# DoE - Design of Experiments Design of a Completely...

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ENGR 102 Fall 2008 Design of Experiments Design of a Completely Randomized 2 2 Factorial Experiment using Four Full Replicates

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ENGR 102 Fall 2008 Two Factors, One Response Factors A and B are inputs to device DEVICE A B Y Device output is response, Y (See Textbook, Chapter 8, pg. 114)
ENGR 102 Fall 2008 Device Model We want to model the device so that we can understand its behavior How does the output change with various inputs? Are the responses to inputs independent or dependent? Testing all possible combinations is impossible so We could select a few levels for A and B In the simplest case, we use just two levels

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ENGR 102 Fall 2008 B high A high B low A high B high A low B low A low Full Factorial, 2 2 To find the response of the device Set the factors to each of two levels Called, “low” and “high”; There are 2 2 = four factor combinations (See Textbook, Chapter 8, pg. 115)
ENGR 102 Fall 2008 (See Textbook, Chapter 8, pg. 115) Treatment Combinations The four combinations are called “treatment combinations” They can be represented more concisely Use - for low and + for high. B + A + B - A + B + A - B - A -

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ENGR 102 Fall 2008 Response Inputs B + B - B + B - ab A + a A + b A - (1) A - Shorthand Notation The combinations of A and B can be represented by simple shorthand terms These four combinations will be used to indicate the responses to the A/B combinations (See Textbook, Chapter 8, pg. 115)
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DoE - Design of Experiments Design of a Completely...

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