Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007
Simple failure biasing is an importance-sampling technique used to reduce the variance of estimates of performance measures and their gradients in simulations of highly reliable Markovian systems. Although simple failure biasing yields bounded relative error for the performance measure estimate when the system is balanced, it may not provide bounded relative error when the system is unbalanced. In this article, we provide a characterization of when the simple failure-biasing method produces estimators of a performance measure and its derivatives with bounded relative error. We derive a necessary and sufficient condition on the structure of the system for when the performance measure can be estimated with bounded relative error when using simple failure biasing. Furthermore, a similar condition for the derivative estimators is established. One interesting aspect of the conditions is that it shows that to obtain bounded relative error, not only the most likely paths to system failure must be examined but also some secondary paths leading to failure as well. We also show by example that the necessary and sufficient conditions for a derivative estimator do not imply those for the performance measure estimator; i.e., it is possible to estimate a derivative more efficiently than the performance measure when using simple failure biasing. © 1994, ACM. All rights reserved.
Donald Samuels, Ian Stobert
SPIE Photomask Technology + EUV Lithography 2007
Hendrik F. Hamann
InterPACK 2013
Lixi Zhou, Jiaqing Chen, et al.
VLDB
Michael C. McCord, Violetta Cavalli-Sforza
ACL 2007