The total time on test transform and the excess wealth stochastic orders of distributions

For nonnegative random variables X and Y we write X .TTTY if .0F-1(p)(1-F(x))dx . .0G-1(p)(1-G(x))dx all p . (0,1), where F and G denote the distribution functions of X and Y respectively. The purpose of this article is to study some properties of this new stochastic order. New properties of the excess wealth (or right-spread) order, and of other related stochastic orders, are also obtained. Applications in the statistical theory of reliability and in economics are included.