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Minimum aberration blocking of regular mixed factorial designs

Institution:	1. LMAM, School of Mathematical Sciences, Peking University, Beijing 100871, People''s Republic of China;2. Department of Statistics, Tianjin University of Finance and Economics, Tianjin 300222, People''s Republic of China;3. LPMC and School of Mathematical Sciences, Nankai University, Tianjin 300071, People''s Republic of China;1. College of Information Science and Engineering, Xinjiang University, Urumqi, 830046, China;2. College of Software, Xinjiang University, Urumqi, 830046, China;3. Key Laboratory of Signal Detection and Processing, Xinjiang University, Urumqi, 830046, China;4. Department of Rheumatology & Immunology, People''s Hospital of Xinjiang Uygur Autonomous Region, Urumqi, 830046, Xinjiang, China;5. Xinjiang Clinical Research Center for Rheumatoid Arthritis, Urumqi, 830046, Xinjiang, China;1. School of Statistics, Qufu Normal University, Qufu 273165, China;2. Department of Statistics, Pennsylvania State University, University Park, PA 16802, USA;3. Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, ON N2L 3G1, Canada

Abstract:	It is known by Zhang and Park (J. Statist. Plann. Inference 91 (2000) 107) that there are no minimum aberration (MA) designs with respect to both treatments and blocks for blocked regular mixed-level factorial designs. So it should be compromised between the block wordlength pattern and treatment wordlength pattern. Two methods are considered in this article. The first is MA blocking scheme of an MA design. The other is to combine the components of the two wordlength pattern vectors into one combined wordlength pattern according to the modified hierarchical assumptions and an appropriate ordering of the numbers of alias or confounding relations. The relationship between the two types of optimal blocked designs is investigated. A complete catalogue of optimal blocked regular mixed factorial designs of the above two types with 16 or 32 runs is given.

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