GWLP

GWLP stands for Generalized Word Length Pattern, a summary used in the design of experiments to describe the aliasing structure of two-level fractional factorial designs. The concept applies to both regular and nonregular designs and provides a way to compare designs by how effects are confounded with each other.

For a given design, the defining relation (the set of words that equate to the identity) determines the pattern of aliasing. The GWLP is the vector (A1, A2, A3, …), where Ak denotes the number of defining words of length k. In regular designs this is a straightforward count of words of length k in the defining relation; in nonregular designs Ak is generalized to reflect the strength of aliasing among k-factor interactions and lower-order effects. In practice, smaller values of the early components, especially A1 and A2, indicate less aliasing between main effects and low-order interactions, and fewer confounded estimates.

Designers use the GWLP within the minimum aberration criterion, which seeks a design with the lexicographically smallest GWLP. This makes GWLP a standard tool for evaluating and selecting fractional factorial designs in industrial experiments and related fields.

Calculation is typically based on the design’s defining relation or contrast structure; software tools and statistical packages with DOE capabilities can compute GWLP from a design matrix. The concept remains a foundational element in assessing aliasing and guiding design choice, particularly when resource constraints require efficient experimental setups.