Some applications of the Laplace transform ratio order

Recently the new Laplace transform ratio stochastic order has been identified and studied in some detail. In this paper we first note a simple useful property of the Laplace transform ratio order. We apply this property to families of non-negative random variables that have the generalized semigroup property. We thus obtain a Laplace transform ratio order comparison for a host of non-negative random variables. Examples and applications of the resulting Laplace transform ratio order comparisons, which are of interest in reliability theory, are then described.