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Lec 08 - Fractional Factorial

# Lec 08 - Fractional Factorial - Fractional Factorial...

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Fractional Factorial Experimental Designs The Problem: 5 factors, 2 levels each. You can't afford 32 runs. Fractional Factorial experiment is the solution: design doesn’t include all possible combinations Advantage: fewer runs Disadvantage: estimate one-way and maybe two- way effects but not all effects.

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Notation for Factorial Experiments 2 K full factorial experiment k factors - 2 levels each number of tests=2 K can estimate all parameters 2 K-p fractional factorial experiment k factors - 2 levels each number of tests=2 K-p can estimate the most important parameters b 0 , b 1 , … , b k , maybe b 12 , b 13 , … etc. 2 4-1 experiment How many factors? How many tests? 2
Design vs. Calculation Matrix Consider a 2 2 Experiment: Calculation Matrix Test I x 1 x 2 x 12 1 1 -1 -1 +1 2 1 +1 -1 -1 3 1 -1 +1 -1 4 1 +1 +1 +1 Design Matrix Test x 1 x 2 1 -1 -1 2 +1 -1 3 -1 +1 4 +1 +1 Example of a Fractional Factorial Experiment 3

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The experiment has 3 factors: 2 2 full factorial is 8 runs 2 3-1 fractional factorial is 4 runs Write out calculation matrix for 2 3-1 =2 2 Assign extra factor to high order term test I x 1 x 2 x 1 x 2 ( x 3 ) 1 1 -1 -1 +1 2 1 +1 -1 -1 3 1 -1 +1 -1 4 1 +1 +1 +1 The Design Matrix test x 1 x 2 x 3 1 -1 -1 +1 2 +1 -1 -1 3 -1 +1 -1 4 +1 +1 +1 4
Alias Structure test I x 1 x 2 x 1 x 2 ( x 3 ) Y 1 1 -1 -1 +1 10 2 1 +1 -1 -1 11 3 1 -1 +1 -1 15 4 1

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