Chapter 9 - Applications

Abstract

The contribution of reliability theory to some other disciplines is discussed in this chapter. Eventhough the concepts and theorems in reliability analysis are widely applied to many areas of study, we restrict our attention only to some selected areas in survival analysis, social sciences, risk analysis, information theory, mathematics, and statistics. In survival analysis, the discussion centers on proportional hazards and reversed hazards models, additive hazards models, proportional mean residual life models, and proportional odds models in the discrete case. The section on social sciences focuses attention on discrete income distributions, income inequality and wealth distributions in economics, the impossibility theorem of Arrow, and models for voting games in political science. A recent development is the interface of information theory with reliability functions. Information measures like Shannon entropy, Kullback-Leibler divergence and cumulative entropy and their extensions in determining the uncertainty in residual and past lifetime in the discrete case have been discussed considerably. Lastly, we mention certain mathematical concepts developed in the course of reliability analysis and their subsequent interactions in different fields.