Recently new partial orderings s-SFR, s-FR, s-ST, s-CV and s-CX have been defined in the literature. These are more general in the sense that most of the earlier known partial orderings reduce to particular cases of these orderings. Moreover, these orderings have helped in defining a new and useful ageing criterion. In this paper, we discuss preservation properties of these orderings under mixtures. Results are expected to be useful in engineering and reliability, where mixtures of distributions arise naturally in numerous situations. Moreover, existing results, specifically for LR, FR and ST orderings under the operation of mixtures, reduce to special cases.

Recently defined classes of life distributions are considered, and some relationships among them are proposed. The life distribution H of a device subject to shocks occurring randomly according to a Poisson process is also considered, and sufficient conditions for H to belong to these classes are discussed.

This paper is about representations for equilibrium sojourn time distributions in Jackson networks of queues. For a network with N single-server nodes let hi be the Laplace transform of the residual system sojourn time for a customer ‘arriving' to node i, ‘arrival' meaning external input or internal transfer. The transforms {hi : i = 1, ···, N} are shown to satisfy a system of equations we call the network flow equations. These equations lead to a general recursive representation for the higher moments of the sojourn time variables {Ti : i = 1, ···, N}. This recursion is discussed and then, by way of illustration, applied to the single-server Markovian queue with feedback.