A Generalized Age Replacement Policy for Systems Under Renewing Repair-Replacement Warranty

This paper presents a warranty cost model for repairable products when an age replacement policy is adopted in conjunction with the renewal of a minimal repair-replacement warranty. A study of the optimal choice of the preventive replacement age is also presented. When renewing a minimal repair-replacement warranty, either minimal repair is carried out or the product is replaced, depending on the length of repair time when the product failures occur during the warranty period. In this study, we develop mathematical formulas to evaluate the long-run expected cost rates during the life cycle of the product under the proposed cost models and determine the optimal preventive replacement ages by minimizing the objective functions. Furthermore, the effects of the renewing warranty on the optimal preventive replacement age and its corresponding expected cost rate are investigated for various situations regarding the warranty policy. This study extends the existing results on the age replacement policy by considering situations that are more practical, where both minimal repair and replacement are considered simultaneously upon product failure. Assuming that the product deteriorates with age, we illustrate our proposed cost model and its optimization using numerical examples and observe the impact of relevant parameters on the optimal solutions regarding the preventive replacement age.