Box-Hunter resolution in nonregular fractional factorial designs

TL;DR

This paper extends the concept of Box-Hunter resolution from regular to simple nonregular fractional factorial designs, proving that the maximum resolution equals the maximum strength plus one, aligning with the minimum generalized wordlength.

Contribution

It proves that the maximum Box-Hunter resolution in simple nonregular designs equals the maximum strength plus one, unifying different resolution definitions.

Findings

Maximum Box-Hunter resolution equals maximum strength plus one.

Resolution in simple nonregular designs aligns with minimum generalized wordlength.

The paper discusses alternative approaches to defining resolution.

Abstract

In a 1961 paper, Box and Hunter defined the resolution of a regular fractional factorial design as a measure of the amount of aliasing in the fraction. They also indicated that the maximum resolution is equal to the minimum length of a defining word. The idea of a wordlength pattern has now been extended to nonregular designs by various authors, who show that the minimum generalized wordlength equals the maximum strength plus 1. Minimum generalized wordlength is often taken as the definition of resolution. However, Box and Hunter's original definition, which does not depend on wordlength, can be extended to nonregular designs if they are simple. The purpose of this paper is to prove that the maximum Box-Hunter resolution does equal the maximum strength plus 1, and therefore equals the minimum generalized wordlength. Other approaches to resolution are briefly discussed.