### Abstract

Genetic algorithms are useful techniques for generating statistical designs when standard factorial and response surface methods either cannot be easily applied or they perform poorly. These situations often occur when the design space is highly constrained and irregular, we are using nonstandard models, or the criteria for design evaluation are complicated. We consider statistical designs for experiments involving mixture variables and process variables, some of which are noise variables that cannot be controlled under general operating conditions. For these types of experiments, 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 slope of the response. When considering experimental designs to use for these situations, low prediction variances for the mean and slope models are desirable. We evaluate some standard mixture-process variable designs with respect to these criteria and demonstrate how an experimenter can create designs with improved scaled prediction variance (SPV) properties using a genetic algorithm.

Original language | English (US) |
---|---|

Pages (from-to) | 60-74 |

Number of pages | 15 |

Journal | Journal of Quality Technology |

Volume | 37 |

Issue number | 1 |

State | Published - Jan 2005 |

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### Keywords

- Genetic Algorithm
- Mixture-Process Experiments
- Noise Variables
- Optimal Designs
- Response Surface Methodology
- Robust Parameter Design

### ASJC Scopus subject areas

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

### Cite this

*Journal of Quality Technology*,

*37*(1), 60-74.

**Using genetic algorithms to generate mixture-process experimental designs involving 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. 37, no. 1, pp. 60-74.

}

TY - JOUR

T1 - Using genetic algorithms to generate mixture-process experimental designs involving control and noise variables

AU - Goldfarb, Heidi B.

AU - Borror, Connie M.

AU - Montgomery, Douglas

AU - Anderson-Cook, Christine M.

PY - 2005/1

Y1 - 2005/1

N2 - Genetic algorithms are useful techniques for generating statistical designs when standard factorial and response surface methods either cannot be easily applied or they perform poorly. These situations often occur when the design space is highly constrained and irregular, we are using nonstandard models, or the criteria for design evaluation are complicated. We consider statistical designs for experiments involving mixture variables and process variables, some of which are noise variables that cannot be controlled under general operating conditions. For these types of experiments, 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 slope of the response. When considering experimental designs to use for these situations, low prediction variances for the mean and slope models are desirable. We evaluate some standard mixture-process variable designs with respect to these criteria and demonstrate how an experimenter can create designs with improved scaled prediction variance (SPV) properties using a genetic algorithm.

AB - Genetic algorithms are useful techniques for generating statistical designs when standard factorial and response surface methods either cannot be easily applied or they perform poorly. These situations often occur when the design space is highly constrained and irregular, we are using nonstandard models, or the criteria for design evaluation are complicated. We consider statistical designs for experiments involving mixture variables and process variables, some of which are noise variables that cannot be controlled under general operating conditions. For these types of experiments, 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 slope of the response. When considering experimental designs to use for these situations, low prediction variances for the mean and slope models are desirable. We evaluate some standard mixture-process variable designs with respect to these criteria and demonstrate how an experimenter can create designs with improved scaled prediction variance (SPV) properties using a genetic algorithm.

KW - Genetic Algorithm

KW - Mixture-Process Experiments

KW - Noise Variables

KW - Optimal Designs

KW - Response Surface Methodology

KW - Robust Parameter Design

UR - http://www.scopus.com/inward/record.url?scp=18144412011&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=18144412011&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:18144412011

VL - 37

SP - 60

EP - 74

JO - Journal of Quality Technology

JF - Journal of Quality Technology

SN - 0022-4065

IS - 1

ER -