A use-rate based failure model for two-dimensional warranty

We consider the problem of constructing probability model for product failure instances indexed by two scales, namely, age and usage. This is an important element in the analysis of two-dimensional warranty for automobiles. Specifically, we deal with models that apply to components or parts. The motivation for the same is stressed, and a model is proposed. The key feature of this model is: how use-rate affects life. Some existing models are then analyzed in the light of this feature, and the results are presented. Numerical examples are also provided to illustrate the application of this model in calculating warranty cost.