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 language | English (US) |
|---|---|
| Pages (from-to) | 245-262 |
| Number of pages | 18 |
| Journal | Journal of Quality Technology |
| Volume | 36 |
| Issue number | 3 |
| State | Published - Jul 2004 |
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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
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 journal › Article
}
TY - JOUR
T1 - Evaluating mixture-process designs with control and noise variables
AU - Goldfarb, Heidi B.
AU - Borror, Connie M.
AU - Montgomery, Douglas
AU - Anderson-Cook, Christine M.
PY - 2004/7
Y1 - 2004/7
N2 - 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.
AB - 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.
KW - Fraction of Design Space Plots
KW - Mixture Experiments
KW - Response Surface Methodology
KW - Robust Parameter Design
KW - Variance Dispersion Graphs
UR - http://www.scopus.com/inward/record.url?scp=11344253564&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=11344253564&partnerID=8YFLogxK
M3 - Article
AN - SCOPUS:11344253564
VL - 36
SP - 245
EP - 262
JO - Journal of Quality Technology
JF - Journal of Quality Technology
SN - 0022-4065
IS - 3
ER -