Bounds on optimal replacement time of age replacement policy

Preventive replacement of units is an important maintenance activity to avoid failures and associated cost/down-time. One of the basic and simple replacement policies is the age replacement policy, where the unit is replaced upon a failure or at a prefixed age, whichever occurs first. In the literature, optimal policies are studied to find the prefixed replacement age in order to minimize the long-run average cost/down-time per replacement cycle. Due to its simplicity, the age replacement policy is easy to implement in practice and is one of the replacement polices that is included in undergraduate level courses and text books. However, the procedures to find the optimal replacement time have not been studied in detail, and in some cases the results are stated incorrectly or imprecisely. In this paper, we show the lower and upper bounds for optimal replacement time considering a general failure time distribution and present the conditions for the existence of a finite optimal replacement time for all types of distributions. Further, the bounds are presented for most of the well-known distributions that are used in reliability engineering. Finally, an algorithm is proposed to find the accurate optimal replacement time of this policy.