stats chap8.1 - Chapter 8 Two-Level Fractional...

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Chapter 8 Two-Level Fractional Factorials (cont.)
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Complementary Half-Fraction : In Example 8-1, a 2 4-1 Fraction was constructed using the generator; I = ABCD This is called the principal fraction. An alternate (complementary) one-half can be constructed using I = - ABCD . This will consist of runs a , b , c , abc , d , abd , acd and bcd .
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Alternate Alias Structure : [ ] [ ] on. . so and ACD B B BCD A A - - Thus, the two designs can be augmented (in blocks) to de-alias the main effects by adding and subtracting estimates from the two fractions.
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Example 8-3 Consider the alternative fraction of Example 8-1, with filtration rates shown in p. 301
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[ ] [ ] [ ] on. . so and ABD C C ACD B B BCD A A 75 . 5 4 23 75 . 4 4 19 25 . 24 4 97 = = - = = - = = -
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These estimates are combined with those calculated from the principal fraction (see Table 8-4, p. 296) to obtain: [ ] [ ] [ ] [ ] 625 . 2 ) 25 . 24 0 . 19 ( 2 1 ) ( 2 1 625 . 21 ) 25 . 24 0 . 19 ( 2 1 ) ( 2 1 - = - = - = + = + BCD A A A A A and so on (see p. 301).
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Half Normal plot Half Normal % probability |Effect| 0.00 5.41 10.81 16.22 21.63 0 20 40 60 70 80 85 90 95 97 99 A C D AC AD
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The ANOVA Table : Source SS df MS F 0 P-value Blocks 7.56 1 7.56 Model 5535.81 5 1107.16 53.13 < 0.0001 A 1870.56 1 1870.56 89.76 < 0.0001 C 390.06 1 390.06 18.72 0.0019 D 855.56 1 855.56 41.05 0.0001 AC 1314.06 1 1314.06 63.05 < 0.0001 AD 1105.56 1 1105.56 53.05 < 0.0001 Error 187.56 9 20.84 Total 5730.94 15
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Conclusion : Results of the alternative fraction offers a confirmation to our initial conclusions regarding the two-factor interaction effects.
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Projection of Fractions : Every 2 k-1 fractional factorial design can be projected into: Full factorial in any (k-1) of the original k factors, Two replicates of a full factorial in any subset of (k-2) factors, Four replicates of a full factorial in any subset of (k-3) factors, and so on.
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Projection of a 2 3-1 design: B A C a c b abc
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The One-Quarter Fractional Factorial : These designs require two generators (P,Q) and their generalized interaction PQ. The
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This note was uploaded on 05/03/2010 for the course ME 250-750 taught by Professor Signer during the Summer '10 term at Wichita State.

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stats chap8.1 - Chapter 8 Two-Level Fractional...

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