Optimal non-periodic inspection scheme for a multi-component repairable system using A 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.     

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.     

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.     

Optimal lot size and offline inspection policy

In this study, we investigate the effects of using process status at the end of the production lot (PSPL), on determining the optimal policies for products inspection and production lot size. First, we obtain the optimal product inspection policies for different PSPL for a given lot in the in-control or out-of-control state. Properties for the inspection policy are explored. Then, the expected total cost function, which includes setup cost, process maintenance cost and quality-related control cost, is obtained. The optimal production lot size that minimizes the expected total cost per item is determined. Our proposed inspection policy is compared with the three policies of no inspection, full inspection, and disregarding the first s items policy, in which only items from s+1 until the end of the production lot are inspected. Differences in the minimum expected total cost per item between our proposed inspection policy and the other three policies are investigated with a numerical example.     

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 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.     

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。     

Inspection allocation in manufacturing systems using stochasticsearch techniques

Quality is the hallmark of a competitive product. It is necessary to use inspection stations to check product quality and process performance. In this paper, the authors are concerned with the problem of location of inspection stations in a multistage manufacturing system. The authors present two stochastic search algorithms for solving this problem, one based on simulated annealing and the other on genetic algorithms. These algorithms are developed to determine the location of inspection stations resulting in a minimum expected total cost in a multistage manufacturing system. The total cost includes inspection, processing and scrapping cost at each stage of the production process. A penalty cost is also included in it to account for a defective item which is not detected by the inspection scheme. A set of test examples are solved using these algorithms. The authors also compare performance of these two algorithms     

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.     

Contribution of simulation to the optimization of inspection plans for multi-stage manufacturing systems

In this paper we develop a new mathematical model to optimize inspection plans for multi-stage manufacturing systems with possible misclassification errors. The presented model minimizes total inspection related costs while still assuring a required output quality. Because of the complexity of the proposed mathematical model, a simulation algorithm is presented to model the multistage manufacturing system subject to inspection and to estimate the resulting inspection costs. We use the popular Arena simulation software to implement our simulation algorithm and then we utilize OptQuest, Arena’s built-in optimization package, to find the optimal inspection plan. Finally, a numerical example is presented and simulation experiments are also conducted in order to examine the effects of several model parameters.     

A study for optional inspection policies in a flexible manufacturing cell

The objective of the paper is to determine the location of inspection stages in order to minimize the expected total manufacturing cost while satisfying the high-quality product demand of customers in a flexible manufacturing cell (FMC). This allows a designer to examine alternative designs in order to select those which are optimal, or near optimal, in manufacturing cost terms. To accomplish this objective, we have formulated a total manufacturing decision model consisting of machine set-up and processing costs. Inspection set-up and inspection costs, and cost due to defective. A case study and sensitivity analysis are presented to demonstrate the application of the decision model developed.     

Cost allocation with learning and forgetting considerations in a monopolistically competitive market

The objective of this study is to investigate the optimal cost-allocation rate for a new product in order to minimise the incumbent firm's cost under a monopolistically competitive market. From the incumbent's perspective, within a given length of the production run in the introduction or growth stage of the product life cycle, the impacts of the competitors’ entry and the learning and forgetting effects are taken into account in estimating the incumbent's costs. Furthermore, a Bayesian decision model is proposed to determine the optimal cost-allocation rate by considering both expert opinions and available information. Such a rate may assist the managers in evaluating a favourable percentage of the production cost borne by the incumbent firm. A case illustration demonstrates the application of the proposed model. The sensitivity analyses indicate that a higher increasing rate of competition, or a smaller degree of dispersion of the competitors’ entry scale in the introduction or growth stage would incur a higher optimal cost-allocation rate with a higher incumbent's expected total cost. In addition, the optimal cost-allocation rate and the incumbent's expected total cost would be positively correlated with the learning and forgetting rates, regardless of being under setup or production. Finally, it is suggested that managers should pay more attention to the learning and forgetting effects at the production stage than those at the setup stage.     

Ranking software components for reuse based on non-functional properties

One of the biggest obstacles to software reuse is the cost involved in evaluating the suitability of possible reusable components. In recent years, code search engines have made significant progress in establishing the semantic suitability of components for new usage scenarios, but the problem of ranking components according to their non-functional suitability has largely been neglected. The main difficulty is that a component’s non-functional suitability for a specific reuse scenario is usually influenced by multiple, “soft” criteria, but the relative weighting of metrics for these criteria is rarely known quantitatively. What is required, therefore, is an effective and reliable strategy for ranking software components based on their non-functional properties without requiring users to provide quantitative weighting information. In this paper we present a novel approach for achieving this based on the non-dominated sorting of components driven by a specification of the relative importance of non-functional properties as a partial ordering. After describing the ranking algorithm and its implementation in a component search engine, we provide an explorative study of its properties on a sample set of components harvested from Maven Central.     

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.     

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.     

Dynamic buffer management using optimal control of hybrid systems

This paper studies a dynamic buffer management problem with one buffer inserted between two interacting components. The component to be controlled is assumed to have multiple power modes corresponding to different data processing rates. The overall system is modeled as a hybrid system and the buffer management problem is formulated as an optimal control problem. Different from many previous studies, the objective function of the proposed problem depends on the switching cost and the size of the continuous state space, making its solution much more challenging. By exploiting some particular features of the problem, the best mode sequence and the optimal switching instants are characterized analytically using a variational approach. Simulation results based on real data shows that the proposed method can significantly reduce the energy consumption compared with another heuristic scheme in several typical situations.     

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.     

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.     

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*).