Stochastic ordering for populations of manufactured items

Abstract

We develop a theory of stochastic orders for the age and the residual (remaining) lifetime for populations of manufactured identical items. The obtained theoretical results can be used by manufacturers or users for the justified decisions with respect to, e.g., the increase or decrease in the production rate or with respect to the necessary maintenance actions. Specifically, we show that if the random age of a population is smaller (resp. larger) in some stochastic sense than the defined equilibrium age, then it is also smaller (resp. larger) than the corresponding residual lifetime with respect to different stochastic orders. We discuss various stochastic comparisons between the random age and the residual lifetime for one or more populations. Some ageing properties of the random age and the residual lifetime have also been studied.