Correcting Misconceptions About Optimal Design
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This document discusses common misconceptions about optimal experimental designs. It notes that while optimal designs are not always orthogonal, standard orthogonal textbook designs are optimal under certain models. Orthogonal designs also depend on the assumed model. The document introduces alias optimal designs as a new criterion that can reduce aliasing in optimal designs compared to traditional D-optimal designs. It provides examples of custom designs in JMP and concludes that optimal designs generally perform well across a range of models without requiring an exact pre-specified model.
Correcting Misconceptions About Optimal Design
- 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.