Contributed Session: Experiment Design
2^n-m Designs with Minimum Aberration
Minimum aberration designs play a fundamental role in the practical choice of factorial designs. Their characterization is an important problem in design theory. This presentation will focus on the approach for characterizing minimum aberration 2^n-m designs in terms of their complementary designs. We will discuss some general and explicit relationships between the wordlength pattern of a 2^n-m design and that of its complementary design and their application to the characterization of minimum aberration designs. Results on construction of minimum aberration 2^n-m designs will be presented. [Hegang Chen, Dept. of Epidemiology & Biostatistics, Case Western Reserve Univ., Cleveland, OH 44106, USA; firstname.lastname@example.org ]
Algorithmic Construction of Optimal Mixed-Level Designs
William W. Li
For mixed-level designs orthogonality can be hard to achieve without a large number of runs. Some methods have been proposed to construct mixed-level designs with high efficiencies. While most of the existing methods depend on the combinatorial structures of designs, this paper provides a general algorithmic approach which can be applied to any mixed-level designs. The columnwise-pairwise (CP) algorithms proposed in the paper produce many designs with higher efficiencies in comparison with the existing results, such as the nearly orthogonal array proposed by Wang and Wu (1992).
[William W. Li, 3011 Woodland Hills Drive, #22; Ann Arbor, MI 48108 USA; email@example.com ]
Estimation Capacity Aspects of Experimental Designs
Don X. Sun
Plackett-Burman and related non-group theoretic designs have traditionally been used only for main-effect plans due to their complex aliasing structure of factor interactions. However, as shown in a successful data analysis example by Hamada and Wu (1992), such complex aliasing structure can be turned into advantages for estimating factor interactions with great flexibility. In this paper, we propose a new design criterion called estimation capacity to quantify the characteristics of such designs. Unlike the commonly used design criteria such as resolution and aberration that rely on the group structure, estimation capacity takes a direct approach to assessing a design's capability of estimating models. Therefore, this criterion can be used for both group-theoretic and non-group theoretic designs. The application of estimation capacity criterion is demonstrated in choosing optimal experimental plans from Plackett-Burman designs and related Hadamard matrices, blocking schemes for fractional factorial designs, and irregular fractions of factorial designs.
[Don X. Sun, Statistical Models & Methods Research Dept., Bell Laboratories 600 Mountain Avenue, Murray Hill, NJ 07974 USA; firstname.lastname@example.org ]
Exact Optimal Designs on a Circle or a Circular Arc
Fitting a circle to a set of data points on a plane has become very common in engineering, computer science and physics. An important practical problem is how to choose the locations of measurements on a circular feature. So far little attention has been paid to this design issue and only some simulation results are available. In this paper, under Berman's circular model, we show all phi_p-criteria (p in (-infty, +infty)) are equivalent and derive exact optimal designs on a circle or a circular arc for any sample size and sampling range. The optimal designs are then used to evaluate the efficiency of equidistant sampling method widely used in practice. These results also provide guidelines for users on sampling method and sample size selections.
[Huaiqing Wu, Dept. of Statistics, Univ. of Michigan, Ann Arbor, MI 48109, USA; email@example.com ]
Date created: 6/5/2001