Critical values of the Lenth method for unreplicated factorial designs

Kenny Q. Ye, Michael Hamada

Research output: Contribution to journalArticlepeer-review

45 Scopus citations


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
Issue number1
StatePublished - Jan 1 2000
Externally publishedYes


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

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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