Aggregate discounted warranty cost forecasting considering the failed-but-not-reported events

Warranty claims usually incur substantial costs to the manufacturers. In practice, it is not accurate or economical to reserve money for future claims based on the prediction of the overall (life cycle) warranty cost. As a more appropriate alternative, the aggregate warranty cost forecast technique can reduce the liquidity risks and improve the warranty service efficiency. In addition, when a product fails during the warranty period, a warranty claim will be counted only when the customer reports the failure to the manufacturer. This paper focuses on forecasting the discounted warranty cost, which depends on the product sales and failure processes, warranty terms, and customer behaviors, over arbitrary time interval. To characterize the failed-but-not-reported phenomenon, a flexible time-dependent function is proposed. We derive the mathematical formulations of related factors to discuss the modeling process of total discounted warranty cost over an arbitrary time interval (TDWCATI). The impacts of warranty length and customer reporting behavior are explored. The expectation and variance of the TDWCATI are obtained under the pro-rata warranty policy and the nonrenewable minimal-repair policy, which shows that the TDWCATI is useful in planning future warranty services and budgets over a specific time period.