Analyses of field data under two-dimensional warranty

Abstract

This thesis is concerned with the analyses of field data under two-dimensional warranty. To analyze such two-dimensional warranty data, reliability models including both age and usage should be considered since they are used simultaneously to determine the eligibility of a warranty claim. 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 have a joint bivariate distribution from the multivariate extension model. This thesis is divided into the following three parts. i) A method of estimating the lifetime distribution without covariates is considered. Methods of obtaining maximum likelihood estimators are outlined, and specific formulas are obtained for the cases where marginal distributions are Weibull. The bivariate approach is compared with the univariate approach, and it is shown that the bivariate approach is a more effective way of analyzing two-dimensional warranty data and, that the two approaches give comparable estimates when the two variables are strongly correlated. When a weak correlation exists, however, the bivariate approach performs considerably better than the univariate approach. ii) A method of estimating the lifetime distribution under the parametric regression model is considered. It is assumed that supplementary samples are available from the follow-up survey to obtain information about regressor variables of items not reported. A method of pseudo maximum likelihood is proposed and the asymptotic property is studied. The properties of the estimators are investigated by Monte Carlo simulation with respect to follow-up portion and the degree of dependency between the two variables. iii) A method of estimating lifetime distribution is proposed when after-warranty failures are incompletely reported to the original manufacturer. It is assumed that within-warranty failures are reported with probability ...