Preventive maintenance models with random maintenance quality

In real-world environments it is usually difficult to specify the quality of a preventive maintenance (PM) action precisely. This uncertainty makes it problematic to optimise maintenance policy. This problem is tackled in this paper by assuming that the quality of a PM action is a random variable following a probability distribution. Two frequently studied PM models, a failure rate PM model and an age reduction PM model, are investigated. The optimal PM policies are presented and optimised. Numerical examples are also given.     

Availability optimisation for stochastic degrading systems under imperfect preventive maintenance

This paper deals with imperfect preventive maintenance (PM) optimisation problem. The system to be maintained is typically a production system assumed to be continuously monitored and subject to stochastic degradation. To assess such degradation, the proposed maintenance model takes into account both corrective maintenance (CM) and PM. The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modelled on the basis of the hybrid hazard rate model. The objective of the proposed PM optimisation model consists on finding the optimal reliability threshold together with the optimal number of PM actions to maximise the average availability of the system. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is presented to illustrate the proposed maintenance optimisation model.     

Optimal economic production quantity policy for a parallel system with repair,rework, free-repair warranty and maintenance

Hot standby redundancy maintains the working order of a system, repairs offer restoration in case of failure, and preventive maintenance (PM) prevents trouble. Warranties provide assurance to customers, and a superior warranty signifies higher product quality. The running costs of redundancy, maintenance and warranties influence decisions during product manufacture. Therefore, this paper presents an economic production quantity (EPQ) model for a parallel system with maintenance, production, and free-repair warranty (FRW) programmes. The production system begins with a basic unit and produces conforming items. PM is performed after the production run period and is classified as imperfect or perfect. If the basic unit fails, it is repaired and returned to operation after perfect PM; the spare unit is online only during the repair time of the basic unit. The spare will produce some number of defective goods, which are reworked in the same inventory cycle. The hot spare is minimally repaired if it fails in its standby or online mode. In this study, an inferior item is defined as one that satisfies specifications on inspection and is usable but is likely to incur postsale servicing costs when sold under an FRW. The total cost of this EPQ model includes setup, holding, PM, restoration, minimal repair, and warranty costs. The optimal production runtime is determined by minimising the total cost. Several cases are discussed in this paper, and the proposed model is illustrated using a numerical example and sensitivity.     

Impact of the use-based maintenance policy on the performance of cellular manufacturing systems

In this paper, a multi-objective integer programming approach is developed to investigate the impact of the use-based preventive maintenance (UPM) policy on the performance of the cellular manufacturing system (CMS). Under the UPM policy a maintenance schedule is established which provides for the performance of preventive maintenance (PM) only after a predetermined number of operating hours of machine use. This research indicates how PM and failure repair (FR) actions affect the effective availability of the machines and accordingly the machine and inter/intra-cell material handling costs under the UPM policy. The objective is to minimise the machine cost, inter- and intra-cell material handling and PM/FR costs. The proposed model is solved by an interactive fuzzy programming (IFP) approach to determine the best compromise solution from the decision maker point of view. IFP assumes that each objective function has a fuzzy goal and focuses on minimising the worst upper bound to obtain an efficient solution which is close to the best lower bound of each objective function. Compromise solutions are prioritised by two efficiency criteria, i.e. grouping efficiency and system availability. The performance of the proposed model is verified by a comprehensive numerical example.     

Optimal preventive maintenance strategy using two repair crews having different efficiencies: a quasi renewal process based modelling approach

This paper considers randomly failing, single-unit equipment subject to a periodic preventive maintenance (PM) policy. In case of failure between successive perfect PM actions (renewals), imperfect repairs are performed following a decreasing quasi-renewal process. One of two different maintenance crews can perform the repairs. One team is more experienced, and consequently more efficient than the other, but more costly. A mathematical model is developed in order to determine the PM period, T, and the kth repair, during a PM period, after which the repair team should be changed, minimising the average total cost per time unit over an infinite time span. It is also proved that an optimal solution in terms of the PM period always exists for any given system lifetime distribution and any set of maintenance costs. Numerical examples are presented and the obtained results are discussed.     

