Critical values of the Lenth method for unreplicated factorial designs

Qian K. Ye, Michael Hamada

Research output: Contribution to journalArticle

44 Citations (Scopus)

Abstract

The Lenth method is an objective method for testing effects from unreplicated factorial designs and eliminates the subjectivity in using a half-normal plot. The Lenth statistics are computed for the factorial effects and compared to corresponding critical values. Since the distribution of the Lenth statistics is not mathematically tractable, we propose a simple simulation method to estimate the critical values. Confidence intervals for the estimated critical values can also easily be obtained. Tables of critical values are provided for a large number of designs, and their use is demonstrated with data from three experiments. The proposed method can also be adapted to estimate critical values for other methods.

Original languageEnglish (US)
Pages (from-to)57-66
Number of pages10
JournalJournal of Quality Technology
Volume32
Issue number1
StatePublished - 2000
Externally publishedYes

Fingerprint

Factorial Design
Critical value
Statistics
Testing
Factorial
Simulation Methods
Experiments
Estimate
Confidence interval
Tables
Eliminate
Factorial design
Experiment

Keywords

  • Confidence intervals
  • Experimentwise error rate
  • Factorial designs
  • Fractional factorial designs
  • Individual error rate
  • Mixed-level designs
  • Plackett-burman designs
  • Simulation

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Statistics and Probability

Cite this

Critical values of the Lenth method for unreplicated factorial designs. / Ye, Qian K.; Hamada, Michael.

In: Journal of Quality Technology, Vol. 32, No. 1, 2000, p. 57-66.

Research output: Contribution to journalArticle

@article{7b3b274a009e4645b91bae76163995f8,
title = "Critical values of the Lenth method for unreplicated factorial designs",
abstract = "The Lenth method is an objective method for testing effects from unreplicated factorial designs and eliminates the subjectivity in using a half-normal plot. The Lenth statistics are computed for the factorial effects and compared to corresponding critical values. Since the distribution of the Lenth statistics is not mathematically tractable, we propose a simple simulation method to estimate the critical values. Confidence intervals for the estimated critical values can also easily be obtained. Tables of critical values are provided for a large number of designs, and their use is demonstrated with data from three experiments. The proposed method can also be adapted to estimate critical values for other methods.",
keywords = "Confidence intervals, Experimentwise error rate, Factorial designs, Fractional factorial designs, Individual error rate, Mixed-level designs, Plackett-burman designs, Simulation",
author = "Ye, {Qian K.} and Michael Hamada",
year = "2000",
language = "English (US)",
volume = "32",
pages = "57--66",
journal = "Journal of Quality Technology",
issn = "0022-4065",
publisher = "American Society for Quality",
number = "1",

}

TY - JOUR

T1 - Critical values of the Lenth method for unreplicated factorial designs

AU - Ye, Qian K.

AU - Hamada, Michael

PY - 2000

Y1 - 2000

N2 - The Lenth method is an objective method for testing effects from unreplicated factorial designs and eliminates the subjectivity in using a half-normal plot. The Lenth statistics are computed for the factorial effects and compared to corresponding critical values. Since the distribution of the Lenth statistics is not mathematically tractable, we propose a simple simulation method to estimate the critical values. Confidence intervals for the estimated critical values can also easily be obtained. Tables of critical values are provided for a large number of designs, and their use is demonstrated with data from three experiments. The proposed method can also be adapted to estimate critical values for other methods.

AB - The Lenth method is an objective method for testing effects from unreplicated factorial designs and eliminates the subjectivity in using a half-normal plot. The Lenth statistics are computed for the factorial effects and compared to corresponding critical values. Since the distribution of the Lenth statistics is not mathematically tractable, we propose a simple simulation method to estimate the critical values. Confidence intervals for the estimated critical values can also easily be obtained. Tables of critical values are provided for a large number of designs, and their use is demonstrated with data from three experiments. The proposed method can also be adapted to estimate critical values for other methods.

KW - Confidence intervals

KW - Experimentwise error rate

KW - Factorial designs

KW - Fractional factorial designs

KW - Individual error rate

KW - Mixed-level designs

KW - Plackett-burman designs

KW - Simulation

UR - http://www.scopus.com/inward/record.url?scp=1642582109&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=1642582109&partnerID=8YFLogxK

M3 - Article

VL - 32

SP - 57

EP - 66

JO - Journal of Quality Technology

JF - Journal of Quality Technology

SN - 0022-4065

IS - 1

ER -