By exploring the wordlength patterns of a two-level fractional factorial design, we introduce a concept of alias pattern and give accurate formulas for calculating the number of alias relations for any pair of orders of treatment effects as well as of treatment and block effects.
Based on an analytical expression between the generalized wordlength pattern and a uniformity measure, this paper converts the generation of GMA designs to a constrained optimization problem, and provides effective algorithms for solving this particular problem.
So it should be compromised between the block wordlength pattern and treatment wordlength pattern.
By introducing a concept of blocked consulting design and using MacWilliams identities and Krawtchouk polynomials in coding theory, we obtain combinatorial identities that govern the relationships between the partitioned wordlength patterns of a blocked regular mixed factorial design and that of its blocked consulting design.
The relationship between MD and the generalized wordlength pattern for multi-level design is given, then the level permutation technique is shown as a useful tool to search uniform designs.
A generalized version of the MacWilliams' identity is employed to express the detailed wordlength pattern in terms of complementary sets.
The generalized wordlength pattern (GWLP) introduced by Xu and Wu [2001. Generalized minimum aberration for asymmetrical fractional factorial designs. Ann. Statist.
Xu and Wu (2001) defined the generalized wordlength pattern (A1,…,Ak) of an arbitrary fractional factorial design (or orthogonal array) on k factors.
However, ambiguities exist in combining the two wordlength patterns and therefore, the optimality of such designs can be challenged.
Moreover, the relationships between MD and other design criteria such as the balance pattern and generalized wordlength pattern are also given.
By considering level permutation, the relationship between average wrap-around L2-discrepancy and generalized wordlength pattern is obtained.
