Assessing mixture-model goodness-of-fit with an application to automobile warranty data

Changing market conditions and improved manufacturing quality are reflected in recent extensions of automobile warranty coverage from 12 month/12,000 miles to 5 years/50,000 miles and better. The reliability engineer´s challenge to predict future warranty claims over a longer lifetime becomes even more difficult as the number of possible causal factors evolve from the “vital few” associated with early Pareto problem solving, to more diverse external contributing factors. Using initial vehicle warranty claim data to predict future warranty claims becomes even more difficult as automobile design and the assembly process continuously evolve via engineering changes throughout the product life cycle. This paper demonstrates graphical techniques, hazard analysis, and likelihood ratio tests for testing goodness-of-fit, the hypothesis of predictive validity for the proposed models. This work shows that automobile warranty data appear more appropriately predicted as Weibull/uniform and Poisson/binomial mixtures than individual Weibull and Poisson processes. Changes in the way automobile manufacturers store and view warranty data are necessary to implement the types of models in this work and will allow linking to engineering and manufacturing data to evaluate the effectiveness of ongoing product and process design changes