Modeling And Optimization Of Dynamic Condtion-based Mainteance Considering The Proportional Hazards Model

Preventive maintenance is very crucial in maintaining the performance and reliability of a system.With the development of advanced sensor technology and signal processing techniques,condition-based maintenance(CBM)has been widely applied in a variety of industries and it has nowadays become a key preventive maintenance type for important systems.CBM decisions are made based on failure mechanisms.In many practical situations,the failure rate of a system depends not only on its age but also on covariates such as wind speed and vibration.The proportional hazards model(PHM)is very popular in reliability engineering for quantifying the effects of covariates and then integrating them into the failure rate function of a system.CBM considering the PHM is currently a hot topic in the research field of maintenance.Although various CBM policies have been proposed,most of them focused on the replacement policy or setting constant control limits for action-selection.The former omits that an effective and practical maintenance policy usually involves multiple maintenance actions.The latter challenges the uncertainty of the PHM which affects maintenance decision-making greatly.To overcome these drawbacks,this dissertation investigates the optimization problem of CBM policies with multiple maintenance actions and dynamic thresholds for systems using the PHM.The semi-Markov decision process and dynamic programming are employed for modeling and optimizing optimization problems,respectively.The graphical representations of obtained optimal policies are provided to guide practical maintenance implementation.The contributions are summarized as follows:(1)The evaluation of health state is a basis for CBM optimization.Existing methods for the PHM are subject to the disadvantages of low accuracy,low efficiency,and high memeory requirement.A recursive approach is proposed to handle this issue.In the approach,both the aging process and the covariate process are discretized,and then a transition probability matrix for each covariate state under an arbitrary time unit is constructed.These matrixes are recursively applied for calculating conditional reliability function and mean residual lifetime.The result of numerical examples shows that the proposed approach has high accuracy,fast computation speed,and small memory requirement.(2)A dynamic CBM policy for a single-unit repairable system is proposed.The system is subject to minor failure and catastrophic failure.At each inspection epoch,two dynamic control limits are set for selecting preventive maintenance actions.A modified policy-iteration algorithm is developed to handle the complex optimization problem,and the effectiveness of the algorithm is proved.The comparison with the traditional CBM policies confirms the superiority of the proposed policy.(3)The research objective is extended to a single-unit production-inventory system.The effects of the production process on maintenance decision-making are investigated.Taking advantage of the downtime while the maximum inventory level is reached,condition monitoring is performed and appropriate action is selected from no maintenance,preventive imperfect maintenance,and preventive replacement.When a failure occurs,corrective maintenance decisions can be made based on 1)The age at failure and the covariate state at the beginning of the production run(Scenario 1);or 2)Both the age and the covariate state at the beginning of the production run(Scenario 2).The optimization problems of the two scenarios are solved based on the policy-iteration algorithm by minimizing the long-run average cost rate.The result of numerical examples shows that scenario 1 is more cost-effective than scenario 2,while its optimal maintenance policy is more complex.(4)The research objective is further extended to a two-unit production-inventory system.Unit 1 deteriorates gradually and the deterioration state can only be revealed by condition monitoring.Unit 2 is subject to hard failure and the failure time follows a general lifetime distribution.The deterioration and failure processes of the two units are interdependent.Besides the stochastic dependence,economic dependence and structural dependence are integrated into the maintenance model.The dynamic CBM policy and the inspection interval are jointly optimized based on the policy-iteration algorithm by minimizing the long-run average cost rate.The result of numerical examples confirms the effectiveness of the proposed policy.This thesis covers several possible application areas of dynamic CBM.The proposed policies can save operation and maintenance cost obviously.The graphical representation of obtained policy provides efficient guildline for practical maintenance implementation.