New repairable system model with two types repair based on extended geometric process

A simple repairable system with one repairman is con-sidered. 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 re-placement policy which is usually based on the failure number or the working age of the system, the bivariate policy (T, N) is con-sidered. 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 sensi-tivity analysis of the parameters is carried out.