### 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 |

### Fingerprint

### 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

*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.

Research output: Contribution to journal › Article

*Journal of Quality Technology*, vol. 36, no. 3, pp. 245-262.

}

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 -