Statistics for Environmental Engineers

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I — Run 2


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I — Run 3



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II


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I — Run 5




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II


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II



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I — Run 8


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Note: The eight settings opposite I — Run 1, I — Run 2, etc. were used in the 2 fractional design of the case study. The other eight combinations, marked II, are a second 24 1 fractional design that could be run as a follow-up.


Fractional factorial designs are often used in an iterative experimental strategy. Chapter 29 illustrates a 25-1 design for evaluating five factors in 16 runs. Box et al. (1978) give two examples of 27-t designs for evaluating eight variables in 23 = 8 runs. They also show other fractional factorial designs, their confounding pattern, and give a detailed explanation of how the confounding pattern is discovered.

References


Box, G. E. P. and J. S. Hunter (1961a). “The 2k p Fractional Factorial Designs. Part I,” Technometrics, 3(3), 311-351.


Box, G. E. P. and J. S. Hunter (1961b). “The 2kp Fractional Factorial Designs. Part II,” Technometrics, 3(4), 449-458.


Box, G. E. P., W. G. Hunter, and J. S. Hunter (1978). Statistics for Experimenters: An Introduction to Design, Data Analysis, and Model Building, New York, Wiley Interscience.

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