First and Last Triggering Event Approaches for Replacement With Minimal Repairs

To make effective use of a running system, this paper proposes that, when replacement times could be scheduled at a planned time T of operation, and at a number N of minimal repairs, the newly proposed approach of whichever occurs last should be employed into optimizations for policy consideration. The replacement policy with the classical approach of whichever occurs first is also used to make comparison with the approach of whichever occurs last. Further, using the overtime technique, a replacement scheduled at time T in this paper is modified to be done at the first failure after T has arrived, to avoid probable interruptions for running jobs. That is, the system is replaced at failure N before time T, or at the first failure after T has arrived, whichever occurs first, and last, respectively. The policies acting on the approaches of first and last with minimal repairs are analyzed in detail, and their expected cost rates are formulated. Optimal solutions for separate and bivariate T and N are obtained and compared analytically.