Explanation Calculation: Fractional factorial experiment: In the experimental design, when there is large number of factors, it may not practical to perform a design for one replicates for each treatments. In such case, fraction of the treatments will be taken. The design which takes the fraction values of the factor is known as fractional factorial. The experiments produce the proper way to obtain the information regarding the factors when the treatments are chosen correctly. The fractional factorial may be denoted as 2 p , Where, 2 denotes the number of levels of factors and p denotes the number of factors. The fraction of the factor should always contain the power of 2 which means one half-replicate, one quarter replicate and so on. Half-replicate may be defined as the experiment which has half of the treatments and it is denoted as 2 p − 1 . In the same way, quarter replicate contains one-quarter of the treatments and it is denotes as 2 p − 2 . Principle fractional factorial design: The principle fraction may be defined as the set of treatments combination in the main effects and their interactions were evaluated to (+) sign. Now, the effect of factor A is, A = 1 2 4 [ ( a − 1 ) ( b + 1 ) ( c + 1 ) ( d + 1 ) ] = 1 2 4 [ a − b + a b − c + a c − b c + a b c − d + a d − b d + a b d − c d + a c d − b c d + a b c d − 1 ] Now, the effect of factor B is, B = 1 2 4 [ ( a + 1 ) ( b − 1 ) ( c + 1 ) ( d + 1 ) ] = 1 2 4 [ b − a + a b − c − a c + b c + a b c − d − a d + b d + a b d − c d − a c d + b c d + a b c d − 1 ] Now, the effect of factor C is, C = 1 2 4 [ ( a + 1 ) ( b + 1 ) ( c − 1 ) ( d + 1 ) ] = 1 2 4 [ − b − a − a b + c + a c + b c + a b c − d − a d − b d − a b d + c d + a c d + b c d + a b c d − 1 ] Now, the effect of factor D is, D = 1 2 4 [ ( a + 1 ) ( b + 1 ) ( c + 1 ) ( d − 1 ) ] = 1 2 4 [ − b − a − a b − c − a c − b c − a b c + d + a d + b d

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ISBN: 9780073401331

Author: William Navidi Prof.

Publisher: McGraw-Hill Education

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Chapter 9.5, Problem 1E

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Create a sign table for the principle fraction for a 2⁴ factorial design.

Indicate the alias pairs for the fraction factorial design.

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Chapter 9.4, Problem 10E

Chapter 9.5, Problem 2E

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Create a sign table for the principle fraction for a 2 4 factorial design. Indicate the alias pairs for the fraction factorial design.

Solution Summary: The author explains the principle tion for a 2 4 factorial design.

Create a sign table for the principle fraction for a 2⁴ factorial design.

Indicate the alias pairs for the fraction factorial design.

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Chapter 9 Solutions

Create a sign table for the principle fraction for a 2 4 factorial design. Indicate the alias pairs for the fraction factorial design.

Solution Summary: The author explains the principle tion for a 2 4 factorial design.

Create a sign table for the principle fraction for a 24 factorial design. Indicate the alias pairs for the fraction factorial design.

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Chapter 9 Solutions

Create a sign table for the principle fraction for a 2⁴ factorial design.

Indicate the alias pairs for the fraction factorial design.