Title page for ETD etd-130211739741061

Type of Document Dissertation
Author McMahan, Angela Renee
Author's Email Address mcmahan@vt.edu
URN etd-130211739741061
Title Measurement Error in Designed Experiments for Second Order Models
Degree PhD
Department Statistics
Advisory Committee
Advisor Name Title
Birch, Jeffrey B.
Myers, Raymond H.
Reynolds, Marion R. Jr.
Ye, Keying
Smith, Eric P. Committee Chair
  • berkson error
  • designed experiments
  • measurement error
Date of Defense 1997-11-04
Availability unrestricted
Measurement error (ME) in the factor levels of

designed experiments is often overlooked in the

planning and analysis of experimental designs. A

familiar model for this type of ME, called the Berkson

error model, is discussed at length. Previous research

has examined the effect of Berkson error on two-level

factorial and fractional factorial designs. This

dissertation extends the examination to designs for

second order models. The results are used to suggest

optimal values for axial points in Central Composite

Designs. The proper analysis for experimental data

including ME is outlined for first and second order

models. A comparison of this analysis to a typical

Ordinary Least Squares analysis is made for second

order models. The comparison is used to quantify the

difference in performance of the two methods, both of

which yield unbiased coefficient estimates. Robustness

to misspecification of the ME variance is also

explored. A solution for experimental planning is also

suggested. A design optimality criterion, called the

DME criterion, is used to create a second-stage

design when ME is present. The performance of the

criterion is compared to a D-optimal design

augmentation. A final comparison is made between

methods accounting for ME and methods ignoring


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