Joint determination of production run length and number of standbys in a deteriorating production process

Two economic manufacturing quantity models with unrepairable and repairable standby key modules are proposed in this study that determine the economic production run length and the economic number of standbys in a deteriorating production process, where the key module of the production unit deteriorates over time and incurs some portion of defective items. For the model with unrepairable standbys, the active key module, once deteriorating, is replaced by a standby and the module itself is disposed. For the model with repairable standbys, the deteriorating key module is replaced by a standby and the module is then sent to the service center for maintenance. When completing the maintenance, it then joins the standbys for later production use. By minimizing the annual cost, which takes into account setup cost, holding cost, costs due to standbys and defective items, the economic production run length and the economic number of standbys are obtained for each of the proposed models.     

Choice of the best time scale for preventive maintenance in heterogeneous environments

A principal feature of the model considered in this paper is the presence of several time scales for lifetime measurements when similar objects operate in heterogeneous conditions. A typical example are lifetimes of an aircraft module which can be measured in the total time in air and in the number of flights. A family of lifetimes can be generated by considering a linear combination of the above two principal time scales. We consider a problem of finding an optimal maintenance period for an equipment operating during a single maintenance/replacement cycle, in heterogeneous environmental conditions. Our main concern is finding the time scale which provides the maximal value of the return (cost) functional. We consider two “principal” time scales (the operation time and the total number of shocks) and show numerically that the optimal linear combination of these two scales has also the minimal coefficient of variation (c.v.) of system lifetime. We develop some general theory to connect the optimality in terms of the return functional with the optimality in terms of c.v.     

Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair

The series system is one of the most important and common systems in reliability theory and applications. This paper investigates availability, maintenance cost, and optimal maintenance policies of the series system with n constituting components under the general assumption that each component is subject to correlated failure and repair, imperfect repair, shut-off rule, and arbitrary distributions of times to failure and repair. Imperfect repair is modeled through the basic idea of the quasi renewal processes introduced by H. Wang, H. Pham, A quasi renewal process and its applications in imperfect maintenance, International Journal of Systems Science 27(10) (1996) 1055–1062; 28(12) (1997) 1329. System availability, mean time between system failures, mean time between system repairs, asymptotic fractional down time of the system, etc., are derived, and a numerical example is presented to compare with the existing models by R.E. Barlow, F. Proschan, Satistical Theory of Reliability of Life Testing, Holt, Renehart & Winston, NY, 1975. Then two classes of maintenance cost models are proposed and system maintenance cost rates are modeled. Finally, properties of system availability and maintenance cost rates are studied. Optimization models to optimize system availability and/or system maintenance costs are developed, and optimum system maintenance policies are discussed through a numerical example.     

Forecasting both time varying MTBF of fighter aircraft module and expected demand of minor parts

A fundamental aspect of inventory management of fighter aircraft is to forecast the demand of minor parts installed in the main module. Most of the existing inventory models do not take into account the time-varying characteristics of modules composed of minor parts even though the demand rate of minor parts is sensitive to the conditions of module. In this paper, we propose random-effects regression models to forecast the mean time between failure (MTBF) of modules and the expected demand for the minor parts in the module based on time-varying characteristics of modules. Subsequently, we show how they can be applied to find necessary seasonal demand of minor parts. Our study is expected to contribute to ROKAF (Republic of Korea Air Force) in terms of providing base information for inventory policy for minor parts.     

Scheduling preventive maintenance for modular designed components: A dynamic approach

One of the benefits of modular design is ease-of-service. While modular design helps simplify field maintenance, extensive depot maintenance and spare modules are required to support the field maintenance. This study develops a dynamic approach for scheduling preventive maintenance at a depot with the limited availability of spare modules and other constraints. A backward allocation algorithm is proposed and applied to scheduling the preventive maintenance of an engine module installed in T-59 advanced jet trainers in the Republic of Korea Air Force. The algorithm developed by this study can be used to solve similar problems for various systems such as aerospace vehicles, heavy machinery, and medical equipment. The contribution of this study includes the uniqueness of the algorithm, the flexibility to deal with variables changing over time, and the ability to incorporate additional variables to handle complex situations.     

Optimum preventive maintenance policies maximizing the mean time to the first system failure for a two-unit standby redundant system

A two-unit standby redundant system with repair and preventive maintenance is considered under the following assumptions: (I) the inspection of an operative unit is made only if the other unit is in standby; and (II) an operative unit, which forfeited inspection due to assumption (I), undergoes inspection just upon repair completion of the failed unit (or inspection completion). We derive the Laplace-Stieltjes transform of the cumulative distribution function of the time to the first system failure and the mean time to the first system failure. Further, we obtain the necessary and sufficient conditions for an optimum preventive maintenance policy to exist with respect to the mean time to the first system failure. More importantly, under certain conditions, we find the analytical form of an optimum inspection time maximizing the mean time to the first system failure. A numerical example is presented.The work reported in this article was supported by the National Institutes of Health under Grant No. GM-16197-05. The authors would like to express their appreciation to Professor D. L. Jaquette and Professor R. Vasudevan, University of Southern California, for their advice and encouragement.     

