The Optimal Maintenance Policy Of Several Repairable Systems

In the past several decades,the maintenance modeling of the system has attracted great attention of researchers.The single component system,two-component system and multi component system are also concerned by scholars.The optimal replacement policy of the repairable model mainly include the single variable policy based on the working time or failure numbers of the system and the bivariate policy based on the working time and failure times.The degradation process of the system is generally described by geometric process,that is,the continuous working time and repair time of system are described by geometric process.In this dissertation,the extended geometric process is quoted to describe the continuous working time and repair time of system,which overcomes the shortcoming of strict monotonicity of geometric process.It is also considered that repairman having vacation when the system is working,which can increase system revenue.The traditional model is only based on the repair after system failure,this dissertation considers the catastrophic failure which can not be repaired and generalizes repairable failure to two types of failure,and preventive repair is also considered.The single component system,two-component system and series(parallel) system are studied,the following five repairable models are established by using the renewal process theory,and the optimal maintenance policy is studied.1.A simple system with preventive repair is considered.As the system working age is up to a specified time T,the system is repaired preventively.When the system failure,it is repaired immediately.The time interval of preventive repair and the failure correction is described by the extended geometric process.The bivariate policy(T,N) based on the failure number N and the working threshold T is considered,and the average cost rate function C(T,N) is derived.The existence and uniqueness of optimal bivariate replacement policy is obtained theoretically when minimum the C(T,N).Numerical cases verify the theoretical analysis,and the sensitivity analysis of the parameters is carried out.2.A single component system with a repairman is proposed.The repairman completes other work to increase the profit of the system when the component is working.It is assumed that the successive working time and the successive repair time are described by the extended geometric process.The average cost rate function based on the type ? failure and two types of failures(type ? and type ?) are derived respectively,the optimal replacement policy is studied and sensitive analysis of parameters is carried out.3.A new repair model of two-component system with two types of failures(type ? and type ?) is proposed,component 2 has random failure and the system is repaired after type ? failure.The system is replaced preventively at the N th type ? failure or at the total damage level of component 2 exceeds Z but less than l,or is replaced correctively at the first type ? failure or cumulative damage level of component 2 exceeds l.Successive working time and continuous repair time are described by extended geometric process.The repairman has multiple vacation when the system is working.The average cost rate function and is derived and an alternate optimization algorithm is designed to obtain the optimal replacement policy,and sensitive analysis of parameters is performed.4.A new repair two-component cold standby system.It is assumed that the consecutive working time follows decreasing geometric process,and the repair time is a constant for component 1.For component 2,the failure process during working time follows Generalized Polya Process,and it is rectified by Generalized Polya Process repair when it fails.Component 1 is assumed to have priority in use.The average cost rate function of the system is deduced based on the failure number of component 1.The existence and uniqueness of the optimal replacement policy is proved theoretically.Sensitivity of system parameters is analyzed.5.Extended preventive replacement models for series(parallel) system with n independent non-identical components are proposed.It is assumed that the system suffers from two types of failure(type ? and type ?).The system can be rectified by minimal repair when type ? failure occurs,and it is replaced when type ? failure occurs.The system is replaced preventively at the planned time T or random working time,and is replaced correctively at the type ? failure occurs.Preventive replacement first model and preventive replacement last model are studied.The average cost rate function of the series(parallel) system under the different cases are obtained respectively.The optimal preventive replacement time based on minimization of the average cost rate function is obtained theoretically.Numerical examples verify our theoretical results.