Fractional Factorial Essay

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Materials Engineering 14 Fractional Factorial Recall: 2k Factorial Experiment In an experiment conducted by the Mining Engineering Department at the Virginia Polytechnic Institute and State University to study a particular filtering system for coal, a coagulant was added to a solution in a tank containing coal and sludge, which was then placed in a recirculation system in order that the coal could be washed. 3 factors were varied in the experimental process; 2 levels of each factor was used. The amount of solids in the underflow of the cleansing system determines how clean the coal has become. Recall: 2k Factorial Experiment A: percent solids circulated initially in the overflow/B: flow rate of the polymer/C: pH level in the tank. The following table summarizes the results: Response Treatment Combination (1) Replicate 1 4.65 Replicate 2 5.81 a b ab c ac bc abc 21.42 12.66 18.27 7.93 13.18 6.51 18.23 21.35 12.56 16.62 7.88 12.87 6.26 17.83 Should a full-2k design always be implemented? • One of the advantages of the full design is that it assigns a degree of freedom for each treatment combination • However, there are situations where certain interactions are negligible, resulting in a waste of experimental effort Fractional Factorial Experiments • a 2k design becomes demanding as k becomes extremely large number of factors being considered k 2 3 4 5 6 Treatment combinations 4 8 16 32 64 k 7 8 9 10 Treatment combinations 128 256 512 1024 Sparsity-of-Effects Principle • States that a system is usually dominated by main effects and low-order interactions, thus it is most likely that main (single factor) effects and two-factor interactions are the most significant responses • Formally, Wu and Hamada explained this as the idea that only a few effects in a factorial experiment will be statistically significant Fractional
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