Asymptotics of Moments of Order Statistics and Failure Occurrence Sequences

The purpose of this paper is to develop new analytical techniques for the computation of asymptotics of the Laplace transforms (moments) of order statistics for several underlying distributions, among them the truncated Weibull and Makeham-Gompertz distributions. One of the main reasons to use moments of order statistics is their importance in practical applications for solving economic and technical problems in near real time. For example, with such techniques, one can form simple expressions for expectations of early failure times of big (multi-component) systems compounded from similar components. Applied statistics, optimal life-testing, operations research and prediction theory are also possible fields of applications of the approach developed here. The method presented here permits one to calculate estimates of remainder terms giving, thereby, the possibility of improving the precision of a result by increasing the number of terms in an expansion.