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

TL;DR

This paper develops methods to compute moments of order statistics from dependent, non-identically distributed discrete variables and applies these results to analyze the reliability of complex systems.

Contribution

It introduces exact and approximate formulas for moments of order statistics from discrete variables, including applications to reliability of heterogeneous systems.

Findings

Derived formulas for moments of order statistics from discrete variables.

Tabulated moments for specific discrete distributions.

Applied results to compute system lifetime expectations and variances.

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.