Two-dimensional warranty policies based on the Weibull processes with synthesized indices

Abstract

The warranty concept is important to both the seller and the buyer of any consumer or commercial product. The development of warranty policies has been extensive but much of this work has concentrated on the one-dimensional problem. We consider in this thesis the two-dimensional case, where the warranty covers two scales (usage and age). So far, most of two-dimensional warranty regions are unfair according to the usage pattern of a customer. In this thesis, we develop new two-dimensional warranty policies, which are fair to all customers regardless of their various (and stochastic) usage pattern. To model and analyze new two-dimensional warranty policies, we also introduce the concept of "Reliability-Equivalent Curve". It is a new methodology for representing reliability of a system as a function of two variables - two different indices of a stochastic process. We define some specific models, which are appropriate and useful for reliability as a function of two variables, and develop estimation procedures of the model parameters including the synthesizing parameter. Then an empirical case study is performed with real data to confirm the applicability and the appropriateness and properties are explored by Monte Carlo simulation.