Replacement Costs Under Warranty: Cost Moments and Time Variability

We consider a product that is sold under one of the two common warranty policies. Under the “pro rata” warranty policy, a failed item is replaced by a new one or is repaired at a cost prorated to the age of the failed item. Under the “free replacement” warranty policy, replacements or repairs during the warranty period are provided by the supplier free of charge to the buyer. Assuming that successive failure times form a renewal process, we derive moments of the total replacement cost for both policies during the product life cycle (0, t]. We also provide an extension to time-varying failure time distributions in the case of the pro rata warranty policy.