An extended geometric process repair model for a cold standby repairable system with imperfect delayed repair

摘要

This paper proposes an extended geometric process repair model (EGPRM) to generalise the geometric process repair model (GPRM), and studies a repair-replacement problem for a cold standby repairable system consisting of two dissimilar components and one repairman. Assume that each component after repair in the system is not always successive degenerative, and the failure component in the system is not always immediately repaired. Under these assumptions, using the extended geometric process, we consider a replacement policy N based on the failure number of Component 2 under which the system is replaced when the failure number of Component 2 reaches N. Our problem is to choose an optimal replacement policy N~* such that the average cost rate (i.e. the long-run average cost per unit time) of the system is minimised. The explicit expression of the average cost rate of the system is derived, and the corresponding optimal replacement policy N~* can be determined by minimising the average cost rate of the system. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.