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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
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
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
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
example2
Example
  • Would like to have as few short words as possible
  • Why?
example3
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
    • D2: I=ABCF=ADEG=BCDEG
example4
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
example5
Example
  • Table 4A.3, MA design is:
    • 6=123
    • 7=124
    • 8=1345
  • Design for our factors:
  • Word length pattern:
example6
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
example7
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
example8
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
example10
Example
  • Results
example11
Example
  • Which effects can we estimate?
  • Defining Contrast Sub-Group: I=ABCE=ABDF=CDEF
  • Word-Length Pattern:
  • Resolution:
example12
Example
  • Effect Estimates and QQ-Plot:
comments
Comments
  • 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
  • Trade-off run-size for information about interactions