RESEARCH PAPERS: Reliability and Failure Analysis

Rank Transformations of Order Statistics

[+] Author and Article Information
J. H. Saringer

Department of Mechanical Engineering, University of Toronto, Toronto, Canada MSS 1A4

J. Mech. Des 104(3), 599-603 (Jul 01, 1982) (5 pages) doi:10.1115/1.3256393 History: Received May 04, 1981; Online November 17, 2009


Distributions of order statistics are shown to describe themselves recursively; hence items of a population of one order statistic, when ordered, can themselves be described by distributions of order statistics. A transformation carried out analytically or with a simple Fortran algorithm supplied transforms ranks from one level to another, making it possible to describe an ordered item of a population, which is itself an order statistic of some larger population, in terms of the larger parent population itself. This process is described as a “rank transformation” where an item “rank” is defined as the proportion of the population falling below that item. Examples are presented that demonstrate applications of this technique to the analysis of accelerated life data, probability plotting, and analysis of systems with redundancy.

Copyright © 1982 by ASME
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