A prototype cost model of functional check decisions in reliability-centred maintenance

In this paper, the functional check task specified in reliability-centred maintenance (RCM) is discussed and a general cost model under the assumption of a non-decreasing degradation process is established to jointly optimise the threshold of potential failure and inspection intervals to minimise the expected operating cost per unit time. A gamma process is used to describe a random wear degradation process and illustrate the model.     

Reliability-centred maintenance analysis for a complex military system

The preventive-maintenance (PM) programme is a very importantdocument in the life cycle of a piece of equipment or system.The traditional method used within China to determine PM programmeshas many disadvantages, and some tasks in old programmes haveproved to be unnecessary. Through analysing a complex militarysystem (X system) by means of the reliability-centred maintenance(RCM) analysis, it is found that RCM analysis is more successfulthan the traditional method in deciding the PM programme. Thenew PM programme does not include unnecessary PM tasks includedin the old programme. Thus the performance of the X system isenhanced, because the cost is reduced without compromising availability.It is believed that RCM analysis in military industry will makea valuable contribution to the maintenance of weapon systemsand equipment.     

The availability model and parameters estimation method for the delay time model with imperfect maintenance at inspection

The delay time model (DTM) is widely used to model the two-stage failure process and is helpful for developing cost-effective inspection/maintenance plans. Imperfect maintenance is common in practice, but seldom considered in DTM. An improved DTM with imperfect maintenance at inspection has been developed based on the assumption of imperfect inspection maintenance and perfect failure maintenance. The model of the long-run availability for the improved DTM is established. Parameters estimation method and the test for goodness of fit method are given. Numerical simulations are performed to study the influence of imperfect maintenance on the long-run availability and to validate the credibility of the parameters estimation method. The results show that imperfect maintenance will decrease the long-run availability. The existence of the optimal inspection interval regarding the maximum long-run availability is tightly related to the improvement factor, which denotes the maintenance effect. The parameters estimation method proves credible. The maximum likelihood estimations of the reliability parameters can be easily achieved by the Genetic Algorithms (GAs) searching tool.     

Optimum policy for a production system with major repair and preventive maintenance

This study applies periodic preventive maintenance (PM) to a repairable production system with major repairs conducted after a failure. This study considers failed PM due to maintenance workers incorrectly performing PM and damages occurring after PM. Therefore, three PM types are considered: imperfect PM, perfect PM and failed PM. Imperfect PM has the same failure rate as that before PM, whereas perfect PM makes restores the system perfectly. Failed PM results in system deterioration and major repairs are required. The probability that PM is perfect or failed depends on the number of imperfect maintenance operations conducted since the previous renewal cycle. Mathematical formulas for expected total production cost per unit time are generated. Optimum PM time that minimizes cost is derived. Various special cases are considered, including the maintenance learning effect. A numerical example is given.     

On some properties of the Laplacian matrix revealed by the RCM algorithm

In this paper we present some theoretical results about the irreducibility of the Laplacian matrix ordered by the Reverse Cuthill-McKee (RCM) algorithm. We consider undirected graphs with no loops consisting of some connected components. RCM is a well-known scheme for numbering the nodes of a network in such a way that the corresponding adjacency matrix has a narrow bandwidth. Inspired by some properties of the eigenvectors of a Laplacian matrix, we derive some properties based on row sums of a Laplacian matrix that was reordered by the RCM algorithm. One of the theoretical results serves as a basis for writing an easy MATLAB code to detect connected components, by using the function “symrcm” of MATLAB. Some examples illustrate the theoretical results.     

The elixir of life: using a maintenance, repair and replacement model based on virtual and operating age in the water industry

Processing equipment in the water industry is subject to decayand requires maintenance, repair and eventual replacement. Thechallenge of competition within the water industry and the accompanyingregulatory regime requires that actions be integrated and costeffective. This is an industry, which has considerable dataon the failure of its equipment, but until recently very fewmodels of the maintenance process have been built. This paper describes the context of this problem for cleanwater processing where the equipment is that required to purifywater. It proposes a model based on the virtual and operatingage of the components. The operating age reflects the true ageof the equipment while the virtual age allows for the cumulativeeffect of maintenance actions performed on the equipment. Themodel also allows for different types of equipment by describingdegradation by Cox's proportional hazards model. Thus the specialfeatures of the equipment and environment in which the equipmentoperates are described by a set of characteristics, which modifythe hazard rate of the failure time of the equipment. This approachusing Cox's model with virtual and operating age can be appliedto other processing industries including the gas industry andthe ‘dirty water’ side of the water industry. The model is formulated as a stochastic dynamic programmingor Markov decision process and the form of the optimal policyis determined. This shows that repair and replacement shouldonly be performed when the equipment has failed and describesgeneral conditions when replacement is appropriate. The optimalpolicy is calculated numerically using the value iteration algorithmfor a specific example based on data on failure.     

