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Numerous simulation softwares have been used in the past to evaluate the performance of the optimization models as regards maintenance activities, some of which are discussed below.
2.6.1Monte Carlo Simulation
The researchers used a Monte Carlo continuous time simulation to model the age of equipment, availability of equipment, maintenance activity backlog, and preventive maintenance policies and considered different wafer production scenarios. They analyzed and compared the different maintenance strategies on the status ofmanufacturing equipment and operating conditions of the wafer production flow. Theyfurther described how the combination of age and availability-based models increased the throughput and provided better results than the simple agebased models. In the same capacity,Bottaziet al(1992)presented the results of a systematic collection of actual failure times and preventive and corrective maintenance activities of 900 buses over a period of five years. They created an updatable database to estimate the failure distributions and to evaluate the influence of systematic preventive and corrective maintenance actions. They considered the total cost and availability as the objective functions, applied Monte Carlo simulation approach to evaluate and compare different maintenance policies, and presented the computational results. Billiton et al(2000), developed a model, which was based on the use of Monte Carlo simulation, to determine the total failure frequency and the optimum maintenance interval for a parallel-redundant system. The authors presented a modified distribution function assuming an exponential distribution for component useful life period and theWeibull distribution for the wear out period.
The procedure included construction ofa mathematical model and definition of the stopping rule in simulation for a parallel-redundant system. They stated that if the shape parameter β of the Weibulldistribution increases, the optimum
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maintenance interval could not be determined. Zhou et al(2005) developed an approach for sequential preventive maintenance scheduling based on the concept of age reduction due to imperfect maintenance actions. They considered an assumption for the time of imperfect maintenance actions basedon required reliability of the system. They utilized a hybrid recursive method based on an assumed improvement factor and increasing failure rate and developed an optimization model with a maintenance cost rate in the life cycle of the system as the objective function. Finally, they applied Monte Carlo simulation and described how their computational results can be used in decision support systems for maintenance scheduling. Marquez et al(2006) developed a simulation model to find the best preventive maintenance strategy in semiconductor manufacturing plants.
2.6.2Discrete-Event and Continuous Simulation
The researchers had in various ways considered various subsystems such as preventive maintenance subsystem, defects subsystem, condition-based subsystem, failure subsystem, corrective maintenance subsystem, and performance subsystemapplying discrete event and continuous simulation models and utilized SIMULINK to build up the model. They analyzed the structure of components and the relation of their constraints in a maintenance system and present the advantages of the model over classical stochastic process methods in a numerical example. In addition, they mentioned that obtained simulation results expressed the dynamic nature of maintenance systems.Burton et al(1989) developed a simulation model to evaluate the performance of a job shop while Goelet al(1973)presented a simulation model and developed a statistical analysis that considered three different types of preventive maintenance activities for components by defining stochastic and deterministic decision variables as well as unavailability and cost as the objectives. In addition, they made a 2-level sequential fractional factorial design in order to
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facilitate their simulation. By designing the simulation model based on experimental design approach, their model produced the preventive maintenance schedule for ground electronics systems.
In this research, the effectiveness of the preventive maintenance scheduling under different conditions such as shop load, job sequencing rule, maintenance capacity, and strategy was not displayed. Krishnan(1992)developed a simulation model to determine the maintenance schedule for an automated production line in a steel rolling mill plant. He considered three different maintenance policies as opportunistic, failure, and block with the percent of availability as the objective function. He showed that the existing maintenancepolicy only included the failure and block maintenance actions. By using the historical data of maintenance activities in the simulation model, the optimal preventive maintenance schedule was obtained in the form of checklist.Martorell and Serradell(1999)presented a simulation model in order to determine the frequency of the shutdown for periodic system overhaul, preventive and corrective maintenance, and inspections in a sugar manufacturing plant. They utilized a timedependentsimulation model to minimize the total cost including maintenance costs and downtime losses.
One of the most recent studies on application of simulation in preventive maintenance scheduling was presented by Hag mark et al(2007). They developed a simulation model to determine the level of reliability, availability and corrective and preventive maintenance at the early stage of design. After running the simulation model and analyzing the computational results, they mentioned that preventive maintenance and corrective maintenance policies have a high impact on the performance measures of just-in-time production systems and by combining the maintenance activities and just-in-time operations one can improve the effectiveness of the this kind of systems.
Greasley(2000)presented a simulation model to find the optimal maintenance
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planning in train maintenance depot for an underground transportation facility in UK.
He developed a simulation based on two different situations. The first situation assumed there is no random arrival and the second one consideredrandom arrivals and investigated the effect of the arrival on service level performance measures. He utilized ARENA as the simulation software and showed the effectiveness of the maintenance policies obtained by the simulation model.
Chan(2001) developed a simulation model to analyze the effects of preventive maintenance policies on buffer size, inventory sorting rules, and process interruptions in a flow line of a push production system. He presented the performance of the production system underdifferent operational conditions and preventive maintenance policies.Duffuaaet al(2001)presented a generic conceptual simulation model formaintenance systems. They defined this simulation model by constructing sevenmodules including an input module, maintenance load module, planning and scheduling module, materials and spares module, tools and equipment module,quality module and finally, a performance measure module. The authors mentioned that this model could be used to develop a discrete event simulation models in one ofthe commercial simulation software. In addition, they suggested that by using thismodel one can evaluate the need for contract maintenance and effect of availabilityof spare parts on performance measures in the system. Hanet al(2004)developed a finite time horizon model to achieve preventive maintenance scheduling of manufacturing equipment based on setback based residual factors, and used simulation to solve the model. They mentioned the consistencyof computational results and showed that simulation is a useful and effective method to solve such finite time problems. Jaturonnatee, Murthy and Boondiskulchok(2006)developed a preventive maintenance optimization model for a multi-component production process. They defined a combination of mechanical service, repair, and replacement activities for each component and
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useMarkov decision process to present the transition function of probability for maintenance activities. In addition, they considered required reliability of the system as the constraint and total preventive maintenance cost as the objective function of the model.
A simulation approach was utilized to find the optimal schedule as the solution procedure. The authors described that considering the combination of preventive maintenance activities could reduce more cost in comparison with the situation that different activities are considered separately. Their method only considered repair time delays and effect of preventive maintenance on the system‟s failure observed by condition monitoring and diagnostic resources.