Queueing Models for Optimizing System Availability of a Flexible Manufacturing System

This research investigates two maintenance float models in a flexible manufacturing system (FMS). We use classical queueing theory to study the characteristics of the fractional utilization of the system. A mathematical program is constructed to determine the optimal number of floats of an important module used in the FMS and the optimal capacity of the repair station.     

Determination of the optimal accelerated burn-in time under Arrhenius–Lognormal distribution assumption

Burn-in has been widely used as an effective procedure for screening out failed electronic products during the early-failure period, before shipment to the customers. Environmental stress such as temperature is increasingly being used to effectively shorten the burn-in time, and this method is usually called an accelerated burn-in test. When different stress levels are chosen for the burn-in operation, the burn-in times must be determined. An Arrhenius–Lognormal distribution can describe the lognormal lifetime of electronic products under different temperature levels. In this paper, the Arrhenius–Lognormal distribution and its mean residual life function are applied to the accelerated burn-in cost model, and a genetic algorithm is used to solve for the optimal burn-in time. We choose a real TFT–LCD module as an example, and determine its optimal accelerated burn-in time. A sensitivity analysis of the TFT–LCD module case shows the effect of model parameters on optimal burn-in time.     

A novel optimal preventive maintenance policy for a cold standby system based on semi-Markov theory

A novel optimal preventive maintenance policy for a cold standby system consisting of two components and a repairman is described herein. The repairman is to be responsible for repairing either failed component and maintaining the working components under certain guidelines. To model the operational process of the system, some reasonable assumptions are made and all times involved in the assumptions are considered to be arbitrary and independent. Under these assumptions, all system states and transition probabilities between them are analyzed based on a semi-Markov theory and a regenerative point technique. Markov renewal equations are constructed with the convolution of the cumulative distribution function of system time in each state and corresponding transition probability. By using the Laplace transform to solve these equations, the mean time from the initial state to system failure is derived. The optimal preventive maintenance policy that will provide the optimal preventive maintenance cycle is identified by maximizing the mean time from the initial state to system failure, and is determined in the form of a theorem. Finally, a numerical example and simulation experiments are shown which validated the effectiveness of the policy.     

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.     

Stationary availability of a semi‐Markov system with random maintenance

We consider a reparable system with a finite state space, evolving in time according to a semi‐Markov process. The system is stopped for it to be preventively maintained at random times for a random duration. Our aim is to find the preventive maintenance policy that optimizes the stationary availability, whenever it exists. The computation of the stationary availability is based on the fact that the above maintained system evolves according to a semi‐regenerative process. As for the optimization, we observe on numerical examples that it is possible to limit the study to the maintenance actions that begin at deterministic times. We demonstrate this result in a particular case and we study the deterministic maintenance policies in that case. In particular, we show that, if the initial system has an increasing failure rate, the maintenance actions improve the stationary availability if and only if they are not too long on the average, compared to the repairs ( a bound for the mean duration of the maintenance actions is provided). On the contrary, if the initial system has a decreasing failure rate, the maintenance policy lowers the stationary availability. A few other cases are studied. Copyright © 2000 John Wiley & Sons, Ltd.     

The maintenance of bidirectionally patrolled machines

The problem considered is that of maintaining a set of N stations(machines, production facilities) which are set out along aline and numbered, say, from left to right, 1 to N. The stations(which are not necessarily identical) are maintained and repairedif necessary by one operative, who patrols them first from leftto right in the order 1 to N and then from right to left inthe order N - 1 down to 1 and so on. It is assumed that breakdowns at station i occur completelyat random in running time at an average rate 1,. The time forthe operative to travel from left to right from station i -1 to station i (or from right to left from station i to stationi - 1) and then to carry out routine maintenance at stationi is assumed to be a constant for this pair of stations, andis denoted by w,. If, on amval at station i, the operative findsthe station out of action, then an additional time r, is neededto repair station i. It is assumed that r, is a constant forstation i. It is{small tilde}alsoa ssumed that a repair attemptat station i is successful with probability a, (not n d l y1). Thus the model caters for a heterogeneous set of stations,unequally spaced. Important performance measures for the system include the averagetime to traverse the line of stations, along with the mean availability.For individual stations, the availability, the mean time spentwaiting for attention, and the mean length of the stopped periodare all important. It is shown how all of these quantities canbe computed.     

Availability optimization of systems subject to competing risk

This paper considers a competing risk (degradation and sudden failure) maintenance situation. A maintenance model and a repair cost model are presented. The degradation state of the units is continuously monitored. When either the degradation level reaches a predetermined threshold or a sudden failure occurs before the unit reaches the degradation threshold level, the unit is immediately repaired (renewed) and restored to operation. The subsequent repair times increase with the number of renewals. This process is repeated until a predetermined time is reached for preventive maintenance to be performed. The optimal maintenance schedule that maximizes the unit availability subject to repair cost constraint is determined in terms of the degradation threshold level and the time to perform preventive maintenance.     

