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Interactions - factorial designs

Interactions - factorial designs. A typical application. catalyst. temperature. Synthesis. Yield of product. Yield= f (catalyst, temperature). Is there an optimal combination of catalyst and temperature?. Univariate Design Check the whole temperature interval for all catalysts.

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Interactions - factorial designs

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  1. Interactions - factorial designs

  2. A typical application catalyst temperature Synthesis Yield of product Yield=f (catalyst, temperature) Is there an optimal combination of catalyst and temperature?

  3. Univariate Design Check the whole temperature interval for all catalysts Multivariate DesignCheck different Combinations of temperature and catalyst Designs

  4. Variable Levels Temperature range : 120 - 200 °C Catalyst : Type 1, Type 2 Select levels Temperature : 140 °C, 180 °C Catalyst : c1, c2

  5. Multivariate design

  6. Coding the design

  7. Design Matrix22 Factorial Design (FD) -1 represents the low value, while +1 represents the high value

  8. Catalyst (140 °C, c2) (180 °C, c2) Temperature (140 °C, c1) (180 °C, c1) Variable space

  9. Result of experiments22 Factorial Design

  10. Catalyst (140 °C, c2) 57 70 (180 °C, c2) Temperature 48 81 (140 °C, c1) (180 °C, c1) Response in variable space

  11. Calculation of Mean Response

  12. Calculation of Main Effects Temperature +1: -1:  Main Effect = 23.0 Catalyst +1: -1:  Main Effect = -1.0

  13. Apparent conclusion Yield = function of temperature only

  14. Predicted responses ^ ^ Significant lack of fit between Model and Experiments!

  15. Residuals and variable levels Lack of fit () follows the same pattern as the interaction between temperature and catalyst (tc)!

  16. Orthogonality and Yates algorithm Columns in Design Matrix are orthogonal!  Yates algorithm for calculation of main effects and interaction.

  17. Model

  18. 2 57 70 Catalyst 1 48 81 Temp. 140°C 180°C Interpretation i) Large increase in yield for catalyst 1 with increasing temperature ii) Small increase in yield for catalyst 2 with increasing temperature

  19. Multivariate vs. Univariate design • Multivariate Design gives a single model for the response • Multivariate Design gives an interpretation of the differences between catalysts in terms of an interaction term • Multivariate Design gives a lot of information by means of few (orthogonal) experiments

  20. Next step Multivariate orthogonal designs such as Factorial Designs can be reduced to obtain Fractional Factorial Designs, Plackett-Burman designs etc., for screening of many factors simultaneously.

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