Estimation of missing observations in two-level split-plot designs

Douglas Montgomery, Ashraf A. Almimi, Murat Kulahci

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


Inserting estimates for the missing observations from split-plot designs restores their balanced or orthogonal structure and alleviates the difficulties in the statistical analysis. In this article, we extend a method due to Draper and Stoneman to estimate the missing observations from unreplicated two-level factorial and fractional factorial split-plot (FSP and FFSP) designs. The missing observations, which can either be from the same whole plot, from different whole plots, or comprise entire whole plots, are estimated by equating to zero a number of specific contrast columns equal to the number of the missing observations. These estimates are inserted into the design table and the estimates for the remaining effects (or alias chains of effects as the case with FFSP designs) are plotted on two half-normal plots: one for the whole-plot effects and the other for the subplot effects. If the smaller effects do not point at the origin, then different contrast columns to some or all of the initial ones should be discarded and the plots re-examined for bias. Using examples, we show how the method provides estimates for the missing observations that are very close to their actual values.

Original languageEnglish (US)
Pages (from-to)127-152
Number of pages26
JournalQuality and Reliability Engineering International
Issue number2
StatePublished - Mar 1 2008


  • Alias chains of effects
  • Half-normal plot
  • Missing observations
  • Unreplicated two-level factorial and fractional factorial split-plot designs

ASJC Scopus subject areas

  • Safety, Risk, Reliability and Quality
  • Management Science and Operations Research


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