Two-dimensional reliability modeling from warranty data

The failures of some systems depend on age and amount of accumulated usage. A common example of such systems is the automobile; the life of which is measured by both time in service and mileage. Warranty claims of the systems contain a large amount of information about reliability, such as failure times, usages and failure modes. Using warranty data to model reliability as a function of time and usage provides a more accurate and realistic estimator.This paper describes warranty data structure and censoring mechanism. A sequential regression method is proposed to model mileage accumulation from warranty claim data. The model and mileage failure data are used to evaluate the patterns of failure occurrences at different mileages. The paper then establishes the relationship between reliability and time in service and mileage. The unknown parameters are estimated by maximum likelihood method with time and mileage censoring. The reliability model is used to predict the number of warranty claims, and the number of failed vehicles which do not generate warranty claims due to mileage exceeding warranty limit. In the paper, an example is presented. The example shows that the predicted number of warranty claims has a good agreement with the actual number of claims.