An extended geometric process repair model with imperfect delayed repair under different objective functions

This article studies an extended geometric process repair model for a simple repairable system with imperfect delayed repair. Assume that the system after repair is not always successively degenerative, and the repair is not also always delayed. Under these assumptions, based on the failure number N of the system, an optimal replacement policy N* is determined respectively by minimizing the average cost rate (ACR), maximizing the average availability rate (AAR), and optimizing the trade-off model of the ACR and the AAR. Finally, a numerical example is given to illustrate some theoretical results and the model applicability.