Optimization of a fully adaptive quality and maintenance model in the presence of multiple location and scale quality shifts

This paper presents a new model for the economic-statistical optimization of a Variable-Parameter Shewhart control scheme. The proposed model can be utilized to monitor processes where apart from multiple independent assignable causes, affecting both the mean and variance, failures can also occur. Each time an alarm is issued by the control scheme, preventive maintenance actions are initiated, whereas, corrective maintenance actions are required after a failure. The more realistic assumption of imperfect preventive maintenance actions has been considered. The optimal parameter values are selected through a bi-objective optimization problem formulated by the long-run average cost per time unit minimization, and the long-run expected availability maximization, subject to statistical constraints. A real case example is presented to illustrate the application of the model. An extended numerical investigation is utilized to evaluate the superiority of the proposed model.     

Hybrid block replacement and inspection policies for a multi-component system with heterogeneous component lives

Novel replacement policies that are hybrids of inspection maintenance and block replacement are developed for an n identical component series system in which the component parts used at successive replacements arise from a heterogeneous population. The heterogeneous nature of components implies a mixed distribution for time to failure. In these circumstances, a hybrid policy comprising two phases, an early inspection phase and a later wear-out replacement phase, may be appropriate. The policy has some similarity to burn-in maintenance. The simplest policy described is such a hybrid and comprises a block-type or periodic replacement policy with an embedded block or periodic inspection policy. We use a three state failure model, in which a component may be good, defective or failed, in order to consider inspection maintenance. Hybrid block replacement and age-based inspection, and opportunistic hybrid policies will also arise naturally in these circumstances and these are briefly investigated. For the simplest policy, an approximation is used to determine the long-run cost and the system reliability. The policies have the interesting property that the system reliability may be a maximum when the long-run cost is close to its minimum. The failure model implies that the effect of maintenance is heterogeneous. The policies themselves imply that maintenance is carried out more prudently to newer than to older systems. The maintenance of traction motor bearings on underground trains is used to illustrate the ideas in the paper.     

A preventive maintenance policy with sequential checking procedure for a Markov deteriorating system

We consider a repairable system subject to a continuous-time Markovian deterioration while running, that leads to failure. The deterioration degree is measured with a finite discrete scale; repairs follow general distributions; failures are instantaneously detected. This system is submitted to a preventive maintenance policy, with a sequential checking procedure: the up-states are divided into two parts, the “good” up-states and the “degraded” up-states. Instantaneous (and perfect) inspections are then performed on the running system: when it is found in a degraded up-state, it is stopped to be maintained (for a random duration that depends on the degradation degree of the system); when it is found in a good up-state, it is left as it is. The next inspection epoch is then chosen randomly and depends on the degradation degree of the system by time of inspection. We compute the long-run availability of the maintained system and give sufficient conditions for the preventive maintenance policy to improve the long-run availability. We study the optimization of the long-run availability with respect to the distributions of the inter-inspection intervals: we show that under specific assumptions (often checked), optimal distributions are non-random. Numerical examples are studied.     

考虑不完美检测的两阶段点检与备件订购策略联合优化

针对设备维修与备件管理相互影响与制约的问题, 在基于延迟时间理论的基础上, 提出了两阶段点检与备件订购策略联合优化。点检是不完美的, 当点检识别设备的缺陷状态时, 进行预防更新; 设备故障时, 进行故障更新。结合设备更新时备件的状态, 采用更新报酬理论建立了以第一阶段点检时间、第二阶段点检周期和备件订购时间为决策变量, 以最小化单位时间期望成本为目标的模型。最后, 通过人工蜂群算法对模型求解, 并在数值分析中将两阶段点检策略与定期点检策略进行比较, 结果表明:两阶段点检策略始终优于定期点检策略, 验证了所建模型的有效性。     

A condition based maintenance model for a two-unit series system

This paper discusses a condition based maintenance model with exponential failures and fixed inspection intervals for a two-unit system in series. The condition of each unit, such as vibration or heat, is monitored at equidistant time intervals. The condition indicator variables for each unit are used to decide whether to repair an individual unit or to overhaul the whole system. After a maintenance action is performed the monitored condition indicator variable takes on its initial value. Each unit can fail only once within an inspection interval and when one or both units fail the system fails. The probability of failure is exponential and the failure rate is dependent on the condition. The cost to be minimized is the long-run average cost of maintenance actions and failures. We study the optimal solution to this problem obtained via dynamic programming.     

