On discounted discrete scheduled replacement model

An operating unit sometimes cannot be replaced at the exact optimum replacement time for some reasons. The unit may be rather replaced at idle times, such as a day, a week, a month, a year and so on. So to address such problem of replacing a unit at idle times, this paper come up with a discounted discrete scheduled replacement model for a unit. It is assumed that the replacement is at scheduled times NT(N=1,2,3,…) for a fixed T>0, such that the model constructed involves minimal repair and discounting rate (∝ >0). The unit considered in this paper is subjected to three categories of failures, which are Category I, Category II and Category III failures. Category I failure is an un-repairable one, which occurs suddenly. While Category II and Category III failures are both repairable, which occurs due to time and usage, and the two failures are minimally repaired. A numerical example is provided, so as to investigate the characteristics of the model presented and determine the optimal discrete replacement time (N^*) of the unit.