We develop a theory of stochastic orders for the age and the residual (remain-
ing) 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.

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• Stochastic ordering for populations of manufactured items