a. Explanation Calculations: The given information is that the design used is 2 3 . There were total of 32 observations and four run in each blocks. Construction of blocks with ABC is confounded: Define the contrast, L = α 1 x 1 + α 2 x 2 + .... + α n x n Where, x i is the i th factor appearing in the treatment combination and α i is the exponent appear on the effect that is to be confounded with blocks. Both x i and α i can take values 0 and 1. Treatment with same value L is grouped in one block. Here, x 1 corresponds to factor A, x 2 corresponds to factor B, and x 3 corresponds to factor C and α 1 = α 2 = α 3 = 1 L = ( 1 ) x 1 + ( 1 ) x 2 + ( 1 ) x 3 For treatment combination (1), all factors appear in low level. That is x 1 = x 2 = x 3 = 0 Treatment (1): L = ( 1 ) ( 0 ) + ( 1 ) ( 0 ) + ( 1 ) ( 0 ) = 0 ( mode 2 ) Similarly the other L values can be obtained as shown in the table: Treatment L a ( 1 ) ( 1 ) + ( 1 ) ( 0 ) + ( 1 ) ( 0 ) = 1 ( mode 2 ) = 1 b ( 1 ) ( 0 ) + ( 1 ) ( 1 ) + ( 1 ) ( 0 ) = 1 ( mode 2 ) = 1 c ( 1 ) ( 0 ) + ( 1 ) ( 0 ) + ( 1 ) ( 1 ) = 1 ( mode 2 ) = 1 ab ( 1 ) ( 1 ) + ( 1 ) ( 1 ) + ( 1 ) ( 0 ) = 2 ( mode 2 ) = 0 ac ( 1 ) ( 1 ) + ( 1 ) ( 0 ) + ( 1 ) ( 1 ) = 2 ( mode 2 ) = 0 bc ( 1 ) ( 0 ) + ( 1 ) ( 1 ) + ( 1 ) ( 1 ) = 2 ( mode 2 ) = 0 abc ( 1 ) ( 1 ) + ( 1 ) ( 1 ) + ( 1 ) ( 1 ) = 3 ( mode 2 ) = 1 Therefore, the block with ABC is confounded: Block 1 (1) ab ac bc Block 2 a b c abc Similarly the Construction of blocks with AB is confounded is shown in the below table: L = ( 1 ) x 1 + ( 1 ) x 2 + ( 0 ) x 3 Treatment L (1) ( 1 ) ( 0 ) + ( 1 ) ( 0 ) + ( 0 ) ( 0 ) = 0 ( mode 2 ) = 0 a ( 1 ) ( 1 ) + ( 1 ) ( 0 ) + ( 0 ) ( 0 ) = 1 ( mode 2 ) = 1 b ( 1 ) ( 0 ) + ( 1 ) ( 1 ) + ( 0 ) ( 0 ) = 1 ( mode 2 ) = 1 c ( 1 ) ( 0 ) + ( 1 ) ( 0 ) + ( 0 ) ( 1 ) = 0 ( mode 2 ) = 0 ab ( 1 ) ( 1 ) + ( 1 ) ( 1 ) + ( 0 ) ( 0 ) = 2 ( mode 2 ) = 0 ac ( 1 ) ( 1 ) + ( 1 ) ( 1 ) + ( 0 ) ( 1 ) = 1 ( mode 2 ) = 1 bc ( 1 ) ( 0 ) + ( 1 ) ( 1 ) + ( 0 ) ( 1 ) = 1 b. To determine Show an outline for the analysis of variance for the design.

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118802250

Author: Montgomery

Publisher: WILEY

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Chapter 14, Problem 104SE

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Suggest a blocking scheme will provides some information on all interaction.

To determine

Show an outline for the analysis of variance for the design.

