A simple method for predicting the cumulative failures of consumer products during the warranty period

In the design and manufacturing of both consumer and commercial products, an important design criteria is the length of the warranty period measured in calendar time. It is very important to know the expected number of failures during the warranty period. This paper provides an engineering tool that will predict the cumulative failures over the warranty period based on laboratory life data and the usage rate data for the products that are operated for only a limited fraction of the total available time. This method uses a joint distribution of the usage rate distribution and the laboratory life distribution to translate usage time to calendar time and not the mean usage since the product use in the field also follows a broad statistical distribution. The proposed technique permits an accurate calculation of the cumulative field failure over prospective warranty periods and thus is useful as an engineers' tool in design optimization as well as in decisions on product release.