An application of dynamic linear models for predicting warranty claims

Abstract

Extended warranty claims on consumer products can amount to 10–30% of product costs. The need for accurate forecasts of warranty claims over the term of the warranty is apparent. Current models for forecasting warranty claims utilize time-in-service, or actual product usage figures as the predictor in a linear regression model. At the beginning of the model year, this approach can lead to significant forecast error, as early trends are extrapolated out into the future. Prior model year data is much more mature, and as such, its incorporation into the forecast model can be very useful if there have not been significant changes in the manufacturing process or warranty policy. In particular, “autoregressive” approaches, wherein the regressor which is employed is prior model year failure data, can be very effective for predicting trends which are observed in the current model year. In this paper, both forecast approaches are incorporated into a unifying, linear statistical model. It is shown that the estimators based upon this model are equivalent to Kalman-filter smoothed estimates. Furthermore, it is shown that the Kalman-filter model estimates are a composite of the two regression model approaches. Several techniques are introduced which can be used to estimate the variance structure of the random error terms. In one approach, weighting factors, K t, are used, whose value is determined based upon the input of expert opinion, to adjust the weights given to the treatment of prior model year data.