This thesis is concerned with the methods 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. For such a situation, it is desirable to analyze the field age and usage data with a bivariate lifetime distribution.
Field data with and without covariates are considered. Methods of obtaining maximum likelihood estimators for the case without covariates and pseudo maximum likelihood estimators for the case with covariates are outlined, their asymptotic properties are studied and specific formulas for bivariate weibull distribution are obtained. Numerical examples are given and simulation studies are performed to investigate the effects of the degree of dependency between the two variables. The proposed method is compared with the existing method which assumes a linear relationship between the two variables.
