Relationships Between Some Notions Which are Common to Reliability Theory and Economics

Our objective in writing this paper is to point out some interesting relationships between the commonly referred to indices of economic inequality, and a central notion used in reliability theory. Specifically, we show that the “Lorenz curve” and the “Gini index” of economics are related to the “total time on test” and the “mean residual life” of reliability theory. An advantage of observing these relationships is that we are now able to consolidate knowledge that has independently evolved in two apparently diverse areas, and furthermore, we are able to: show that a recently proposed test for exponentiality based on the Gini index is identical to the one based on the total time on test; obtain some new inequalities for the Lorenz curve, the Gini index, and the “redundancy” which is another measure of economic inequality; present some preservation properties for the Lorenz curve, which do not appear to be known; suggest that the Lorenz curve can be used to obtain a different interpretation of lifetime data; and characterize the limit of a class of lifetime distributions with decreasing failure rate in terms of its Lorenz curve.