Evaluating mixture-process designs with control and noise variables

Heidi B. Goldfarb, Connie M. Borror, Douglas Montgomery, Christine M. Anderson-Cook

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Mixture-process experiments involve two distinct types of variables. The mixture variables are varied through their relative proportions and cannot be adjusted independently. The process variables can be varied independently of one another and of the mixture components. When some of the process variables are noise variables, variables that cannot be controlled in normal process operation, we are in a robust design setting. In these situations, it is customary to fit a response model combining mixture, process, and noise variables and to derive a model for the mean response and a model for the variance of the response for this response model. The variance model is directly related to the directional derivative (slope) of the response surface in the directions of the noise variables. We develop expressions for the scaled and unsealed prediction variances of both the mean and slope models. We then demonstrate the use of variance dispersion graphs (VDGs) and fraction of design space (FDS) plots of the prediction variance values to evaluate a variety of competing designs for such settings.

Original languageEnglish (US)
Pages (from-to)245-262
Number of pages18
JournalJournal of Quality Technology
Volume36
Issue number3
StatePublished - Jul 2004

Fingerprint

Mixture Design
Process Design
Process design
Prediction Variance
Slope
Model
Directional derivative
Robust Design
Response Surface
Derivatives
Proportion
Distinct

Keywords

  • Fraction of Design Space Plots
  • Mixture Experiments
  • Response Surface Methodology
  • Robust Parameter Design
  • Variance Dispersion Graphs

ASJC Scopus subject areas

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

Cite this

Goldfarb, H. B., Borror, C. M., Montgomery, D., & Anderson-Cook, C. M. (2004). Evaluating mixture-process designs with control and noise variables. Journal of Quality Technology, 36(3), 245-262.

Evaluating mixture-process designs with control and noise variables. / Goldfarb, Heidi B.; Borror, Connie M.; Montgomery, Douglas; Anderson-Cook, Christine M.

In: Journal of Quality Technology, Vol. 36, No. 3, 07.2004, p. 245-262.

Research output: Contribution to journalArticle

Goldfarb, HB, Borror, CM, Montgomery, D & Anderson-Cook, CM 2004, 'Evaluating mixture-process designs with control and noise variables', Journal of Quality Technology, vol. 36, no. 3, pp. 245-262.
Goldfarb, Heidi B. ; Borror, Connie M. ; Montgomery, Douglas ; Anderson-Cook, Christine M. / Evaluating mixture-process designs with control and noise variables. In: Journal of Quality Technology. 2004 ; Vol. 36, No. 3. pp. 245-262.
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