Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Minimum aberration designs of resolution III

Jesus Juan, J. Gabriel Palomo

Abstract

In this article we prove several important properties of 2^{k-p} minimum aberration (MA) designs with k>2, where n=2^{k-p} is the number of runs. We develop a simple method to build MA designs of resolution III. Furthermore, we introduce a simple relationship, based on product of polynomials, for computing their word-length patterns.

Minimum aberration designs of resolution III

Abstract

In this article we prove several important properties of 2^{k-p} minimum aberration (MA) designs with k>2, where n=2^{k-p} is the number of runs. We develop a simple method to build MA designs of resolution III. Furthermore, we introduce a simple relationship, based on product of polynomials, for computing their word-length patterns.

Paper Structure

This paper contains 8 sections, 5 theorems, 62 equations.

Table of Contents

  1. Introduction
  2. Definitions and motivation
  3. Screening designs $(k\geq n/2)$ of minimum aberration
  4. Saturated designs of resolution IV $(O_{m})$
  5. Word-length pattern
  6. Conclusions
  7. Appendix: proof of theorem 1.
  8. References

Key Result

theorem \oldthetheorem

Let $d\subset H_{m}$ be a $2^{k-p}$ design and $\bar{d}$ its complementary, $H_{m}=d\cup \bar{d}$. A necessary condition for $d$ to be of minimum aberration is that the set $\bar{d}$ has minimum rank.

Theorems & Definitions (8)

  • definition 1
  • definition 2
  • theorem \oldthetheorem
  • theorem \oldthetheorem
  • theorem \oldthetheorem
  • definition 3
  • theorem \oldthetheorem
  • theorem \oldthetheorem