above viewpoint, this paper first optimises a random inspection policy in accordance with random procedure times, compares it with periodic inspection and computes a modified checking cost for random inspection to determine the case where such a random inspection would be adopted. Second, this paper proposes three new inspection models in which inspections with deterministic policies are scheduled strategically while their performances need to be limited by completion times of operation procedures. These policies are called inspection first, inspection last and inspection overtime. The total expected inspection and downtime costs of each model until failure detection are obtained, and optimal policies which minimise them are derived analytically. Furthermore, the three inspection policies are compared with periodic inspection, inspection first and last are compared with each other, and a modified checking cost for inspection overtime is discussed when the policy would be better than periodic inspection.     

Optimisation of PM scheduling for multi-component systems – a simulated annealing approach

Proper planning of preventive maintenance (PM) is crucial in many industries such as oil transmission pipelines, automotive and food industries. A critical decision in the PM plans is to determine frequencies and types of maintenance actions in order to achieve a certain level of system availability with a minimum total cost. In this paper, we consider the problem of obtaining availability-based non-periodic optimal PM planning for systems with deteriorating components. The objective is to sustain a certain level of availability with the minimal total maintenance-related costs. In the proposed approach, the planning horizon is divided into some inspection periods of equal intervals. For any given interval, a decision must be made to perform one of the three actions on each component; inspection, preventive repair and preventive replacement. Any of these activities has different effects on the reliability of the components and the corresponding distinct costs based on the required recourses. The cost function includes the cost for repair, replacement, system downtime and random failures. System availability and PM resources are the main constraints considered. Since the proposed model is combinatorial in nature involving non-linear decision variables, a simulated annealing algorithm is employed to provide good solutions within a reasonable time.     

基于二阶段时间延迟的多产品生产系统生产与维修联合优化研究

针对多产品生产部件串联系统的生产和维修问题进行了研究,提出了基于二阶段时间延迟的联合优化模型。首先,基于生产周期分段理论,将整个周期等分成若干单位时间段,生产与维修共用每段时间,且若干时间段后采取一次预防维修。其次,考虑生产系统的实际生产时间、可用生产时间和维修耗费时间,建立了生产计划与维修计划总成本模型。其中,维修计划考虑缺陷和故障维修费用、维修检查费用,以及非正常状态下设备运行可能产生的不合格产品损失费用;生产计划考虑生产成本、库存成本、延期未交货成本和维修停机后恢复生产的设备启动成本。最后,通过算例分析,计算最优预防维修周期和各单位时间段各产品产量,验证了模型的有效性。     

Optimal single-replacement for repairable products with different failure rate under a finite planning horizon

This paper provides a replacement policy for repairable products with free-repair warranty (FRW) under a finite planning horizon from the consumer's viewpoint. Assume that the product is replaced once within a finite planning horizon, and the failure rate of the second product is lower than the failure rate of the first product. Within FRW, the failed product is corrected by minimal repair without any cost to the consumers. After FRW, the failed product is repaired with a fixed repair cost to the consumers. However, each failure incurs a fixed downtime cost to the consumers over a finite planning horizon. In this paper, we derive the three models of the expected total disbursement cost within a finite planning horizon and some properties of the optimal replacement policy under some reasonable conditions are obtained. Finally, numerical examples are given to illustrate the features of the optimal replacement policy under various maintenance costs.     

Cost optimization model following extended renewing two-phase warranty

In this paper, we study an extended warranty model under which the customer is offered an additional warranty period after the original two-phase warranty expires. Under the original two-phase warranty, the warranty period is divided into two non-overlapping subintervals, one of which is for replacement warranty, and the other is for minimal repair warranty. If the system failure occurs during the original warranty period, the failed system is either replaced or minimally repaired by the manufacturer, and if the failure occurs during the extended warranty period, only the minimal repair is conducted. For the system failure during the replacement warranty period, the failed system is replaced by a new one, and the warranty term is renewed anew. Following the expiration of extended warranty, the customer is solely responsible for maintaining the system for a fixed length of time period and replaces the system at the end of such a maintenance period. During the maintenance period, only the minimal repair is given for each system failure. Such a maintenance model can be considered as a generalization of several existing maintenance models which can be obtained as special cases. The main purpose of this article is to determine, from the customer’s perspective, the optimal length of maintenance period after the extended warranty expires. As the criterion to determine the optimal replacement strategy, we adopt the expected cost rate per unit time during the life cycle of the system. Given the cost structures incurred during the life cycle of the system, we formulate the expected cost and the expected length of life cycle to obtain the expected cost rate. The uniqueness of optimal solution for the decision variable is verified when the life distribution of the system shows an increasing failure rate. Numerical examples are provided to illustrate the proposed optimal replacement strategy.     

Optimal age and block replacement policies for a multi-component system with failure interaction

In this paper we consider a generalized age and block replacement policy for a multicomponent system with failure interaction. The i-th component (1 i N) has two types of failures. Type I and type II failures are age dependent. Type I failure (minor failure) is removed by a minimal repair, whereas type II failure (catastrophic failure) induces a total failure of the system (i.e. failure of all other components in the system) and is removed by an unplanned (or unscheduled) replacement of the system. For an age replacement maintenance policy, planned (or scheduled) replacements occur whenever an operating system reaches age T , whereas in the block replacement case, planned replacements occur every T units of time. The aim of this paper is to derive the expected long-run cost per unit time for each policy. The optimal T * which would minimize the cost rate is discussed. Various special cases are detailed. A numerical example is given to illustrate the method.     