Analysing maintenance data to gain insight into systems performance

The high cost of maintenance in the processing industry implies the need for optimal planning of maintenance strategy. In order to achieve this there is a need to understand the underlying failure processes, which are often very complex. In this paper, a new semi-parametric approach, combining Cox regression with density kernal smoothing, is introduced to estimate the underlying performance. The approach has been applied to several processes and it allowed insight into each process, which would not have been achieved if traditional approaches had been used. Particularly, the refurbishment of processes had a significant impact on the rate failure. This paper concludes by assessing this impact of refurbishment on the maintenance programme.     

A model of imperfect preventive maintenance with dependent failure modes

Consider a system subject to two modes of failures: maintainable and non-maintainable. A failure rate function is related to each failure mode. Whenever the system fails, a minimal repair is performed. Preventive maintenances are performed at integer multiples of a fixed period. The system is replaced when a fixed number of preventive maintenances have been completed. The preventive maintenance is imperfect because it reduces the failure rate of the maintainable failures but does not affect the failure rate of the non-maintainable failures. The two failure modes are dependent in the following way: after each preventive maintenance, the failure rate of the maintainable failures depends on the total of non-maintainable failures since the installation of the system. The problem is to determine an optimal length between successive preventive maintenances and the optimal number of preventive maintenances before the system replacement that minimize the expected cost rate. Optimal preventive maintenance schedules are obtained for non-decreasing failure rates and numerical examples for power law models are given.     

Bayesian semiparametric analysis for a single item maintenance optimization

We address the problem of a finite horizon single item maintenance optimization structured as a combination of preventive and corrective maintenance in a nuclear power plant environment. We present Bayesian semiparametric models to estimate the failure time distribution and costs involved. The objective function for the optimization is the expected total cost of maintenance over the pre-defined finite time horizon. Typically, the mathematical modeling of failure times are based on parametric models. These models fail to capture the true underlying relationships in the data; indeed, under a parametric assumption, the hazard rates are treated as unimodal, which, as shown in this paper, is incorrect. Importantly, assuming an increasing failure rate, as is typically done, we show, is way off the mark in the present context. Since hazard and cost estimates feed into the optimization phase, from a risk management perspective, potentially gross errors, resulting from purely parametric models, can be obviated. We show the effectiveness of our approach using real data from the South Texas Project Nuclear Operating Company (STPNOC) located in Bay City, Texas.     

Parameter estimation for partially observable systems subject to random failure

In this paper, we present a parameter estimation procedure for a condition‐based maintenance model under partial observations. Systems can be in a healthy or unhealthy operational state, or in a failure state. System deterioration is driven by a continuous time homogeneous Markov chain and the system state is unobservable, except the failure state. Vector information that is stochastically related to the system state is obtained through condition monitoring at equidistant sampling times. Two types of data histories are available — data histories that end with observable failure, and censored data histories that end when the system has been suspended from operation but has not failed. The state and observation processes are modeled in the hidden Markov framework and the model parameters are estimated using the expectation–maximization algorithm. We show that both the pseudolikelihood function and the parameter updates in each iteration of the expectation–maximization algorithm have explicit formulas. A numerical example is developed using real multivariate spectrometric oil data coming from the failing transmission units of 240‐ton heavy hauler trucks used in the Athabasca oil sands of Alberta, Canada. Copyright © 2012 John Wiley & Sons, Ltd.     

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.     

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.     

Life and Decay

The high cost of maintenance encourages managers to ‘optimize’their maintenance schemes. A facet of the ‘optimizing’performance is being able to predict more precisely the timeto failure of components and equipment. In many cases, failureresults from degradation. Modelling the degradation processis likely to give rise to better prediction of failure times.There has been a variety of approaches to the modelling, andmore recent authors have considered the issues of estimationThis paper reviews some of the models used, and the criteriafor selecting models, and considers some of the practical issues.The maintenance context of the modelling is also considered.     

