An Optimal Age for Preventive Replacement Under Fully Renewing Combination Free Replacement and Pro Rata Warranty

Abstract

In the present article, an age-replacement policy is considered for non repairable products under the fully renewing combination free replacement and pro-rata warranty (FRW/PRW) policy. For the fully renewing FRW/PRW policy, whenever a product fails within the warranty period, it is replaced by a new one and a new warranty issued. Meanwhile, if the failure occurs during the first time interval (i.e., the free-replacement warranty (FRW) interval), replacement is made at no cost to the buyer; however, if the failure occurs during the second time interval (i.e., the pro-rata warranty (PRW) interval), replacement is made at a pro-rata cost to the buyer. Pre-determining the age for preventive replacement to be in a different certain interval, cost models from the buyer/user perspective are developed, and the corresponding local optimal replacement ages are derived such that the long-run expected cost rate is minimized. Then, the global optimal replacement age (i.e., without any constraint) is determined. Structural properties of these optimal policies are obtained and presented. Special cases of the model are also discussed. Finally, numerical examples are given for illustration, which provides a comprehensive study about the behavior of the optimal solution.

Keywords:

• Age-replacement policy
• Increasing failure rate
• Long-run expected cost rate
• Optimization
• Pro-rata warranty
• Renewing warranty

Mathematics Subject Classification:

• 90B25
• 90B50

Acknowledgments

The authors are very grateful to the referees for their insightful comments and suggestions which greatly improved the article. This research was supported by the National Science Council of Taiwan, under Grant No. NSC 97-2221-E-025- 004-MY3.