| A system failure usually has significant consequences either in cost or safety,for example,significant economic losses,casualties or environmental hazards.In most circumstances,prior to such failures,the system often undergoes one or several defective states.The discrete degradation model can be used to describe such failure process(normal-defective-failure).In the process,it can effectively reduce possible system failures to discover the defective state of the system through inspection and perform proper preventive maintenance on the system in advance.However,due to limitations of technologies and effects of environment,errors,like human errors and measurement errors of equipment,usually take place in practice,which finally result in imperfect inspections(inspection cannot reveal the health status of a system exactly).Therefore,the study of preventive maintenance modeling and analysis for the system subject to imperfect inspections based on discrete-state deterioration process has important theoretical significance and practical value.Inspired by some practical problems,this dissertation focuses on degrading system.Utilize the discrete degradation model,namely the delay time model,to study the degradation process.The methods,such as probability theory,renewal theory and numerical simulation,are used to develop the inspection and preventive maintenance model under imperfect inspection.The proposed model can be used to obtain the optimal maintenance policy.The main research contents of the dissertation are as follows.Firstly,for the single-component system in the static environment,consider the periodic inspection(same inspection intervals),preventive maintenance policy with imperfect periodic inspection for single-component system in the static environment is discussed.Considering imperfect periodic inspections with non-constant probabilities of inspection errors,combining imperfect repairs and preventive replacement,a novel preventive maintenance policy(inspection-repair-replacement policy)is investigated for a three-state system.Cost rate over an infinite time horizon and reliability of the system are derived by a recursive method.The problem of optimal maintenance policy is formulated by minimizing the cost rate.An optimization algorithm is proposed to obtain the optimal inspection interval and preventive replacement interval.Then,the steel converter system is provided to illustrate the performance and applicability of the proposed policy by sensitivity analysis of parameters and reliability analysis.Finally,limiting the number of imperfect repairs,another inspection-repair-replacement policy based on different imperfect repair models and different replacement strategies is obtained.The inspection interval,the preventive replacement interval and the upper limit of the number of imperfect repairs are jointly optimized.Then,the research is extended from different perspectives,including the type of inspection(periodic or non-periodic),the characteristics of the environment,and single-component/multi-component systems,the problems of inspection and preventive maintenance in three different situations are further discussed:First,the periodic inspection is extended to the non-periodic inspection,and preventive maintenance policy with imperfect non-periodic inspection for single-component system in the static environment is discussed.Considering both inspection-based replacement and age-based replacement,a two-phase imperfect inspection strategy(different inspection phases have different inspection intervals)is considered along with a hybrid preventive maintenance policy for a three-state system.To minimize the cost rate over an infinite time horizon,the length of inspection interval and the number of inspections are jointly determined for each phase of inspection.Numerical examples are provided to illustrate the proposed method and to explore some managerial insights.First,perform sensitivity analysis on some important parameters,and discuss how the optimal maintenance policy changes with pamaters.Then,to show the advantages of the proposed method,several special models,such as perfect inspection model,one-phase imperfect inspection model,pure inspection model,and pure age-based replacement model,are presented for comparison.Finally,an extended model is proposed,in which the system will not be replaced when there is a false positive.Second,the static environment is extended to the dynamic environment,and preventive maintenance policy with imperfect periodic inspection for single-component system in the dynamic environment is discussed.For a three-state system,considering the impact of environment on inspection errors,or considering the impact of environment on both inspection errors and system degradation,two imperfect periodic inspection and preventive maintenance model under dynamic environment are established.For each model,the expected cost over a finite time horizon is derived through the recursive method,and the optimal inspection and maintenance strategy is obtained by minimizing the expected cost.Then,several numerical examples are given to illustrate the performance of the proposed method.The results of the static environment model and the dynamic environment model are compared,and the optimal inspection and maintenance strategies under different model parameters are discussed,and some interesting management insights are obtained.Third,the single-component system is extended to the multi-component system,and preventive maintenance policy with imperfect periodic inspection for multi-component system in the static environment is discussed.Consider a multi-component system with multiple deteriorating components,different components are served by different dedicated teams,which constitutes Maintenance Team Coalition.The concept of Game Theory,namely the Shapley Value,is employed to identify the critical level of components fairly and set the penalty cost of each component failure accordingly to improve the reliability of components,especially those critical components,to improve the reliability performance of the entire system.Considering both imperfect periodic inspection and imperfect repair,a novel Reliability-Centered Hybrid Preventive Maintenance model is proposed.The inspection interval and the age-based replacement interval are regarded as decision variables,and the optimal maintenance strategy for each component is obtained by minimizing the cost rate over an infinite time horizon to balance the reliability of the component and the maintenance cost of the dedicated team.Several numerical examples illustrate that the proposed decision-making method is effective in handling such complex maintenance problems involving a coalition of maintenance teams.Considering various situations of imperfect inspection,e.g.,imperfect periodic inspection,imperfect non-periodic inspection,imperfect inspection in dynamic environment,imperfect inspection in multi-component system.This dissertation focuses on constructing preventive maintenance models for degrading system based on discrete degradation process.The study enriches the theoretical basis of preventive maintenance under imperfect inspection.In addition,through modeling and optimization,the optimal inspection and maintenance strategy can be obtained,which can provide guidance for the maintenance teams(when to schedule inspections,when to perform preventive maintenance,and what kind of maintenance behavior to carry out,etc.).Therefore,this dissertation is of important theoretical and practical significance. |
