### Abstract

D-optimal designs have proved useful in analyzing common factorial experiments involving multilevel categorical factors. When analyzed by ANOVA, they allow the estimation of coefficients in a regression equation and the contributions to the variance by the main effects and interactions. If the measurement of contribution to variance is necessary but the estimation of all interaction coefficients in the regression equation is not, it is possible to reduce the number of experimental runs below a minimum D-optimal design, using what we call truncated D-optimal screening designs. D-efficiency calculations are not available due to the singularity of the design matrix; another method must be used to pare down the matrix while maintaining reasonable estimation of the original full factorial data. Covering arrays are adapted to guide this reduction. Combining properties of D-optimal designs and covering arrays produces designs that perform well at estimating full factorial results. A method is then developed to target specific interactions prior to the design of the experiment when process specific knowledge is available to indicate which interactions are least important.

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

Pages (from-to) | 359-383 |

Number of pages | 25 |

Journal | American Journal of Mathematical and Management Sciences |

Volume | 28 |

Issue number | 3-4 |

State | Published - 2008 |

### Fingerprint

### Keywords

- Covering arrays
- D-efficiency
- D-optimal designs

### ASJC Scopus subject areas

- Business, Management and Accounting(all)
- Applied Mathematics

### Cite this

*American Journal of Mathematical and Management Sciences*,

*28*(3-4), 359-383.

**Truncated D-optimal designs for screening experiments.** / Hoskins, Dean S.; Colbourn, Charles; Kulahci, Murat.

Research output: Contribution to journal › Article

*American Journal of Mathematical and Management Sciences*, vol. 28, no. 3-4, pp. 359-383.

}

TY - JOUR

T1 - Truncated D-optimal designs for screening experiments

AU - Hoskins, Dean S.

AU - Colbourn, Charles

AU - Kulahci, Murat

PY - 2008

Y1 - 2008

N2 - D-optimal designs have proved useful in analyzing common factorial experiments involving multilevel categorical factors. When analyzed by ANOVA, they allow the estimation of coefficients in a regression equation and the contributions to the variance by the main effects and interactions. If the measurement of contribution to variance is necessary but the estimation of all interaction coefficients in the regression equation is not, it is possible to reduce the number of experimental runs below a minimum D-optimal design, using what we call truncated D-optimal screening designs. D-efficiency calculations are not available due to the singularity of the design matrix; another method must be used to pare down the matrix while maintaining reasonable estimation of the original full factorial data. Covering arrays are adapted to guide this reduction. Combining properties of D-optimal designs and covering arrays produces designs that perform well at estimating full factorial results. A method is then developed to target specific interactions prior to the design of the experiment when process specific knowledge is available to indicate which interactions are least important.

AB - D-optimal designs have proved useful in analyzing common factorial experiments involving multilevel categorical factors. When analyzed by ANOVA, they allow the estimation of coefficients in a regression equation and the contributions to the variance by the main effects and interactions. If the measurement of contribution to variance is necessary but the estimation of all interaction coefficients in the regression equation is not, it is possible to reduce the number of experimental runs below a minimum D-optimal design, using what we call truncated D-optimal screening designs. D-efficiency calculations are not available due to the singularity of the design matrix; another method must be used to pare down the matrix while maintaining reasonable estimation of the original full factorial data. Covering arrays are adapted to guide this reduction. Combining properties of D-optimal designs and covering arrays produces designs that perform well at estimating full factorial results. A method is then developed to target specific interactions prior to the design of the experiment when process specific knowledge is available to indicate which interactions are least important.

KW - Covering arrays

KW - D-efficiency

KW - D-optimal designs

UR - http://www.scopus.com/inward/record.url?scp=67650351485&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=67650351485&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:67650351485

VL - 28

SP - 359

EP - 383

JO - American Journal of Mathematical and Management Sciences

JF - American Journal of Mathematical and Management Sciences

SN - 0196-6324

IS - 3-4

ER -