Random fuzzy EOQ model with imperfect quality items

This paper investigates an economic order quantity (EOQ) problem with imperfect quality items, where the percentage of imperfect quality items in each lot is characterized as a random fuzzy variable while the setup cost per lot, the holding cost of each unit item per day, and the inspection cost of each unit item are characterized as fuzzy variables, respectively. In order to maximize the expected long-run average profit, a random fuzzy EOQ model is constructed. Since it is almost impossible to find an analytic method to solve the proposed model, a particle swarm optimization (PSO) algorithm based on the random fuzzy simulation is designed. Finally, the effectiveness of the designed algorithm is illustrated by a numerical example.     

考虑不完全检测的冲击模型最优维修策略

针对制造系统中设备检测不完全的情形,研究基于不完全检测的冲击模型的周期检测、维修联合策略．通过定期检测获知系统的劣化状态以进行必要的预防性维修．在假设系统是退化的且有k个不同故障状态的条件下,以最小化系统运行成本为目标,以检测周期T、系统更换前故障次数Ⅳ为联合决策变量,利用更新过程理论建立了系统平均费用率C（T,N）的数学模型,并且给出最优联合策略的数值算法．最后借助数值例子演示了该模型,分析了检测水平对系统运行成本的影响．     

The signal model: A model for competing risks of opportunistic maintenance

This paper presents a competing risks reliability model for a system that releases signals each time its condition deteriorates. The released signals are used to inform opportunistic maintenance. The model provides a framework for the determination of the underlying system lifetime from right-censored data, without requiring explicit assumptions about the type of censoring to be made. The parameters of the model are estimated from observational data by using maximum likelihood estimation. We illustrate the estimation process through a simulation study. The proposed signal model can be used to support decision-making in optimising preventive maintenance: at a component level, estimates of the underlying failure distribution can be used to identify the critical signal that would trigger maintenance of the individual component; at a multi-component system level, accurate estimates of the component underlying lifetimes are important when making general maintenance decisions. The benefit of good estimation from censored data, when adequate knowledge about the dependence structure is not available, may justify the additional data collection cost in cases where full signal data is not available.     

考虑中间库存缓冲区的多目标设备不完美预防维修策略研究

针对考虑库存缓冲区的多目标设备维修问题,以设备维修能力为约束条件,获得随机故障设备的不完美预防维修策略。首先,利用准更新过程,表示出设备的随机故障次数。其次,结合设备故障次数表达式,以最大设备可用度和最小生产总成本为多目标构建不完美预防维修模型,使用粒子群算法求解,优化设备可用度与生产总成本,获得更新周期内的库存量和预防维修周期两个决策变量的最优值。最后,通过算例分析,验证了多目标不完美预防维修模型的可用性。     

The impact of inspection errors,imperfect maintenance and minimal repairs on an imperfect production system

This paper develops an integrated model of production lot-sizing, maintenance and quality for considering the possibilities of inspection errors, preventive maintenance (PM) errors and minimal repairs for an imperfect production system with increasing hazard rates. In this study, a PM activity is imperfect in that a production system cannot be recovered as good as new and might cause the production system to shift to the out-of-control state with a certain probability. Numerical analyses are used to simulate the effect of changes in various parameters on the optimal solution for which the time that the process remains in the in-control state is assumed to follow a Weibull distribution. In addition, we investigate the effects of inspection errors and PM errors on the minimum total cost of the optimal inspection interval, inspection frequency and production quantity.     

