Interactions - factorial designs. A typical application Synthesis catalysttemperature Yield of product Yield=f (catalyst, temperature) Is there an optimal.

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Presentation transcript:

Interactions - factorial designs

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

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

Variable Levels Temperature range: °C Catalyst: Type 1, Type 2 Select levels Temperature : 140 °C, 180 °C Catalyst: c 1, c 2

Multivariate design

Coding the design

Design Matrix 2 2 Factorial Design (FD) -1 represents the low value, while +1 represents the high value

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

Result of experiments 2 2 Factorial Design

Response in variable space Temperature Catalyst (180 °C, c1) (140 °C, c2) (140 °C, c1) (180 °C, c2)

Calculation of Mean Response

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

Apparent conclusion Yield = function of temperature only

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

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

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

Model

Interpretation Temp Catalyst °C180°C i) Large increase in yield for catalyst 1 with increasing temperature ii) Small increase in yield for catalyst 2 with increasing temperature

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

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.