Correcting Misconceptions About Optimal Design

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This talk was presented live at JMP Discovery Summit 2102 in Cary, North Carolina, USA. More information about design of experiments is available at http://www.jmp.com/applications/doe/

This talk was presented live at JMP Discovery Summit 2102 in Cary, North Carolina, USA. More information about design of experiments is available at http://www.jmp.com/applications/doe/

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  • 1. Copyright © 2011 SAS Institute Inc. All rights reserved. Correcting Misconceptions about Optimal Design Bradley Jones Principal Research Fellow JMP Division/SAS
  • 2. 2 Copyright © 2011, SAS Institute Inc. All rights reserved. Misconception #1 Optimal designs are not orthogonal
  • 3. 3 Copyright © 2011, SAS Institute Inc. All rights reserved. What is true All the standard orthogonal textbook designs are D-optimal for an appropriate model. The default settings in the Custom Designer aim to produce orthogonal designs.
  • 4. 4 Copyright © 2011, SAS Institute Inc. All rights reserved. Custom Design Examples 1. Full Factorial Design 2. Resolution III Fractional Factorial Design 3. Resolution V Fractional Factorial Design 4. Plackett-Burman Design 5. Latin Square Design
  • 5. 5 Copyright © 2011, SAS Institute Inc. All rights reserved. Also true Orthogonal designs are not always good. Example: Orthogonal Latin Hypercube that is not space-filling.
  • 6. 6 Copyright © 2011, SAS Institute Inc. All rights reserved. So what if a design is not orthogonal? Box-Behnken designs have correlated quadratic effects but they are very popular and for good reason. No standard mixture design is orthogonal. So – a design can be non-orthogonal and still be good.
  • 7. 7 Copyright © 2011, SAS Institute Inc. All rights reserved. One Final Truth Optimal designs are certainly not always orthogonal When? 1. The number of runs is not a “magic number”. 2. The model does not allow it. 3. The allowable factor combinations are restricted.
  • 8. 8 Copyright © 2011, SAS Institute Inc. All rights reserved. Misconception #2 Optimal designs depend on a pre-specified model. Desired Inference? 1. An optimal design is not good unless the model fit is the pre-specified model. 2. Orthogonal designs do not depend on a model.
  • 9. 9 Copyright © 2011, SAS Institute Inc. All rights reserved. What is true Yes, to create an optimal design you must specify a model*, but No, the optimal design will generally be efficient for many models, and No, orthogonal designs very much depend on the form of the “true” model. * or group of models – see model robust design literature
  • 10. 10 Copyright © 2011, SAS Institute Inc. All rights reserved. Example – 6 Factors 24 Runs Compare two orthogonal designs and the D-optimal design for the two-factor interactions model.
  • 11. 11 Copyright © 2011, SAS Institute Inc. All rights reserved. Misconception #3 Optimal designs are plagued by complex aliasing.
  • 12. 12 Copyright © 2011, SAS Institute Inc. All rights reserved. What is true Yes, in some cases D-optimal designs have complex aliasing, but There is a new optimality criterion! Introducing Alias Optimal designs.
  • 13. Back to Custom Design in JMP
  • 14. 14 Copyright © 2011, SAS Institute Inc. All rights reserved. Summary Optimal designs are orthogonal for textbook cases. Optimal designs perform competitively with orthogonal designs for a family of models. Alias optimal designs can drastically reduce or eliminate aliasing of a specified model due to higher order terms.
  • 15. 15 Copyright © 2011, SAS Institute Inc. All rights reserved. References Jones, B. and Nachtsheim, C. J. (2011) “Efficient Designs with Minimal Aliasing” Technometrics, 53. 62-71. Jones, B and Nachtsheim, C. (2011) “A Class of Three-Level Designs for Definitive Screening in the Presence of Second- Order Effects” Journal of Quality Technology, 43. 1-15.