The Optimal Maintenance Period for Repairable Product after Warranty Expiration under Renewing Warranty

Abstract

A model of the optimal maintenance period for repairable product after warranty expiration under renewing warranty is proposed. In the process to fulfilling warranty, the failures of product within warranty period happen randomly, the replacements of products successively failed with warranty period form a renewing process. Given failure rate of product, the period of fulfilling warranty is function of warranty period. User purchasing a product is considered an investment; the period of fulfilling warranty and the maintenance period after warranty make up the life cycle of product investment. Taking various cost factors into account, making model of the cost rate in life cycle of product investment under renewing warranty, the cost rate is function of maintenance period. Give the failure rate of product is an increasing function, it is derived that there is unique optimal maintenance period minimizing the cost rate. Finally, numerical example is given for illustration.