A simple repairable system with one repairman is considered. As the system working age is up to a specified time T, the repairman will repair the component preventively, and it will go back to work as soon as the repa...A simple repairable system with one repairman is considered. As the system working age is up to a specified time T, the repairman will repair the component preventively, and it will go back to work as soon as the repair finished. When the system failure, the repairman repair it immediately. The time interval of the preventive repair and the failure correction is described with the extended geometric process. Different from the available replacement policy which is usually based on the failure number or the working age of the system, the bivariate policy (T,N) is considered. The explicit expression of the long-run average cost rate function C(T,N) of the system is derived. Through alternatively minimize the cost rate function C(T,N), the optimal replacement policy (T?,N?) is obtained, and it proves that the optimal policy is unique. Numerical cases illustrate the conclusion, and the sensitivity analysis of the parameters is carried out.展开更多
The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ fai...The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ failure occurs,the system will be repaired immediately,which is failure repair(FR).Between the(n-1)th and the nth FR,the system is supposed to be preventively repaired(PR)as the consecutive working time of the system reaches λ^(n-1) T,where λ and T are specified values.Further,we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type Ⅰ failure or the occurrence of the first type Ⅱ failure,whichever occurs first.In practice,the system will degrade with the increasing number of repairs.That is,the consecutive working time of the system forms a decreasing generalized geometric process(GGP)whereas the successive repair time forms an increasing GGP.A simple bivariate policy(T,N)repairable model is introduced based on GGP.The alternative searching method is used to minimize the cost rate function C(N,T),and the optimal(T,N)^(*) is obtained.Finally,numerical cases are applied to demonstrate the reasonability of this model.展开更多
基金supported by the National Natural Science Foundation of China(61573014)the Fundamental Research Funds for the Central Universities(JB180702)
文摘A simple repairable system with one repairman is considered. As the system working age is up to a specified time T, the repairman will repair the component preventively, and it will go back to work as soon as the repair finished. When the system failure, the repairman repair it immediately. The time interval of the preventive repair and the failure correction is described with the extended geometric process. Different from the available replacement policy which is usually based on the failure number or the working age of the system, the bivariate policy (T,N) is considered. The explicit expression of the long-run average cost rate function C(T,N) of the system is derived. Through alternatively minimize the cost rate function C(T,N), the optimal replacement policy (T?,N?) is obtained, and it proves that the optimal policy is unique. Numerical cases illustrate the conclusion, and the sensitivity analysis of the parameters is carried out.
基金supported by the National Natural Science Foundation of China(61573014)the Fundamental Research Funds for the Central Universities(JB180702).
文摘The maintenance model of simple repairable system is studied.We assume that there are two types of failure,namely type Ⅰ failure(repairable failure)and type Ⅱ failure(irrepairable failure).As long as the type Ⅰ failure occurs,the system will be repaired immediately,which is failure repair(FR).Between the(n-1)th and the nth FR,the system is supposed to be preventively repaired(PR)as the consecutive working time of the system reaches λ^(n-1) T,where λ and T are specified values.Further,we assume that the system will go on working when the repair is finished and will be replaced at the occurrence of the Nth type Ⅰ failure or the occurrence of the first type Ⅱ failure,whichever occurs first.In practice,the system will degrade with the increasing number of repairs.That is,the consecutive working time of the system forms a decreasing generalized geometric process(GGP)whereas the successive repair time forms an increasing GGP.A simple bivariate policy(T,N)repairable model is introduced based on GGP.The alternative searching method is used to minimize the cost rate function C(N,T),and the optimal(T,N)^(*) is obtained.Finally,numerical cases are applied to demonstrate the reasonability of this model.
