Warranty repair demand prediction considering new sales and failed-but-not-reported phenomena

Customers are often offered free warranty repairs for a certain time period. In this paper, we study some important aspects in predicting warranty repair demand that are of interest to the manufacturer. The study is limited to a new product under a non-renewable free minimal-repair warranty policy. We consider that the installed base of the product varies with time due to both new sales and units being taken out of service. We explicitly address the fact that the customers may not always request repairs for failed units, i.e., so called failed-but-not-reported (FBNR) phenomena. For the case where the product failure time is exponential, we derive the closed-form expressions for the warranty repair demands for both an individual unit and the installed base. The insights into some risk-related quantities are also presented. A numerical example illustrates that understanding the properties of warranty repair demand is important for managing such obligatory repair services.