The effect of non-linear delay costs on workforce mix

This paper formulates a simple model to examine the appropriate mix of dedicated and flexible maintenance technicians (servers) required when total delay cost is a non-linear function of mean delay time. The primary decision variable is the number of flexible servers needed to minimize system-related costs. Non-linear delay costs appear to significantly increase the level of cross-training required compared with previous research using a linear cost function, which showed that a small proportion of flexible servers was sufficient. This has important implications for service system designers in regard to the amount of cross-training that might be appropriate.     

基于ARIMA的油田A类物资市场价格预测

本文研究了油田A类物资的市场价格预测。采用时间序列方法中的ARIMA模型,结合油田物资历史价格数据,分析并提出了一套针对油田A类物资的市场价格预测模式。该模式包括两个模块:样本集模块和ARIMA模块。样本集模块的主要功能是样本集的输入和实时更新;ARIMA模块包括了价格预测模型的拟合、检验、预测、评价、动态反馈和调整等主要环节。在该模式的指导下,以大庆油田A类采购物资中的小螺纹钢(20-HRB335)(天津、石家庄和沈阳3个产地)为例,对2011年各月的市场价格进行了模拟预测,预测的平均相对误差分别控制在2.13%,1.64%和1.82%,该结果得到了用户的认可。该预测模式的运用对大庆油田物资集团制定合理的物资采购方案提供了依据。结论部分对该预测模式的意义及存在问题进行了分析,并给出改进建议。     

非正态总体控制图和预防维修策略耦合优化的研究

主要探讨非正态有偏总体的过程监控和预防维修耦合优化问题。假定设备故障率随时间递增,设备发生异常前在正常状态的停留时间服从威布尔分布,一旦发生异常将导致过程均值漂移。采用赋权方差法构造X控制图,将过程监控和预防维修策略联系起来,结合生产不合格品损失、抽样成本及维修成本等,构建综合损失模型,提出动态抽样方案、控制图参数和预防维修间隔的确定方法。最后对模型进行了灵敏度分析。     

Two-stage generalized age maintenance of a queue-like production system

In general, the initiation of preventive maintenance should be based on the technical state as well as the operating state of a production system. Since the operating state of a production system is often subject to fluctuations in time, the planning of preventive maintenance at preset points in time (e.g. age/block replacement) cannot be optimal. Therefore, we propose a so-called two-stage maintenance policy, which - in a first stage - uses the technical state of the production system to determine a finite interval [t, t + At] during which preventive maintenance must be carried out, and - in a second stage - uses the operating state of the production system to determine the optimal starting time t̂ for preventive maintenance within that interval. A generalized age maintenance policy optimizing both t and At is formulated in the first stage. To this end, the actual starting time of preventive maintenance is modelled in terms of a uniform distribution over the maintenance interval. Moreover, the expected costs of preventive maintenance are modelled as a decreasing function of the interval size. An efficient algorithm is developed to demonstrate the optimal strategy for a queue-like production system, via numerical results that offer useful insights.     

Dynamic maintenance decision-making for series–parallel manufacturing system based on MAM–MTW methodology

Proper maintenance schedule is required to improve manufacturing systems’ profitability and productivity. A novel dynamic maintenance strategy is thus developed to incorporate both the single-machine optimization and the whole-system schedule for series–parallel system. Firstly, multiple attribute value theory and maintenance effects are considered in the single-machine optimization. A developed multi-attribute model (MAM) is used to determine the optimal maintenance intervals. Then, a series–parallel structure of the system is investigated in terms of the whole-system schedule. Maintenance time window (MTW) programming is presented to make a cost-effective system schedule by dynamically utilizing maintenance opportunities. The maintenance scheme achieved by using the proposed MAM–MTW methodology is demonstrated through a case study in a hydraulic steering factory. It is concluded that proper consideration of maintenance effects and time window leads to a significant cost reduction.     

基于综合重要度的动车组多部件系统机会维修策略研究

针对我国动车组列车现行维修方式,提出基于综合重要度序列的动车组多部件系统机会维修策略,对提高系统可靠度贡献大的关键部件进行准时优先维修。建立部件综合重要度指数计算模型,并依据其对部件维修优先级进行排序。以维修总成本最低为目标计算单部件最优维修周期及时刻,以系统维修总成本最低为目标,以关键部件的维修时刻为系统停机时刻建立考虑重要度的多部件系统机会维修模型。算例选取某型动车组四级修时更换的四部件系统为研究对象,讨论机会维修里程窗的大小及其偏移量对维修效果的影响,对比结果表明,考虑综合重要度的机会维修策略能够在维修费用基本持平的条件下,保证对系统可靠性贡献大的关键部件的可靠性,进而保证系统的整体可靠性。