Vendor-managed inventory with consignment stock agreement for single vendor–single buyer under the emission-trading scheme

This paper presents a joint economic lot size (JELS) model for coordinated inventory replenishment decisions under the vendor-managed inventory (VMI) with consignment stock (CS) agreement and an emission-trading scheme. The paper assumes a single product that flows along a two-level supply chain system, with a single vendor and a single buyer. The total cost of the system is the performance measure, which is the sum of the vendor’s and the buyer’s total costs. The total cost includes the set-up and order costs, inventory holding costs, greenhouse gases (GHG) emissions tax and penalty costs. A mathematical model is proposed to determine: (1) the vendor’s production lot size quantity; (2) the number of shipments sent by the vendor to the buyer in a cycle; and (3) the production rate that minimises the total cost of the supply chain. Some numerical examples are carried out, as well as comparisons with the traditional JELS model for a classic two-level supply chain. Results show that the performance of the system is better when it is operated under a VMI with CS agreement, which is capable of reducing the traditional inventory holding costs and, for some values of given parameters, the GHG emissions tax and penalty costs.     

Maintenance-outsourcing contracts for a system with backup machines

In this paper, we consider a system with multiple components, each prone to failure, during which production is halted. Minimal repair is performed by an external contractor whenever a component breaks down. The contractor also conducts a general preventive maintenance (PM) for the whole system at pre-determined times. The contractor’s goal is to minimise maintenance-related costs; however, the system (made up of the contractor and the manufacturer, who gains revenue whenever the system is up) profit would be maximised if the revenue is also considered. Since these goals usually require different PM schedules, we propose a cost subsidisation scheme which coordinates the system. We then extend this basic model by considering the existence of a backup machine which will allow the system to continue running (albeit, generating a lower revenue) whenever a component fails. We show that the existence of such a machine reduces the profit difference between uncoordinated and coordinated systems.     

Cost minimization for periodic maintenance policy of a system subject to slow degradation

This paper considers a repairable system which undergoes preventive maintenance (PM) periodically and is minimally repaired at each failure. Most preventive maintenance models assume that the system improves at each PM so that the hazard rate is reduced to that of a new system or to some specified level. In this paper, we consider the situation where each PM relieves stress temporarily and hence slows the rate of system degradation, while the hazard rate of the system remains monotonically increasing. The optimal number and period for the periodic PM that minimize the expected cost rate per unit time over an infinite time span are obtained. We also consider the case when the minimal repair cost varies with time. Explicit solutions for the optimal periodic PM are given for the Weibull distribution case.     

Investigating reliability improvement of second-hand production equipment considering warranty and preventive maintenance strategies

A cost model for optimal reliability improvement of warranted second-hand production equipment is developed. The second-hand production equipment of age x is subjected to an upgrade action of a certain level u before it is sold with a Free Repair Warranty. We look at determining the optimal upgrade level when not performing and when performing periodic preventive maintenance (PM) during the warranty period. Two different PM strategies are considered: (a) periodic PM actions having the same efficiency level; (b) periodic multi-phase PM actions with a maintenance efficiency level which varies according to the phase. The proposed model aims at helping the dealer to find the optimal upgrade level to perform before selling the second-hand equipment, and to assess whether performing PM actions during the warranty period, according to a specific maintenance strategy, is worthwhile in terms of cost reduction. Numerical experimentations considering each PM scenario are performed in order to investigate how each PM strategy impacts the improvement level to be performed and the associated total expected cost. The obtained results showed that the expected total cost incurred by the dealer is governed by a sensitive trade-off between the warranty servicing cost and the costs associated with the reliability improvement, and with the PM performed during the warranty period. It is also found that the proposed new periodic multi-phase PM policy with an increasing maintenance efficiency level yields lower upgrade levels, inducing lower costs for the dealer.     

