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A router is used to cut locating notches on a printed circuit board. The vibration level at the surface of the board as it is cut is considered to be a major source of dimensional variation in the notches. Two factors are thought to influence vibration: bit size (A) and cutting speed (B). Two bit sizes (1/16 and 1/8 inch) and two speeds (40 and 90 rpm) are selected, and four boards are cut at each set of conditions shown below. The response variable is vibration measured as a resultant vector of three accelerometers (x, y, and z) on each test circuit board. (a) Consider the 26 design in eight blocks of eight runs each with ABCD, ACE, and ABEF as the independent effects chosen to be confounded with blocks. Generate the design. Find the other effects confound with blocks

A router is used to cut locating notches on a printed circuit board. The vibration level at the surface of the board as it is cut is considered to be a major source of dimensional variation in the notches. Two factors are thought to influence vibration: bit size (A) and cutting speed (B). Two bit sizes (1/16 and 1/8 inch) and two speeds (40 and 90 rpm) are selected, and four boards are cut at each set of conditions shown below. The response variable is vibration measured as a resultant vector of three accelerometers (x, y, and z) on each test circuit board. (a) Consider the 26 design in eight blocks of eight runs each with ABCD, ACE, and ABEF as the independent effects chosen to be confounded with blocks. Generate the design. Find the other effects confound with blocks

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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  1. A router is used to cut locating notches on a printed circuit board. The vibration level at the surface of the board as it is cut is considered to be a major source of dimensional variation in the notches. Two factors are thought to influence vibration: bit size (A) and cutting speed (B). Two bit sizes (1/16 and 1/8 inch) and two speeds (40 and 90 rpm) are selected, and four boards are cut at each set of conditions shown below. The response variable is vibration measured as a resultant vector of three accelerometers (x, y, and z) on each test circuit board.

(a) Consider the 26 design in eight blocks of eight runs each with ABCD, ACE, and ABEF as the independent effects chosen to be confounded with blocks. Generate the design. Find the other effects confound with blocks.

### Experimental Data Table This table presents data concerning various treatment combinations for an experimental study, with measurements taken across four replicates. #### Table Structure: - **Columns:** - **A**: Represents the presence (+) or absence (-) of factor A. - **B**: Represents the presence (+) or absence (-) of factor B. - **Treatment Combination**: Denotes the specific combination of treatments: - **(1)**: Neither A nor B are present. - **a**: Only A is present. - **b**: Only B is present. - **ab**: Both A and B are present. - **Replicate**: Measurements I through IV for each treatment combination. #### Data: - **Treatment (1)**: - Replicate I: 18.2 - Replicate II: 18.9 - Replicate III: 12.9 - Replicate IV: 14.4 - **Treatment (a)**: - Replicate I: 27.2 - Replicate II: 24.0 - Replicate III: 22.4 - Replicate IV: 22.5 - **Treatment (b)**: - Replicate I: 15.9 - Replicate II: 14.5 - Replicate III: 15.1 - Replicate IV: 14.2 - **Treatment (ab)**: - Replicate I: 41.0 - Replicate II: 43.9 - Replicate III: 36.3 - Replicate IV: 39.9 ### Analysis: This table can serve as a basis for analyzing the impact of factors A and B individually and in combination on the experimental outcomes. The variation across replicates indicates potential experimental variability, while the differences between treatment combinations suggest the effects of the presence of factors A and B.
Transcribed Image Text:### Experimental Data Table This table presents data concerning various treatment combinations for an experimental study, with measurements taken across four replicates. #### Table Structure: - **Columns:** - **A**: Represents the presence (+) or absence (-) of factor A. - **B**: Represents the presence (+) or absence (-) of factor B. - **Treatment Combination**: Denotes the specific combination of treatments: - **(1)**: Neither A nor B are present. - **a**: Only A is present. - **b**: Only B is present. - **ab**: Both A and B are present. - **Replicate**: Measurements I through IV for each treatment combination. #### Data: - **Treatment (1)**: - Replicate I: 18.2 - Replicate II: 18.9 - Replicate III: 12.9 - Replicate IV: 14.4 - **Treatment (a)**: - Replicate I: 27.2 - Replicate II: 24.0 - Replicate III: 22.4 - Replicate IV: 22.5 - **Treatment (b)**: - Replicate I: 15.9 - Replicate II: 14.5 - Replicate III: 15.1 - Replicate IV: 14.2 - **Treatment (ab)**: - Replicate I: 41.0 - Replicate II: 43.9 - Replicate III: 36.3 - Replicate IV: 39.9 ### Analysis: This table can serve as a basis for analyzing the impact of factors A and B individually and in combination on the experimental outcomes. The variation across replicates indicates potential experimental variability, while the differences between treatment combinations suggest the effects of the presence of factors A and B.
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