A note on minimum aberration and clear criteria

Peng Fei Li, Bao Jiang Chen, Min Qian Liu, Run Chu Zhang

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

Minimum aberration and clear criteria are two important rules for selecting optimal fractional factorial designs, in both unblocked and blocked cases. In this paper, we first show that under some given conditions, a blocked design DB = (D, B) having blocked minimum aberration is equivalent to D having minimum aberration. Let m = n/4 and n = 2q. From the results of Tang et al. [Bounds on the maximum number of clear two-factor interactions for 2m-p designs of resolution III and IV. Canad. J. Statist. 30 (2002) 127-136] and Wu and Wu [Clear two-factor interactions and minimum aberration. Ann. Statist. 30 (2002) 1496-1511], we know that the maximum number of clear two-factor interactions (2FIs) in 2IVm-(m-q) designs is n/2-1. Here it is proved that the maximum number of clear 2FIs in 2m-(m-q) designs in 2l blocks, denoted by 2IVm-(m-q): 2l, is also n/2 - 1 when q - l≥2. Furthermore, it is shown that any 2IVm-(m-q) design that contains the maximum number of clear 2FIs is not a minimum aberration design, and this conclusion also holds when the design is a 2IVm-(m-q): 2l design with q - l≥2.

Original languageEnglish (US)
Pages (from-to)1007-1011
Number of pages5
JournalStatistics and Probability Letters
Volume76
Issue number10
DOIs
StatePublished - May 15 2006

Fingerprint

Minimum Aberration
Interaction
Fractional Factorial Design
Design

Keywords

  • Blocked factorial design
  • Clear
  • Minimum aberration
  • Resolution
  • Two-factor interaction

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

Li, P. F., Chen, B. J., Liu, M. Q., & Zhang, R. C. (2006). A note on minimum aberration and clear criteria. Statistics and Probability Letters, 76(10), 1007-1011. https://doi.org/10.1016/j.spl.2005.11.003

A note on minimum aberration and clear criteria. / Li, Peng Fei; Chen, Bao Jiang; Liu, Min Qian; Zhang, Run Chu.

In: Statistics and Probability Letters, Vol. 76, No. 10, 15.05.2006, p. 1007-1011.

Research output: Contribution to journalArticle

Li, PF, Chen, BJ, Liu, MQ & Zhang, RC 2006, 'A note on minimum aberration and clear criteria', Statistics and Probability Letters, vol. 76, no. 10, pp. 1007-1011. https://doi.org/10.1016/j.spl.2005.11.003
Li, Peng Fei ; Chen, Bao Jiang ; Liu, Min Qian ; Zhang, Run Chu. / A note on minimum aberration and clear criteria. In: Statistics and Probability Letters. 2006 ; Vol. 76, No. 10. pp. 1007-1011.
@article{a4d59b24a79a448c90e293444b6e3f69,
title = "A note on minimum aberration and clear criteria",
abstract = "Minimum aberration and clear criteria are two important rules for selecting optimal fractional factorial designs, in both unblocked and blocked cases. In this paper, we first show that under some given conditions, a blocked design DB = (D, B) having blocked minimum aberration is equivalent to D having minimum aberration. Let m = n/4 and n = 2q. From the results of Tang et al. [Bounds on the maximum number of clear two-factor interactions for 2m-p designs of resolution III and IV. Canad. J. Statist. 30 (2002) 127-136] and Wu and Wu [Clear two-factor interactions and minimum aberration. Ann. Statist. 30 (2002) 1496-1511], we know that the maximum number of clear two-factor interactions (2FIs) in 2IVm-(m-q) designs is n/2-1. Here it is proved that the maximum number of clear 2FIs in 2m-(m-q) designs in 2l blocks, denoted by 2IVm-(m-q): 2l, is also n/2 - 1 when q - l≥2. Furthermore, it is shown that any 2IVm-(m-q) design that contains the maximum number of clear 2FIs is not a minimum aberration design, and this conclusion also holds when the design is a 2IVm-(m-q): 2l design with q - l≥2.",
keywords = "Blocked factorial design, Clear, Minimum aberration, Resolution, Two-factor interaction",
author = "Li, {Peng Fei} and Chen, {Bao Jiang} and Liu, {Min Qian} and Zhang, {Run Chu}",
year = "2006",
month = "5",
day = "15",
doi = "10.1016/j.spl.2005.11.003",
language = "English (US)",
volume = "76",
pages = "1007--1011",
journal = "Statistics and Probability Letters",
issn = "0167-7152",
publisher = "Elsevier",
number = "10",

}

TY - JOUR

T1 - A note on minimum aberration and clear criteria

AU - Li, Peng Fei

AU - Chen, Bao Jiang

AU - Liu, Min Qian

AU - Zhang, Run Chu

PY - 2006/5/15

Y1 - 2006/5/15

N2 - Minimum aberration and clear criteria are two important rules for selecting optimal fractional factorial designs, in both unblocked and blocked cases. In this paper, we first show that under some given conditions, a blocked design DB = (D, B) having blocked minimum aberration is equivalent to D having minimum aberration. Let m = n/4 and n = 2q. From the results of Tang et al. [Bounds on the maximum number of clear two-factor interactions for 2m-p designs of resolution III and IV. Canad. J. Statist. 30 (2002) 127-136] and Wu and Wu [Clear two-factor interactions and minimum aberration. Ann. Statist. 30 (2002) 1496-1511], we know that the maximum number of clear two-factor interactions (2FIs) in 2IVm-(m-q) designs is n/2-1. Here it is proved that the maximum number of clear 2FIs in 2m-(m-q) designs in 2l blocks, denoted by 2IVm-(m-q): 2l, is also n/2 - 1 when q - l≥2. Furthermore, it is shown that any 2IVm-(m-q) design that contains the maximum number of clear 2FIs is not a minimum aberration design, and this conclusion also holds when the design is a 2IVm-(m-q): 2l design with q - l≥2.

AB - Minimum aberration and clear criteria are two important rules for selecting optimal fractional factorial designs, in both unblocked and blocked cases. In this paper, we first show that under some given conditions, a blocked design DB = (D, B) having blocked minimum aberration is equivalent to D having minimum aberration. Let m = n/4 and n = 2q. From the results of Tang et al. [Bounds on the maximum number of clear two-factor interactions for 2m-p designs of resolution III and IV. Canad. J. Statist. 30 (2002) 127-136] and Wu and Wu [Clear two-factor interactions and minimum aberration. Ann. Statist. 30 (2002) 1496-1511], we know that the maximum number of clear two-factor interactions (2FIs) in 2IVm-(m-q) designs is n/2-1. Here it is proved that the maximum number of clear 2FIs in 2m-(m-q) designs in 2l blocks, denoted by 2IVm-(m-q): 2l, is also n/2 - 1 when q - l≥2. Furthermore, it is shown that any 2IVm-(m-q) design that contains the maximum number of clear 2FIs is not a minimum aberration design, and this conclusion also holds when the design is a 2IVm-(m-q): 2l design with q - l≥2.

KW - Blocked factorial design

KW - Clear

KW - Minimum aberration

KW - Resolution

KW - Two-factor interaction

UR - http://www.scopus.com/inward/record.url?scp=33645537951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645537951&partnerID=8YFLogxK

U2 - 10.1016/j.spl.2005.11.003

DO - 10.1016/j.spl.2005.11.003

M3 - Article

AN - SCOPUS:33645537951

VL - 76

SP - 1007

EP - 1011

JO - Statistics and Probability Letters

JF - Statistics and Probability Letters

SN - 0167-7152

IS - 10

ER -