Explanation Calculation: The given information is that 1 4 fraction of the 2 5 design used for the calculation. In design of eight runs, the generators in 2 5 − 2 is assumed as D = A B , E = A C . Software procedure: Step-by-step procedure to find the factorial design table using MINITAB is as follows: Choose Stat > DOE > Factorial > Create Factorial Design . Under Type of Design , choose 2 level factorial design . From Number of factors , choose 5 . Click Designs . Select 1/4 fraction . In Number of center points per block choose 0 . Click OK . Enter the corresponding Strength in the newly created factorial design worksheet. Output obtained by MINITAB procedure is as follows: Software procedure: Step-by-step procedure to obtain the data display is as follows: Choose Data > Display Data . In Columns, constants, and matrices to display , enter the column of Strength. Click OK . Step by step procedure to construct normal plot for standardized effects: Choose Stat > DOE > Factorial > Analyze Factorial Design . In Response , enter the corresponding Strength column from the factorial design worksheet. In Terms , select all the terms. Select Graphs. In Residuals for Plots , choose Standardized . Click OK in all the dialog boxes. Output obtained from MINITAB is given below; From the normal probability plot it is clear that A , B and D are significant. State the hypotheses: Main effect of factor A: Null hypothesis: H 0 : Main effect of factor A is not significant. Alternative hypothesis: H 1 : Main effect of factor A is significant. Main effect of factor B: Null hypothesis: H 0 : Main effect of factor B is not significant. Alternative hypothesis: H 1 : Main effect of factor B is significant. Main effect of factor D: Null hypothesis: H 0 : Main effect of factor D is not significant. Alternative hypothesis: H 1 : Main effect of factor D is significant

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.

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Question

Chapter 14.7, Problem 56E

To determine

Construct a design if only 14 fraction of the 25 design in Exercise could be run and analyze the data that are obtained by selecting only the response for the 8 runs in 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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