Reliability Modeling and Optimal Inspection Policy for Degradation System Considering Employee Fatigue and Vacation
In practical applications,engineering systems usually degrade as time goes by.Various inspection and maintenance policies have been designed and optimized for the degradation systems to improve their availability and meanwhile reduce the operational costs.However,in most of the existing studies,incorrect inspection results caused by human factors have been less taken into consideration,which may lead to the inaccuracy of the relia-bility model and then influence the maintenance decision.To address this problem,the fatigue levels of the ma-intenance workers and their negative influences on inspections are taken into consideration to develop a new ma-intenance model for degradation systems.Base on the proposed model,the main objective of this paper is to de-sign an optimal inspection and maintenance strategy that minimize the long-run average cost of the system.More specifically,in this paper we consider a degradation system with three states,which are the good state,defect state and failure state,respectively.Systems in the defect state could still work but with a higher failure rate than those in the good state.When the system enters the failure state,it fails immediately and only a corrective maintenance action could restore it to the state to be as good as a new one.A maintenance worker is arranged to inspect and repair the system periodically during his working time.When the inspection result shows that the system is in the defect state,a preventive maintenance action is executed so as to restore the system to the state to be as good as a new one.Inspection results are assumed to be imperfect in this paper.Two inspection errors are considered:type I errors are that the system is in the good state while the inspection result shows that it is in the defect state,and type Ⅱ errors are that the system is in the defect state while the inspection result shows that it is in the good state.In the literature,the two types of inspection errors have been investigated by some researchers,but most of them have assumed that the probabilities of the errors are constants.The main contribution of this paper is to model the probabilities of the errors as increasing functions of the working time of the maintenance worker,which implies more inspection errors the worker may make when the continuous working time and the fatigue are accumulated.The fatigue accumulated at work could be mitigated or swept away by vacation.Based on this assumption,a new maintenance model is developed for such systems and a simulation algorithm is proposed to calculate the long-run average cost of the system.The cost includes inspection cost,downtime cost and maintenance cost.After that,an optimization problem is formulated:the main objection is to minimize the long-run average cost by taking the continuous working time W,the vacation time Vand the inspec-tion period T as the decision variables.Based on the proposed model and algorithm,a numerical example for the operation and maintenance of elevators is studied.First,we assume that for the maintenance worker the original working time W=5,the vaca-tion time V=2 and the inspection period T=1,respectively.The optimization results are W*=6,V*=1 and T*=0.4,and the long-run average cost is reduced from 359.3 to 307.6,which shows the efficiency of the proposed model.Furthermore,the sensitivity analysis is made for the cost parameters,including the maintenance cost for type I errors,the downtime cost,and so on.Based on the sensitivity analysis,we investigate the influ-ence of changing the cost parameters on the optimization results.The results show that for systems with a high cost of inspection errors,decision makers should increase employee vacation time and reduce the frequency of inspection;for systems with high preventive maintenance costs,decision makers should appropriately increase employee on-duty time and reduce the inspection frequency;systems with high downtime cost are suggested to increase the work period and the frequency of inspections at the same time.To sum up,in this paper the influences of the fatigue levels of the maintenance workers on the inspection results are taken into consideration.By modelling the relationship between the fatigue and the inspection correct-ness,the inspection and maintenance optimization model is developed.The main goal is to minimize the long-run average cost of the system by optimizing the work period,vacation period and the inspection interval of the worker.Future studies could pay more attentions to the multi-component systems,in which the dependence among the components may bring new challenges.Besides,in this paper the maintenance actions are assumed to restore the system to the state to be as good as a new one.More maintenance strategies,such as the imperfect maintenance,could be taken into consideration in the future studies.
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