Optimal maintenance service contract negotiation with aging equipment

In recent years, there has been a growing trend to out-source service operations in which the equipment maintenance is carried out by an external agent rather than in-house. Often, the agent (service provider) offers more than one option and the owners of equipment (customers) are faced to the problem of selecting the optimal option, under the terms of a contract. In the current work, we develop a model and report results to determine the agent’s optimal strategy for a given type of contract. The model derives in a non-cooperative game formulation in which the decisions are taken by maximizing expected profits. This work extends previous models by considering the realistic case of equipments having an increasing failure intensity due to imperfect maintenance, instead of the standard assumption that considers failure times are exponentially distributed (constant failure intensity). We develop a model using a linear function of time to characterize the failure intensity. The main goal, for the agent, is to determine the pricing structure in the contract and the number of customers to service. On the other hand, for the clients, the main goal is to define the period between planned actions for preventive maintenance and the time to replace equipments. In order to give a complete characterization of the results, we also carry out a sensitivity analysis over some of the factors that would influence over the failure intensity.     

Probabilistic analysis of a system with dependent units having a single repair facility subject to preventive maintenance

The paper deals with the availability and the reliability analysis of a system with dependent units having a single repair facility subject to preventive maintenance. The system initially consists of n-identical units (connected in parallel) each with failure rate λ_n. The failure rate of a unit at any given instant of time depends upon the number of units operating at that instant. The time to repair of a failed unit and the time for maintenance of the repair- facility are arbitrarily distributed whereas the time to failure of a unit is exponentially distributed. The results obtained have been compared with those obtained when the repair facility is not subject to preventive maintenance.     

The development of a hybrid intelligent maintenance optimisation system (HIMOS)

This paper reports on the development of a hybrid intelligent maintenance optimisation system (HIMOS) for decision support. It is a follow-up to an earlier paper published in the Journal of the Operational Research Society in 1995. Both papers refer to systems where there are very many components which may break down independently. When a component breaks down, corrective action (CO) is required. The problem is to determine the optimal maintenance policy, essentially the frequency of preventive maintenance (PM) which minimises the sum of down time due to PM and CO.HIMOS, like its predecessor IMOS, uses an ‘intelligent’ decision support system to carry out an automated analysis of the maintenance history data. Maintenance data are presented to the system and the most suitable mathematical model from a model-base is identified utilising a hybrid knowledge/case based system (KBS/CBR). Thus initially a rule base is applied to select a model, as in the case of IMOS. If no model is matched, the system reverts to its historical case-base to match the current case with a similar case that has been previously modelled. This double reasoning adds to the system's true learning capabilities (intelligence) and increases the rate of success of model selection. A prototype system is written in Visual Basic® for an IBM compatible PC. The study results include optimal PM intervals for a sample of industrial data sets. The results of the validation exercise of HIMOS against expert advice has shown that the system functions satisfactorily.     

Bi-objective workforce-constrained maintenance scheduling: a case study

In this paper, a real maintenance workforce-constrained scheduling problem is formulated as a bi-objective mixed-integer programming model with the aim of simultaneously minimizing the workforce requirements and maximizing the equipment availability. The skilled workforce is provided by internal and external resources using regular time, overtime and contracting. The equipment availability is measured by the downtime required for preventive maintenance (scheduled) and failure repair (unscheduled) jobs. We also encounter imminent or potential failures whose priorities depend on the severity of the failure on the system (secondary failure). The total weighted flow time is used as a scheduling criterion to measure the equipment availability; the weight of each job directly depends on the expected downtime resulting from the associated failure. The proposed model is verified using two comprehensive numerical examples and some sensitivity analyses. We conclude by discussing the results.     

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。     

Failure replacement and preventive maintenance spare parts ordering policy

This paper addresses inventory policy for spare parts, when demand for the spare parts arises due to regularly scheduled preventive maintenance, as well as random failure of units in service. A stochastic dynamic programming model is used to characterize an ordering policy which addresses both sources of demand in a unified manner. The optimal policy has the form (s(k),S(k)), where k is the number of periods until the next scheduled preventive maintenance operation. The nature of the (s(k),S(k)) policy is characterized through numeric evaluation. The efficiency of the optimal policy is evaluated, relative to a simpler policy which addresses the failure replacement and preventive maintenance demands with separate ordering policies.