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Let X1, … , Xn be independent random variables with Xi having survival function Fλi, i = 1, … , n, and let Y1, … ,Yn be a random sample with common population survival distribution F, where c = ∑i=1nλi/n. Let Xn:n and Yn:n denote the lifetimes of the parallel systems consisting of these components, respectively. It is shown that Xn:n is greater than Yn:n in terms of likelihood ratio order. It is also proved that the sample range Xn:n − X1:n is larger than Yn:n − Y1:n according to reverse hazard rate ordering. These two results strengthen and generalize the results in Dykstra, Kochar, and Rojo [6] and Kochar and Rojo [11], respectively.

The concept of positive ageing describes the adverse effects of age on the lifetime of units. Various aspects of this concept are described in terms of conditional probability distributions of residual lifetimes, failure rates, equilibrium distributions, etc. In this paper we further analyse this concept and relate it to stochastic dominance of first and higher orders. In the process we gain many insights and are able to define several new kinds of ageing criteria which supplement those existing in the literature.