Are power caldualtions in mixture experiments reliable?

[#1]

In a ternary 12-run mixture experiment using a special Sheffé model I get only 5% power of the compnents; this means 95% chance that component effect can't be observed? Are power calculations in mixture experiments reliable taking into account high collinearity among factors?

[#2]

Yes, they are reliable. First of all, the power is low because of the inherent high degree of correlation between the estimates. Second, any constraints on the individual components or combinations of components further increases the correlations, which decreases the power. Third, we don't usually expect a mixture design to tell us which components are significant. All the components change together, not independently, so it is impossible to assign significance. Mixture experiments are usually about prediction for exploration or optimization.

[#3]

Indeed, as mixture DOE is I-optimal power does not make sense

[#4 · Accepted solution]

Hi @frankderuyck,

Mixture designs are optimization designs, not screening designs. A mixture design is generally run if the number of factors is low and/or the components are known to have an effect on the response(s). So power calculations is not a sensible metric (even if "reliable") I would use to evaluate/compare mixture designs. Try to use predictive metrics like Prediction variance profile, Fraction of Design Space Plot, Prediction Variance Surface, and Design Diagnostics : relative G-Efficiency (related to the maximum prediction variance over experimental space), and average variance of prediction to evaluate and compare mixture designs. 

Moreover, as a mixture design involves factors that are linearly dependant (sum = 100% or 1), this situation creates multicollinearity, which inflates error for effect terms estimations, so this is why you would have very low power for the different effects in your model.

See other relevant discussions : 

Custom Design: Mixture with Process Variables. How to Evaluate Design? 

Should I consider power analysis in DOE? 

How to use the effect summary effectively for a mixture DOE? 

Hope this answer will help you,

[#5]

Thanks Victor, indde muticollinearity is source of unreliable power prediction