冰蓄冷系统运行经济性分析

建筑物的空调制冷系统采用蓄冷方式，可以节约运行费用，减少设备容量，转移用电高峰。蓄冷空调系统与常规空调系统相比，在运行的经济性方面有很多优点。因此开发了冰蓄冷系统运行经济性分析计算机软件，应用这套软件对实际工程项目进行分析，计算出各种冰蓄冷系统与相应常规系统的逐时耗电量、电费、全年运行费用和设备容量减少率等，并以图表的方式对两种系统的经济性作出综合的比较，能全面、直观的显示冰蓄冷系统的优点。     

A quantification algorithm for a repairable system in the GO methodology

The GO methodology is an effective method of system reliability analysis. It has been applied to non-repairable systems. This paper discusses the application of the GO method to a repairable system which is described by a Markov model and presents the quantification algorithm of the steady characteristics of the repairable system. The calculation formulas of the ordinary operators and the logical gates are derived and the steady reliability parameters of the system such as average operation probability and average failure frequency can be directly computed by the GO method. The result of an example shows that the algorithm is correct. The algorithm will be useful for the safety analysis of most engineering repairable systems.     

On the hazard rate process for imperfectly monitored multi-unit systems

The aim of this paper is to present a stochastic model to characterize the failure distribution of multi-unit systems when the current units state is imperfectly monitored. The definition of the hazard rate process existing with perfect monitoring is extended to the realistic case where the units failure time are not always detected (non-detection events). The so defined observed hazard rate process gives a better representation of the system behavior than the classical failure rate calculated without any information on the units state and than the hazard rate process based on perfect monitoring information. The quality of this representation is, however, conditioned by the monotony property of the process. This problem is mainly discussed and illustrated on a practical example (two parallel units). The results obtained motivate the use of the observed hazard rate process to characterize the stochastic behavior of the multi-unit systems and to optimize for example preventive maintenance policies.     

自动化集装箱码头运输系统配置的仿真优化

以新型自动化集装箱码头中间运输系统为研究对象,建立了自动化集装箱码头中间运输系统的仿真优化模型,并利用仿真优化方法搜索优化调度方案,最小化船舶靠岸后装卸作业的总时间和最大化各种设备的操作效率,优化模块使用遗传算法,整个程序使用C#语言编制.通过仿真计算表明能够非枚举地从所有可能的动态调度方案中搜到最佳方案:运输系统的设备利用率、系统作业时间,都得到了相应改善.     

An experiment of state estimation for predictive maintenance using Kalman filter on a DC motor

Preventive maintenance (PM) is an effective approach to promoting reliability. Time-based and condition-based maintenance are two major approaches for PM. No matter which approach is adopted for PM, whether a failure can be early detected or even predicted is the key point. This paper presents the experimental results of a failure prediction method for preventive maintenance by state estimation using the Kalman filter on a DC motor. The rotating speed of the motor was uninterruptedly measured and recorded every 5 min from 1 April until 20 June 2001. The measured data are used to execute Kalman prediction and to verify the prediction accuracy. The resultant prediction errors are acceptable. Futhermore, the shorter the increment time for every step used in Kalman prediction, the higher prediction accuracy it achieves. Failure can be prevented in time so as to promote reliability by state estimation for predictive maintenance using the Kalman filter.     

Optimal cycle time and inventory decisions in coordinated and non-coordinated two-echelon inventory system under inflation and time value of money

In this paper, a mathematical model is developed for a coordinated and non-coordinated two-echelon inventory system comprising of a single manufacturer and a single retailer. The objective of the model is to demonstrate the optimality of cycle time and inventory decisions under the phenomena of different inflation rates at the manufacturer and retailer points. Also, it is aimed at determining the annual net revenue of the supply chain (SC). In the proposed model, the present value of the inflated ordering/set-up costs, purchase/unit costs, carrying costs and the gross revenue is computed for the retailer, manufacturer and the SC. A numerical example is devised to illustrate the optimality of decision variables and the objective function. Also, the sensitivity analysis is carried out. Results show that the present value of the annual net revenue of the retailer, manufacturer and SC decreases with increased inflation rate at the retailer and decreased inflation rate at the manufacturer simultaneously.     

