Moments of order statistics from DNID discrete random variables with application in reliability

Abstract

In this paper, we present methods of obtaining single moments of order statistics arising from posibly dependent and non-identically distributed discrete random variables. We derive exact and approximate formulas convenient for numerical evaluation of such moments. To demonstrate their use, we tabulate means and second moments of order statistics from random vectors having some typical discrete distributions with selected parameter values. Next, we apply our results in reliability theory. We establish moments of discrete lifetimes of coherent systems consisting of heterogeneous and not necessarily independently working components. In particular, we obtain expression for expectations and variances of lifetimes of such systems. We give some illustrative examples.