Stat 470-15

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# Stat 470-15 - PowerPoint PPT Presentation

Stat 470-15. Today: Start Chapter 4 Assignment 3 : 3.14 a, b (do normal qq-plots only),c, 3.16, 3.17 Additional questions : 3.14 b (also use the IER version of Lenth’s method and compare to the qq-plot conclusions), 3.19. Fractional Factorial Designs at 2-Levels.

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## Stat 470-15

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Presentation Transcript
Stat 470-15
• Today: Start Chapter 4
• Assignment 3: 3.14 a, b (do normal qq-plots only),c, 3.16, 3.17
• Additional questions: 3.14 b (also use the IER version of Lenth’s method and compare to the qq-plot conclusions), 3.19
Fractional Factorial Designs at 2-Levels
• Use a 2k-p fractional factorial design to explore k factors in 2k-p trials
• In general, can construct a 2k-p fractional factorial design from the full factorial design with 2k-p trials
• Set the levels of the first (k-p) factors similar to the full factorial design with 2k-p trials
• Next, use the interaction columns between the first (k-p) factors to set levels of the remaining factors
Example
• Suppose have 7 factors, each at 2-levels, but only enough resources to run 16 trials
• Can use a 16-run full factorial to design the experiment
• Use the 16 unique treatments for 4 factors to set the levels of the first 4 factors (A-D)
• Use interaction columns from the first 4 factors to set the levels of the remaining 3 factors
Example
• Would like to have as few short words as possible
• Why?
Example
• Suppose have 7 factors, each at 2-levels, but only enough resources to run 32 trials
• Can use a 27-2 fractional factorial design
• Which one is better?
• D1: I=ABCDF=ABCEG=DEFG
Example
• Suppose have 8 factors (A-H), each at 2-levels, but only enough resources to run 32 trials
• Can use a 28-3 fractional factorial design
• Table 4A gives the minimum aberration (MA) designs for 8, 16, 32 and 64 runs
• From Table 4A.3, MA design gives:
• 6=123
• 7=124
• 8=1345
Example
• Table 4A.3, MA design is:
• 6=123
• 7=124
• 8=1345
• Design for our factors:
• Word length pattern:
Example
• Speedometer cables can be noisy because of shrinkage in the plastic casing material
• An experiment was conducted to find out what caused shrinkage
• Engineers started with 6 different factors:
• A braiding tension
• B wire diameter
• C liner tension
• D liner temperature
• E coating material
• F melt temperature
Example
• Response is percentage shrinkage per specimen
• There were two levels of each factor
• A 26-2 fractional factorial
• The purpose of such an experiment is to determine which factors impact the response
Example
• Constructing the design
• Write down the 16 run full factorial
• Use interaction columns to set levels of the other 2 factors
• Which interaction columns do we use?
• Table 4A.2 gives 16 run MA designs
• E=ABC; F=ABD
Example
• Results
Example
• Which effects can we estimate?
• Defining Contrast Sub-Group: I=ABCE=ABDF=CDEF
• Word-Length Pattern:
• Resolution:
Example
• Effect Estimates and QQ-Plot:
• Use defining contrast subgroup to determine which effects to estimate
• Can use qq-plot or Lenth’s method to evaluate the significance of the effects
• Fractional factorial designs allow you to explore many factors in relatively few trials