Optimal maintenance scheduling for a complex manufacturing system subject to deterioration

We address the problem of determining inspection strategy and replacement policy for a deteriorating complex multi-component manufacturing system whose state is partially observable. We develop inspection and replacement scheduling models and other simple maintenance scheduling models via employing an imperfect repair model coupled with a damage process induced by operational conditions. The system state in performance of the imperfectly repaired system is modelled using a proportional intensity model incorporating a damage process and a virtual age process caused by repair. The system is monitored at periodic times and maintenance actions are carried out in response to the observed system state. Decisions to perform imperfect repair and replacement are based on the system state and crossing of a replacement threshold. The model proposed here aims at joint determination of a cost-optimal inspection and replacement policy along with an optimal level of maintenance which result in low maintenance cost and high operational performance and reliability of the system. To demonstrate the use of the model in practical applications a numerical example is provided. Solutions to optimal system parameters are obtained and the response of the model to these parameters is examined. Finally some features of the model are demonstrated. The approach presented provides a framework so that different scenario can be explored.     

A Condition Based Maintenance Model with Exponential Failures and Fixed Inspection Intervals

This paper discusses a condition based maintenance model with exponential failures, and fixed inspection intervals. A condition of the equipment, such as vibration, is monitored at equidistant time intervals. If the variable indicating the condition is above a threshold an instantaneous maintenance action is performed and the monitored condition takes on its initial value. The equipment can fail only once within an inspection interval. The probability of failure is exponential and the failure rate is dependent on the condition. The cost to be minimized is the long-run average cost of maintenance actions and failures. We study the optimal solution to this problem obtained via dynamic programming and compare it to an approximate steady state solution based on renewal theory.     

基于截断δ-冲击模型的不完全维修更换策略

本文在截断δ-冲击模型的基础上,考虑了因系统劣化而导致的冲击失效门限值与维修时间的变化,扩充失效状态,从而提出一种新的截断δ-冲击模型。以最小费用为目标,稳态可用度为约束条件,建立N型更换策略的不完全维修更换策略模型,并给出三种常用冲击到达间隔分布的期望寿命。最后通过算例验证模型的有效性,并对参数进行灵敏度分析。     

A graphical procedure for an on-condition maintenance policy: imperfect-inspection model and interpretation

This paper considers on-condition maintenance based on periodicinspection and control of a condition parameter which describesthe wear and deterioration of the productive equipment. We developa model based on delay time and imperfect inspection, and builda graphical procedure to choose the best inspection intervalfor different criteria. The interpretation of this graphicalprocedure allows us to emphasize the factors that are relevantfor inspection decision-making.     

Optimal policies for a delay time model with postponed replacement

We develop a delay time model (DTM) to determine the optimal maintenance policy under a novel assumption: postponed replacement. Delay time is defined as the time lapse from the occurrence of a defect up until failure. Inspections can be performed to monitor the system state at non-negligible cost. Most works in the literature assume that instantaneous replacement is enforced as soon as a defect is detected at an inspection. In contrast, we relax this assumption and allow replacement to be postponed for an additional time period. The key motivation is to achieve better utilization of the system’s useful life, and reduce replacement costs by providing a sufficient time window to prepare maintenance resources. We model the preventive replacement cost as a non-increasing function of the postponement interval. We then derive the optimal policy under the modified assumption for a system with exponentially distributed defect arrival time, both for a deterministic delay time and for a more general random delay time. For the settings with a deterministic delay time, we also establish an upper bound on the cost savings that can be attained. A numerical case study is presented to benchmark the benefits of our modified assumption against conventional instantaneous replacement discussed in the literature.     

