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Mixture Design Using Coordinate Exchange

Mixture Design Using Coordinate Exchange. Bradley Jones. Outline. Technical Hurdles for Coordinate Exchange applied to Mixture Experimentation. Demonstration. Technical Hurdles. Find a feasible starting design. Non-independence of mixture factors. Finding a starting design.

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Mixture Design Using Coordinate Exchange

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  1. Mixture Design Using Coordinate Exchange Bradley Jones

  2. Outline • Technical Hurdles for Coordinate Exchange applied to Mixture Experimentation. • Demonstration.

  3. Technical Hurdles • Find a feasible starting design. • Non-independence of mixture factors.

  4. Finding a starting design • For each point: • If the point satisfies the constraints keep it. • Otherwise keep projecting the point onto the nearest constraint until all constraints are satisfied.

  5. Non-independence of Mixture Factors • Usually coordinate exchange works by considering only one coordinate at a time. This is impossible for mixtures. • Solution: • Move only in the Cox direction. • Find best improvement in determinant.

  6. Outline • Technical Hurdles for Coordinate Exchange applied to Mixture Experimentation. • Demonstration.

  7. Demonstration Set Up • Consider three mixture components. • Require that no component comprise more than 50% of the mixture. • Create a six run design to fit an interactions model.

  8. Coordinate Exchange Demo

  9. JMP DOE Demo #5 Continued

  10. Conclusion • The Coordinate Exchange Algorithm with modification can find D-optimal Mixture Designs. • The resulting algorithm is comparatively fast especially as the number of mixture components increases.

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