A step-down lenth method for analyzing unreplicated factorial designs

Kenny Q. Ye, Michael Hamada, C. F.J. Wu

Research output: Contribution to journalArticlepeer-review

43 Scopus citations


Unreplicated factorial designs are frequently used in industrial experiments. A commonly used method to identify active effects from such experiments is the half-normal plot. Many formal testing methods have been developed to overcome the subjectivity of using this graphical method. Among them, the Lenth (1989) method is simple, yet powerful, as shown by Hamada and Balakrishnan (1998). In this paper, we propose a step-down version of the Lenth method. It is compared via simulation with the original Lenth method and with stepwise methods proposed by Venter and Steel (1998). It is shown that the step-down Lenth method is better than the original Lenth method and the Venter and Steel step-down method. The Venter and Steel step-up method controlled by the same experimentwise error rate has more power, but it also has a higher individual error rate. Critical values used in the step-down Lenth method are provided.

Original languageEnglish (US)
Pages (from-to)140-152
Number of pages13
JournalJournal of Quality Technology
Issue number2
StatePublished - Dec 1 2001
Externally publishedYes


  • Experimentwise Error Rate
  • Individual Error Rate
  • Power

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Strategy and Management
  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering


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