Modelling and analysis of two-dimensional warranty policies

Abstract

A two-dimensional warranty policy is a natural extension to a one-dimensional warranty policy. The warranty is characterized by a two-dimensional region in a plane with the horizontal axis representing time and the vertical axis the usage. The cost analysis of one-dimensional warranty policies has received a lot of attention. In contrast, such analysis for two-dimensional warranty policies has received very little attention. In this thesis, we carry out the cost analysis of a variety of two-dimensional warranty policies from the manufacturer's viewpoint. This is done using the System Approach which involves the following three steps - i.e. (i) modelling item failures, (ii) estimation of model parameters and (iii) analysis of models. We examine two approaches to modelling item failures. The first approach is based on a one-dimensional point process formulation involving conditional intensity function. This is an extension of the work of Moskowitz and Chun (1990). The second approach is based on a two-dimensional point process formulation and item failures are characterized through a bivariate distribution function. The shape of the warranty region and the terms of warranty define a family of policies. We consider a variety of two-dimensional failure free warranty (FRW), pro-rata warranty (PRW) and combination warranty policies for different warranty regions. We derive expressions for the expected warranty costs and the expected life cycle costs for models based on the two approaches indicated above and present some numerical results. Also, we discuss issues of interest to the manufacturer and the consumer. The research reported makes significant contribution to the study of two-dimensional warranties. The analysis of many policies involves one- and two-dimensional renewal functions. These require the solving of one- and two-dimensional renewal integral equations. We discuss alternate approaches (i.e. analytical and computational approaches) to solving such equations. In this context, the thesis makes the following new contribution - (i) a comparative evaluation of different estimators (proposed in the literature) for estimating the one-dimensional renewal function using simulation; (ii) two estimators for estimating the two-dimensional renewal function using simulation, and (iii) a numerical method for solving the two dimensional renewal integral equation.The problems of model parameter estimation is discussed briefly and further research are listed at the end of the thesis.