Optimization of cost and downtime for replacement model following the expiration of warranty

This paper deals with the optimal replacement policies following the expiration of warranty: renewing warranty and non-renewing warranty. If the system fails during its warranty period, it is replaced with a new one and if the system fails after the warranty period is expired, then it is minimally repaired at each failure. The criterion used to determine the optimality of the replacement period is the overall value function, which is established based on the expected downtime and the expected cost rate combined. Firstly, we develop the expected downtime per unit time and the expected cost rate per unit time for our replacement model when the cost and downtime structures of maintaining the system are given. The overall value function suggested by Jiang and Ji [Age replacement policy: a multi-attribute value model. Reliab Eng Syst Saf 2002;76:311–8] is then utilized to determine the optimal maintenance period based on the expected downtime and the expected cost rate. Numerical examples are presented for illustrative purpose.