An integrated production–distribution inventory system involving probabilistic defective and errors in quality inspection under variable setup cost

This paper presents a probabilistic defective vendor–buyer integrated inventory model with the consideration of quality inspection errors at the buyer's end and setup cost as function of capital investment. An integrated inventory model is established to find the optimal solutions of lot size, setup cost, and the total number of shipments from the vendor to the buyer in one production run, so that the joint expected total cost incurred has the minimum value. We consider three types of continuous probabilistic defective function to find the associated cost of the system. The expected total cost function is derived for each of these three distributions, its convexity is proved via differential calculus. An efficient iterative algorithm is designed to obtain the optimal solution of the model. The computational effort and time are small for the proposed algorithm and it is simple to implement. Numerical examples and sensitivity analysis are used to demonstrate the application and the performance of the proposed methodology. The computational results indicate that if we make decisions with the capital investment in reducing setup cost, it will help to lower the system cost, and we obtain a significant amount of savings to increase the competitive edge in business.     

按单装配系统中组件生产和库存分配控制策略研究

针对由两种组件、三类顾客需求组成的按单装配系统, 本文研究了其中的组件生产控制与库存分配问题. 在各类顾客需 求是泊松到达过程, 各种组件加工时间服从指数分布的假设下, 我们运用马尔科夫决策理论建立了无限期折扣总成本模型, 根据Lippman转换得到了相应归一化后的离散最优方程, 在此基础之上分析了生产和库存分配联合最优控制策略的结构性质. 本文证明了最优策略是依赖于系统状态的动态策略. 组件的最优生产策略是动态基库存策略, 其中基库存水平是关于系统中其他组件库存水平的非减函数. 而最优的分配策略是动态的阈值策略, 对于只需一种组件构成的顾客需求, 组件的分配阈值是系统中另一组件库存水平的增函数; 而对于同时需要两种组件组成的顾客需求, 其各组件的分配阈值是另一组件库存水平的减函数. 最后通过数值试验给出了各个参数对联合最优控制策略的影响, 并得到了相应的管理启示.     

基于延迟时间理论的n中取k系统检测区间模型

延迟时间理论广泛应用于系统维修领域,能够更为细致和准确地反映系统的运行状态.不同于一般维修理论只用一个阶段描述系统的故障过程,该理论将系统的故障过程分为两个阶段:正常阶段和缺陷运行阶段.系统部件的状态有正常、缺陷和故障3种情况.延迟时间理论主要应用于单部件系统和串联系统的维修和检测,目前尚未应用于n中取k系统.对此,运用延迟时间理论确定n中取k系统的最优维修检测区间,分别针对两种情况进行分析:一种是系统中部件的初始缺陷发生时间服从指数分布的情况,一种是其服从非指数分布的情况.建立单位时间维修费用模型和设计仿真过程,以单位时间维修费用最小为目标进行优化,求解系统的最优维修检测区间.最后通过数值案例表明所提出方法的有效性.     

Optimal periodic testing policy for circuit with self-testing

This paper considers periodic testing policies for a system with self-testing. The system can detect its failure by either self-testing or periodic inspection. If the system fails then its failure is detected by self-testing while it is on-line, or otherwise, it is detected at the next periodic test. Introducing the loss cost elapsed between a failure and its detection, the expected costs are obtained. Optimal intervals of periodic testing which minimize the expected costs are analytically derived. Numerical examples are given when both times of failure and its detection by self-testing are exponential distributions.     

相依多模失效下冷贮备系统最优切换及视情维护决策

针对存在冲击影响的冷贮备系统,研究其最优切换及视情维护决策问题.首先,在系统结构和切换式运行和维护特性分析的基础上,制定基于周期切换和状态检测的切换式离线视情维护策略;其次,建立累积冲击过程影响下系统退化所致的软失效和极端冲击过程所致的硬失效竞争可靠性模型;再次,通过分析两类冲击过程影响下系统运行与备用设备交替使用、维修过程中的状态转移特性,重点推导各检测周期时刻系统状态概率分布的迭代计算模型;然后,以系统平均费用率最小为目标,建立解析决策模型,以求解系统的最优切换周期和维护阈值.最后,以矿井主通风系统为案例验证策略及模型的有效性,并分析模型对参数的灵敏度.结果表明,系统的最优维修策略随机冲击影响的不同而变化显著.     

