Assessing Risk of a Serious Failure Mode Based on Limited Field Data

Nowadays, many consumer products are designed and manufactured so that the probability of failure during the technological life of the product is small. Most product units in the field retire before they fail. Even though the number of failures of such products is small, there is still a need to model and predict field failures for purposes of risk assessment in applications that involve safety. Challenges in modeling and predictions of failures arise because the retirement times are often unknown, few failures have been reported, and there are delays in field failure reporting. Motivated by an application to assess the risk of failure for a particular product, we develop a statistical prediction procedure that considers the impact of product retirements and reporting delays. Based on the developed method, we provide the point predictions for cumulative number of reported failures over a future time period and corresponding prediction intervals to quantify uncertainty. We also conduct sensitivity analysis to assess the effects of different assumptions on failure-time and retirement distributions