基于历史故障数据的租赁设备预防维护策略优化

针对租赁设备的特殊性,提出了一种周期预防维护策略模型。该策略综合考虑设备的当前维护周期、预防维护、小修以及惩罚机制等因素对维护成本的影响,从设备的当前维护周期出发,构造出故障率分布的平滑函数,以设备的历史故障数据信息为依据,使用最大似然估计解析方法对设备的故障率分布函数参数进行有效估计,建立以租赁企业维护成本最小化为目标的周期预防维护策略模型。最后是算例分析,研究表明,该策略符合租赁设备维护的实际情况,可为租赁企业提供有效的维护解决方案。     

Reliability analysis for Weibull distribution with homogeneous heavily censored data based on Bayesian and least-squares methods

The reliability for Weibull distribution with homogeneous heavily censored data is analyzed in this study. The universal model of heavily censored data and existing methods, including maximum likelihood, least-squares, E-Bayesian estimation, and hierarchical Bayesian methods, are introduced. An improved method is proposed based on Bayesian inference and least-squares method. In this method, the Bayes estimations of failure probabilities are focused on for all the samples. The conjugate prior distribution of failure probability is set, and an optimization model is developed by maximizing the information entropy of prior distribution to determine the hyper-parameters. By integrating the likelihood function, the posterior distribution of failure probability is then derived to yield the Bayes estimation of failure probability. The estimations of reliability parameters are obtained by fitting distribution curve using least-squares method. The four existing methods are compared with the proposed method in terms of applicability, precision, efficiency, robustness, and simplicity. Specifically, the closed form expressions concerning E-Bayesian estimation and hierarchical Bayesian methods are derived and used. The comparisons demonstrate that the improved method is superior. Finally, three illustrative examples are presented to show the application of the proposed method.     

自保护相依多部件系统的预防维修建模及策略优化

自保护技术作为自愈技术的一种,能够使系统在环境或工况条件变化的干扰下以较高可靠性运行。本文构建了一个新的具有相依主要部件和辅助部件的系统可靠性模型,其中主要部件的退化速率与工作中的辅助部件的数量有关。此外,基于定期检测和预防维修策略,本文利用半再生过程技术求解了系统的长期运行平均成本,并以长期运行平均成本最小化为目标给出了系统的最优预防维修策略。最后,以镗刀系统为例,利用所提方法给出了预防更换阈值和检测周期的最优值,以期望为实际维修行为决策提供理论参考。     

Optimal economic production quantity policy for imperfect process with imperfect repair and maintenance

This study integrates maintenance and production programs with the economic production quantity (EPQ) model for an imperfect process involving a deteriorating production system with increasing hazard rate: imperfect repair and rework upon failure (out of control state). The imperfect repair performs some restorations and restores the system to an operating state (in-control state), but leaves its failure until perfect preventive maintenance (PM) is performed. There are two types of PM, namely imperfect PM and perfect PM. The probability that perfect PM is performed depends on the number of imperfect maintenance operations performed since the last renewal cycle. Mathematical formulas are obtained for deriving the expected total cost. For the EPQ model, the optimum run time, which minimizes the total cost, is discussed. Various special cases are considered, including the maintenance learning effect. Finally, a numerical example is presented to illustrate the effects of PM, setup, breakdown and holding costs.     

Exact formulation of stochastic EMQ model for an unreliable production system

The purpose of this paper is to present an exact formulation of stochastic EMQ model for an unreliable production system under a general framework in which the time to machine failure, corrective (emergency) and preventive (regular) repair times are assumed to be random variables. For exact financial implications of the lot-sizing decisions, the EMQ model is formulated based on the net present value (NPV) approach. Then, by taking limitation on the discount rate, the traditional long-run average cost model is obtained. The criteria for the existence and uniqueness of the optimal production time in both the models are derived under general failure and specific repair time distributions. Numerical examples are devoted to find the optimal production policies of the developed models and examine the sensitivity of the parameters involved. Computational results show that the optimal decision based on the NPV approach is superior to that based on the long-run average cost approach, though the performance level strongly depends on the pertinent failure and repair time distributions.