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【期刊论文】Minimum aberration blocking of regular mixed factorial designs
张润楚, Mingyao Aia, *, GuijunYangb, Runchu Zhangc
Journal of Statistical Planning and Inference 136(2006)1493-1511,-0001,():
-1年11月30日
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 isMAblocking 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.
Blocking, Fractional factorial design, Minimum aberration, Mixed-level, Regular
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张润楚, AI Mingyao & ZHANG Runchu
Series A Mathematics 4(2006)494-512,-0001,():
-1年11月30日
It is very powerful for constructing nearly saturated factorial designs to character-iza fractional factorial (FF) designs through their consulting designs when the consulting designs are small. Mukerjee and Fang employed the projective geometry theory to find the secondary worldength pattern of a regular symmetrical fractional factorial split-plot (FFSTP) design in terms of its complementary subset, but not in a unified form. In this paper, based on the connection between factorial dwsign theory and coding theory, we obtain some general and unified combinato-rial identities that relate the secondary wordlength pattern of a regular symmetrical or mixed-level FFSP design to that of its consulting design. According to theses identites, we further estab-lish some general and unified ruleds for identifying minimum secondary aberration, symmetrical or mixed-level, FFSP designs through their consulting designs.
coding theory, consulting design, minimum secondary aberrration, fractional factorial split-plot design,, projective geometry, wordlength pattern.,
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【期刊论文】Optimal criteria and equivalence for nonregular fractional factorial designs
张润楚, Ming-Yao Ai, , Peng-Fei Li and Run-Chu Zhang
Metrika (2005) 62: 73-83,-0001,():
-1年11月30日
By considering the so-called algebraic orthogonality among experimental runs, this paper introduces a new criterion, minimum inner-product moment (MIPM), for general asymmetrical designs, and shows that MIPM is equivalent to the minimum moment aberration (MMA) criterion for the natural weights. Furthermore, the relationship between the generalized minimum aberration (GMA) and some model-dependent efficiency criteria is investigated by using the complex contrasts. Thus, two new justifications of GMA criterion is given from the points of view of orthogonality among experimental runs and design efficiency. They are generalizations of the related results of Butler (2003) and Cheng, Deng, and Tang (2002) for twolevel factorial designs.
Design efficiency, Fractional factorial design, Generalized minimum aberration, Minimum moment aberration, Minimum inner-product moment, Minimum projection variance, Mixed-level, Nonregular.,
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【期刊论文】Choice of optimal initial designs in sequential experiments
张润楚, Peng-Fei Li, Min-Qian Liu*, Run-Chu Zhang
Metrika (2005) 61: 127-135,-0001,():
-1年11月30日
Combined-optimal designs (Li and Lin, 2003) are obviously the best choices for the initial designs if we partition the experiment into two parts with equal size to obtain some information about the process, especially for the case not considerign the blocking factor. In this pape, the definition of combined-optimal design is extended to the case when blocking factor is significant, and this new class of designs is called blocded combined-optimal designs. Some general results are obtained which relate 2k-pIII inital designs with their complementary designs when k>5n8, where n=2k-p. By applying these results, we are able to characterize 2k-pIII combined-optimal designs or blocked combined-optimal dwdigns in terms of their complementary designs. It is also proved that both 2k-pIII compbined-optimal and blocked combined-optimal designs are not minimum aberration designs when k>5n8 and n-1-k>2. And some combined-optimal and bloked combined -optimal designs with 16 and 32 runs are constructed fo rillustration.
Combined design, combined-ooptiimal design, complementary design, foldover, minimum aberration, wordlength pattern
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【期刊论文】Characterization of minimum aberration mixed factorials in terms of consulting designs*
张润楚, Mingyao Ai, , Runchu Zhang
Statistical Papers 46, 157-171 (2005),-0001,():
-1年11月30日
In this paper, by introducing a concept of consulting design and based on the connection between factorial design theory and coding theory, we obtain combinatorial identities that relate the wordlength pattern of a regular mixed factorial design to that of its consulting design. According to these identities, we further-more establish the general and unified rules for idejntifying mini-mum aberration mixed factorial designs through their consulting designs. It is an improvement and generalization of the results in Mukerjee and Wu (2001).
Coding theory, Consulting design, Minimum aber-ration, Mixed factorial design, Projective geometry, Wordlength pattern.,
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