Optimizing preventive maintenance for mechanical components using genetic algorithms

This paper presents periodic preventive maintenance (PM) of a system with deteriorated components. Two activities, simple preventive maintenance and preventive replacement, are simultaneously considered to arrange the PM schedule of a system. A simple PM is to recover the degraded component to some level of the original condition according to an improvement factor which is determined by a quantitative assessment process. A preventive replacement is to restore the aged component by a new one. The degraded behavior of components is modeled by a dynamic reliability equation, and the effect of PM activities to reliability and failure rate of components is formulated based on age reduction model. While scheduling the PM policy, the PM components within a system are first identified. The maintenance cost and the extended life of the system under any activities-combination, which represents what kind of activities taken for these chosen components, are analyzed for evaluating the unit-cost life of the system. The optimal activities-combination at each PM stage is decided by using genetic algorithm in maximizing the system unit-cost life. Repeatedly, the PM scheduling is progressed to the next stage until the system's unit-cost life is less than its discarded life. Appropriately a mechatronic system is used as an example to demonstrate the proposed algorithm.     

Experimental investigation of the mechanical properties of polymer mortars with nanoparticles

The present paper examines the mechanical properties of polymer mortar (PM), with different weight fraction of nano-Al₂O₃ and nano-Fe₂O₃. The results showed that flexural and compressive strength measured of PM filled with nanoparticles were lower than plain polymer mortar but a considerably stiffness increase was observed for all formulations tested.     

Optimal imperfect preventive maintenance policy for equipment leased during successive periods

In this paper, we consider randomly failing equipment leased several times during their life cycle with a given warranty period. A mathematical model is developed to determine the optimal efficiency levels of preventive maintenance (PM) to be performed on the equipment between successive lease periods, maximising the expected total profit of the lessor over the equipment life cycle. The model considers the expected leasing revenue as well as the equipment acquisition cost and the average PM and repair costs. PM actions allow reducing the age of the equipment to a certain extent with a corresponding cost depending on the PM level adopted. The efficiency of the PM is determinant of the expected revenue during the next lease period. Given a set of K possible PM levels and the number of lease periods n over the equipment life cycle, K^{n?1 PM} strategies are possible. A genetic algorithm is proposed in order to obtain nearly optimal policies in situations where the number of possibilities K^n?1 is very high. Obtained numerical results are discussed. Small- and big-size instances of the problem are considered in the case of a service company in the oil and gas industry specialised in leasing specific equipment such as separators, to oil companies for production activities with a limited duration of several months like well testing or short production tests.     

Integrating run-based preventive maintenance into the capacitated lot sizing problem with reliability constraint

A joint model for integrating run-based preventive maintenance (PM) into the capacitated lot sizing problem (CLSP) is proposed, in which the production system is subject to deterioration with usage and PM operations are implemented to restore the system. In this model, both production and PM operations are restricted by the system's maximum capacity, and the system reliability has to be maintained above a threshold value throughout the planning horizon. By linearisation of the reliability constraints, the problem is formulated as a mixed-integer linear programming. An explanatory example is given to illustrate the advantage of the joint model comparing with the interval-based PM policy in terms of system's overall cost. A three-stage heuristic is proposed to solve this integrated model, which includes a Lagrangian-based heuristic for the CLSP. The numerical experiments are conducted to evaluate the performance of the developed heuristics and the computational results show that the heuristics can provide good feasible solutions for the corresponding models. The discussion of the results is finally given in detail.     

A new approach to reliability prediction is needed

This paper starts from the main objections regarding MIL-HDBK-217 and the BELLCORE method for reliability prediction, objections asserting that these methods are approximate, complicated and unconvincing. To support these assertions, and by applying techniques specific to reliability theory, the author has developed a reliability model which is plausible for certain elements of technical systems. The existence of such a model, which in practice is useless because the failure rate expression is too complicated, proves clearly the inefficiency of classical methods.