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Chapter 14 Solutions

Applied Statistics and Probability for Engineers

Ch. 14.3 - 14-1. An article in Industrial Quality Control...Ch. 14.3 - Prob. 2E Ch. 14.3 - Prob. 3E Ch. 14.3 - 14-4. An experiment was conducted to determine...Ch. 14.3 - Prob. 5E Ch. 14.3 - 14-6. Johnson and Leone (Statistics and...Ch. 14.3 - 14-7. An article in the IEEE Transactions on...Ch. 14.3 - Prob. 8E Ch. 14.3 - Prob. 9E Ch. 14.3 - Prob. 10E

Ch. 14.3 - Prob. 11E Ch. 14.4 - Prob. 12E Ch. 14.4 - Prob. 13E Ch. 14.5 - Prob. 14E Ch. 14.5 - 14-15. Four factors are thought to influence the...Ch. 14.5 - Prob. 16E Ch. 14.5 - Prob. 17E Ch. 14.5 - Prob. 18E Ch. 14.5 - 14-19. An experiment was run in a semiconductor...Ch. 14.5 - Prob. 20E Ch. 14.5 - Prob. 21E Ch. 14.5 - 14-22. A 24 factorial design was run in a chemical...Ch. 14.5 - Prob. 23E Ch. 14.5 - Prob. 24E Ch. 14.5 - Prob. 25E Ch. 14.5 - Prob. 26E Ch. 14.5 - Prob. 27E Ch. 14.5 - Prob. 28E Ch. 14.5 - Prob. 29E Ch. 14.5 - Prob. 30E Ch. 14.5 - Prob. 31E Ch. 14.5 - Prob. 32E Ch. 14.5 - 14-33. An article in Analytica Chimica Acta...Ch. 14.5 - Prob. 34E Ch. 14.5 - 14-35. The book Using Designed Experiments to...Ch. 14.6 - 14-36. Consider the data from the first replicate...Ch. 14.6 - Prob. 37E Ch. 14.6 - Prob. 38E Ch. 14.6 - Prob. 39E Ch. 14.6 - 14-40. Consider the data from the first replicate...Ch. 14.6 - Prob. 41E Ch. 14.6 - 14-43. An article in Quality Engineering...Ch. 14.6 - Prob. 44E Ch. 14.6 - Prob. 45E Ch. 14.6 - 14-46. An article in Advanced Semiconductor...Ch. 14.6 - Prob. 47E Ch. 14.6 - Prob. 48E Ch. 14.7 - Prob. 49E Ch. 14.7 - Prob. 50E Ch. 14.7 - Prob. 51E Ch. 14.7 - Prob. 52E Ch. 14.7 - 14-54. An article in Quality Engineering [“A...Ch. 14.7 - Prob. 56E Ch. 14.7 - Prob. 57E Ch. 14.7 - Prob. 58E Ch. 14.7 - 14-59. An article in the Journal of...Ch. 14.7 - Prob. 60E Ch. 14.7 - Prob. 61E Ch. 14.7 - Prob. 62E Ch. 14.8 - Prob. 63E Ch. 14.8 - 14-64. An article in Quality Engineering [“Mean...Ch. 14.8 - 14-65. Consider the first-order model where −1 <...Ch. 14.8 - 14-66. A manufacturer of cutting tools has...Ch. 14.8 - Prob. 67E Ch. 14.8 - 14-68. In their book Empirical Model Building and...Ch. 14.8 - 14-69. Consider the first-order model y = 12...Ch. 14.8 - Prob. 73E Ch. 14.8 - Prob. 74E Ch. 14 - Prob. 75SE Ch. 14 - Prob. 76SE Ch. 14 - Prob. 77SE Ch. 14 - Prob. 78SE Ch. 14 - Prob. 79SE Ch. 14 - Prob. 80SE Ch. 14 - Prob. 81SE Ch. 14 - Prob. 82SE Ch. 14 - Prob. 83SE Ch. 14 - 14-84. Construct a design in 16 runs. What are...Ch. 14 - Prob. 85SE Ch. 14 - Prob. 87SE Ch. 14 - Prob. 88SE Ch. 14 - Prob. 89SE Ch. 14 - 14-90. An article in Biotechnology Progress (2001,...Ch. 14 - 14-93. The rework time required for a machine was...Ch. 14 - Prob. 94SE Ch. 14 - Prob. 95SE Ch. 14 - Prob. 97SE Ch. 14 - Prob. 98SE Ch. 14 - Prob. 99SE Ch. 14 - 14-101. Consider an unreplicated 2k factorial, and...Ch. 14 - Prob. 102SE Ch. 14 - Prob. 103SE Ch. 14 - Prob. 104SE Ch. 14 - Prob. 105SE Ch. 14 - Prob. 106SE Ch. 14 - Prob. 107SE Ch. 14 - 14-108. Set up a 27 − 4 design using D = AB, E =...Ch. 14 - Prob. 109SE

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