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Order statistics for correlated random variables and its application to at-speed testing

Order statistics for correlated random variables and its application to at-speed testing Order Statistics for Correlated Random Variables and Its Application to At-Speed Testing YIYU SHI, Missouri University of Science and Technology JINJUN XIONG and VLADIMIR ZOLOTOV, IBM T. J. Watson Research Center CHANDU VISWESWARIAH, IBM Microelectronics Although order statistics have been studied for several decades, most of the results are based on the assumption of independent and identically distributed (i.i.d.) random variables. In the literature, how to compute the mth order statistics of n correlated random variables is still a problem. This article proposes a recursive algorithm based on statistical min/max operations to compute order statistics for general correlated and not necessarily identically distributed random variables. The algorithm has an O(mn) time complexity and O(m+ n) space complexity. A binary tree-based data structure is further developed to allow selective update of the order statistics with O(nm2 ) time. As a vehicle to demonstrate the algorithm, we apply it to the path selection algorithm in at-speed testing. A novel metric multilayer process space coverage metric is proposed to quantitatively gauge the quality of path selection. We then show that such a metric is directly linked to the order statistics, and our recursive algorithm can thus be applied. By employing a http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Design Automation of Electronic Systems (TODAES) Association for Computing Machinery

Order statistics for correlated random variables and its application to at-speed testing

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References (31)

Publisher
Association for Computing Machinery
Copyright
Copyright © 2013 by ACM Inc.
ISSN
1084-4309
DOI
10.1145/2491477.2491486
Publisher site
See Article on Publisher Site

Abstract

Order Statistics for Correlated Random Variables and Its Application to At-Speed Testing YIYU SHI, Missouri University of Science and Technology JINJUN XIONG and VLADIMIR ZOLOTOV, IBM T. J. Watson Research Center CHANDU VISWESWARIAH, IBM Microelectronics Although order statistics have been studied for several decades, most of the results are based on the assumption of independent and identically distributed (i.i.d.) random variables. In the literature, how to compute the mth order statistics of n correlated random variables is still a problem. This article proposes a recursive algorithm based on statistical min/max operations to compute order statistics for general correlated and not necessarily identically distributed random variables. The algorithm has an O(mn) time complexity and O(m+ n) space complexity. A binary tree-based data structure is further developed to allow selective update of the order statistics with O(nm2 ) time. As a vehicle to demonstrate the algorithm, we apply it to the path selection algorithm in at-speed testing. A novel metric multilayer process space coverage metric is proposed to quantitatively gauge the quality of path selection. We then show that such a metric is directly linked to the order statistics, and our recursive algorithm can thus be applied. By employing a

Journal

ACM Transactions on Design Automation of Electronic Systems (TODAES) – Association for Computing Machinery

Published: Jul 1, 2013

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