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August 1998 Two-level factorial designs with extreme numbers of level changes
Ching-Shui Cheng, R. J. Martin, Boxin Tang
Ann. Statist. 26(4): 1522-1539 (August 1998). DOI: 10.1214/aos/1024691252


The construction of run orders of two-level factorial designs with extreme (minimum and maximum) numbers of level changes is considered. Minimizing the number of level changes is mainly due to economic considerations, while the problem of maximizing the number of level changes arises from some recent results on trend robust designs. The construction is based on the fact that the $2^k$ runs of a saturated regular fractional factorial design for $2^k -1$ factors can be ordered in such a way that the numbers of level changes of the factors consist of each integer between 1 and $2^k -1$. Among other results, we give a systematic method of constructing designs with minimum and maximum numbers of level changes among all designs of resolution at least three and among those of resolution at least four. It is also shown that among regular fractional factorial designs of resolution at least four, the number of level changes can be maximized and minimized by different run orders of the same fraction.


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Ching-Shui Cheng. R. J. Martin. Boxin Tang. "Two-level factorial designs with extreme numbers of level changes." Ann. Statist. 26 (4) 1522 - 1539, August 1998.


Published: August 1998
First available in Project Euclid: 21 June 2002

zbMATH: 0929.62084
MathSciNet: MR1647693
Digital Object Identifier: 10.1214/aos/1024691252

Primary: 62K15

Rights: Copyright © 1998 Institute of Mathematical Statistics


Vol.26 • No. 4 • August 1998
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