Disassembly planning and sequencing for end-of-life products with RFID enriched information

When a product reaches its end of lifecycle, components of the product can be reused, recycled, or disposed, depending on their conditions and recovery value. In order to make an optimal disassembly plan to efficiently retrieve the reusable and recyclable items inside a product, knowing the true condition of each component is essential. Practically, the recovery value of a used product is often estimated roughly via visual inspection, and the inaccurate estimates would lead to suboptimal disassembly plans. This paper proposes the use of radio-frequency identification (RFID) technology to support disassembly decisions for end-of-life products. RFID can track pertinent data throughout a product’s lifecycle. With the enriched information, a fuzzy-based disassembly planning and sequencing model is proposed to maximize net profit. First, a Bayesian method translates the RFID data into a quality index of the components. Then, a fuzzy logic model, solved by genetic algorithm, synthesizes input variables (i.e., product usage, component usage, and component condition) into a solution of optimal disassembly sequence that maximizes profit considering recovery value and disassembly cost. This paper verifies the merits of using RFID to improve disassembly decisions that help reuse and recycle end-of-life products to reduce environmental impact.     

Optimization of predetermined standby mode transfers in 1-out-of-N: G systems

Warm standby redundancy is an important fault-tolerant design technique for improving the reliability of many systems used in life-critical or mission-critical applications. Traditional warm standby models aim to reduce the operational cost and failure rate of the standby elements by keeping them partially powered and partially exposed to operational stresses. However, depending on the level of readiness of a standby element, significant restoration delays and replacement costs can be incurred when the standby element is needed to replace the failed online element. To achieve a balance between the operation cost of standby elements and the replacement costs, this paper proposes a new warm standby model with scheduled (or time-based) standby mode transfer of standby elements. In particular, each standby element can be transferred from warm standby mode to hot standby mode (a mode in which the standby element is ready to take over at any time) at a fixed/predetermined time instants after the mission starts. To facilitate the optimal design and implementation of the proposed model, this paper first suggests a new algorithm for evaluating the reliability and expected mission cost of 1-out-of-N: G system with standby elements subject to the time-based standby mode transfer. The algorithm is based on a discrete approximation of time-to-failure distributions of the elements and can work with any type of distributions. Based on the suggested algorithm the problem of optimizing transfer times of standby elements to the hot standby mode and optimal sequencing of their transfer to the operation mode is formulated and solved. In this problem the expected mission cost associated with elements’ standby and operation expenses and mode transfer expenses is minimized subject to system reliability constraint. Illustrative examples are provided.     

Optimal replacement policy for a two-dissimilar-component cold standby system with different repair actions

In this paper, a cold standby repairable system consisting of two dissimilar components and one repairman is studied. When failures occur, the repair of both component 1 and component 2 are not ‘as good as new’. The consecutive operating times of component 1 after repair constitute a decreasing geometric process, while the repair times of component 1 are independent and identically distributed. For component 2, its failure is rectified by minimal repair, and the repair time is negligible. Component 1 has priority in use when both components are good. The replacement policy N is based on the failure number of component 1. Under policy N, we derive the explicit expression of the long-run average cost rate C(N) as well as the average number of repairs of component 2 before the system replaced. The optimal replacement policy N*, which minimises the long-run average cost rate C(N), is obtained theoretically. If the failure rate r(t) of component 2 is increasing, the existence and uniqueness of the optimal policy N* is also proved. Finally, a numerical example is given to validate the developed theoretical model. Some sensitivity analyses are provided to show the influence of some parameters, such as the costs for replacement and repair, and the parameters of the lifetime and repair time distributions of both components, to the optimal replacement policy N* and corresponding average cost rate C(N*).     

Simultaneous control of maintenance and production rates of a manufacturing system with defective products

In the past three decades, studies of simultaneous maintenance and production planning have been focusing on age-dependent machine failure and inventory. This paper presents the interaction between defective products and optimal control of production rate, lead time and inventory. Our aim is to minimize the expected discounted overall cost due to maintenance activities, inventory holding and backlogs. Through Condition-Based Maintenance, we monitor in a real time the manufacturing system’s health by describing N operational states. We consider two maintenance states of a machine controlled by two decision variables: production and maintenance rates. The optimal policy is characterized by the dynamic programming solution to a piecewise deterministic optimal control problem. A numerical illustration and a sensitive analysis are developed with a set of parameters calibrated on an existing manufacturing system.     

Automated network troubleshooting knowledge acquisition

Troubleshooting knowledge acquisition is a notorious network maintenance expert systems development bottleneck. We present an improved methodology to generate automatically a skeleton of network troubleshooting knowledge base given the data about network topology, test costs, and network component failure likelihood. Our methodology uses AO ^* search where a suitable modification of the Huffman code procedure is found to be an admissible heuristic. Our heuristic uses synergistically information about both component failure rates and test costs while relaxing topology constraints. The resulting expert system (XTAR) minimizes expected troubleshooting cost faster and learns better troubleshooting techniques during its operation.     

Minimizing control variation in nonlinear optimal control

In any real system, changing the control signal from one value to another will usually cause wear and tear on the system’s actuators. Thus, when designing a control law, it is important to consider not just predicted system performance, but also the cost associated with changing the control action. This latter cost is almost always ignored in the optimal control literature. In this paper, we consider a class of optimal control problems in which the variation of the control signal is explicitly penalized in the cost function. We develop an effective computational method, based on the control parameterization approach and a novel transformation procedure, for solving this class of optimal control problems. We then apply our method to three example problems in fisheries, train control, and chemical engineering.