A generalized geometric process based repairable system model with bivariate policy

Abstract

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 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n-1</sup> 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) <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">∗</sup> is obtained. Finally, numerical cases are applied to demonstrate the reasonability of this model.