Analysis of field data under two-dimensional warranty

This paper proposes a method of estimating lifetime distribution for products under two-dimensional warranty in which age and usage are used simultaneously to determine the eligibility of a warranty claim. To analyze two-dimensional warranty data, univariate and bivariate approaches which use a reliability model including both age and usage can be considered. Most of previous works are centered on the univariate approach which assumes a functional relationship between age and usage. We consider a bivariate approach which assumes that the two variables are statistically correlated in a bivariate distribution. Methods of obtaining maximum likelihood estimators are outlined, and specific formulas are obtained for the cases where marginal distributions are Weibull. An illustrative example is given and numerical studies are performed to compare the two approaches.