On discounted discrete scheduled replacement model

This paper gives a chance of incorporating a discounting rate with discrete scheduled replacement model involving minor repair. 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. To address such problem of replacing a unit at idle times, this paper come up with an explicit expression of a discounted discrete scheduled replacement model for a unit subjected to three categories of failures (which are Category I, Category II and Category III failures). It is assumed that the replacement is at scheduled times 𝑁𝑇(𝑁=1,2,3,…) for a fixed 𝑇 0, is such that the model involves minimal repair and discounting rate (∝ 0). Finally, a numerical example is given to illustrate the theoretical results of this model.