A trigonometric approach to quaternary code designs with application to one-eighth and one-sixteenth fractions
The study of good nonregular fractional factorial designs has received significant attention over the last two decades. Recent research indicates that designs constructed from quaternary codes (QC) are very promising in this regard. The present paper shows how a trigonometric approach can facilitate a systematic understanding of such QC designs and lead to new theoretical results covering hitherto unexplored situations. We focus attention on one-eighth and one-sixteenth fractions of two-level factorials and show that optimal QC designs often have larger generalized resolution and projectivity than comparable regular designs. Moreover, some of these designs are found to have maximum projectivity among all designs.
An Algorithm for Sequentially Constructing Non-Isomorphic Orthogonal Designs and its Applications
We propose an algorithm for sequentially constructing nonis morphic orthogonal designs (including both regular and non-regular orthogonal design ). An essential element of the algorithm is using minimal column base to reduce the computation s f r determining isomorphism between any two designs. By using this algorithm, we obtain t he complete catalogs of n k (k = 2; : : : ; n 1) two-level orthogonal designs for n = 12; 16, and 20. Based on this result, we study the statistical properties of the designs usi ng the extended word length pattern (EWLP) criterion. The minimum-aberration designs accordi ng to this criterion are obtained and provided for practical use. For 20-run designs, we disco ver two minimum-aberration designs that are not the projections of Hadamard matrices. The se d signs were not given in the literature previously.
Generating Systematic Supersaturated Designs
Practitioners are routinely faced with distinguishing between factors that have real effects and those whose apparent effects are due to random error. When there are many factors, the usual advice given is to run so-called main-effect designs (Resolution III designs in the orthogonal case), that require at least k + 1 runs for investigating k factors. This may be wasteful, however, if the goal is only to detect those active factors. This is particularly true when the number of factors is large. In such situations, a supersaturated design can often save considerable cost. A supersaturated design is a (fraction of a factorial) design composed of n observations where n < k + 1. When such a design is used, the abandonment of orthogonality is inevitable. This article examines the maximum number of factors that can be accommodated when the degree of the nonorthogonality is specified. Furthermore, interesting properties of systematic supersaturated designs are revealed. For example, such a design may be adequate...