Fractional Factorial Designs with Admissible Sets of Clear Two-Factor Interactions

Date
2008-11-01
Authors
Wu, Huaiqing
Mee, Robert
Tang, Boxin
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Altmetrics
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Statistics
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Statistics
Abstract

We consider the problem of selecting two-level fractional factorial designs that allow joint estimation of all main effects and some specified two-factor interactions (2fi’s) without aliasing from other 2fi’s. This problem is to find, among all 2m−p designs with given m and p, those resolution IV designs whose sets of clear 2fi’s contain the specified 2fi’s as subsets. A 2fi is clear if it is not aliased with any main effect or any other 2fi. We use a linear graph to represent the set of clear 2fi’s for a resolution IV design, where each line connecting two vertices represents a clear 2fi between the two vertices. We call a 2m−p resolution IV design admissible if its graph is not a real subgraph of any other graphs of 2m−p resolution IV designs. We show that all even resolution IV designs are inadmissible. In fact, the number of admissible designs is much smaller than the number of non-isomorphic designs. This leads to a concise catalog of all admissible designs of 32 and 64 runs. We also use an algorithm to determine all admissible 128-run resolution IV designs, but only provide some representative designs here.

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This preprint was published as Huaiqing Wu, Robert Mee & Boxin Tang, "Fractional Factorial Designs with Admissible Sets of Clear Two-Factor Interactions", Technometrics (2012): 191-197, doi: 10.1080/00401706.2012.676956.

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