Three‐level regular designs with general minimum lower‐order confounding |
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| Authors: | Zhiming Li Tianfang Zhang Runchu Zhang |
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| Institution: | 1. LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, China;2. School of Mathematical Sciences, Xinjiang University, Urumqi 830046, China;3. College of Mathematics and Information Sciences, Jiangxi Normal University, Nanchang 330046, China;4. KLAS and School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China;5. Department of Statistics, University of British Columbia, BC, Canada V6T 1Z4 |
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| Abstract: | In this paper, we extend the general minimum lower‐order confounding (GMC) criterion to the case of three‐level designs. First, we review the relationship between GMC and other criteria. Then we introduce an aliased component‐number pattern (ACNP) and a three‐level GMC criterion via the consideration of component effects, and obtain some results on the new criterion. All the 27‐run GMC designs, 81‐run GMC designs with factor numbers $n=5,\ldots,20$ and 243‐run GMC designs with resolution $IV$ or higher are tabulated. The Canadian Journal of Statistics 41: 192–210; 2013 © 2012 Statistical Society of Canada |
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| Keywords: | Aliased effect‐number pattern clear effects criterion factorial design general minimum lower‐order confounding minimum aberration resolution MSC 2010: Primary 62K15 Secondary 62K05 |
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