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Lecture 12. Today: 4.2, 4.3-4.6 Next day: more 4.3-4.6 Assignment #4: Chapter 4 - 13 (a,b), 14, 15, 23, additional question at end of these notes Due in 2 weeks. Example. Speedometer cables can be noisy because of shrinkage in the plastic casing material

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lecture 12
Lecture 12
  • Today: 4.2, 4.3-4.6
  • Next day: more 4.3-4.6
  • Assignment #4: Chapter 4 - 13 (a,b), 14, 15, 23, additional question at end of these notes
  • Due in 2 weeks
example
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
example1
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
example2
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 minimum aberration (MA) designs
    • E=ABC; F=ABD
example4
Example
  • Results
example5
Example
  • Which effects can we estimate?
  • Defining Contrast Sub-Group: I=ABCE=ABDF=CDEF
  • Word-Length Patter:
  • Resolution:
example6
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
techniques for resolving ambiguities
Techniques for Resolving Ambiguities
  • Suppose the experiment in the previous example was performed and the AC=BE interaction was identified as significant (in addition to the A and E main effects)
  • Which is the important interaction AC or BE or both?
  • Prior knowledge may indicate that one of the effects is not important
  • Can conduct a follow-up experiment
optimal design approach 4 4 2
Optimal Design Approach (4.4.2)
  • Can perform a follow-up experiment to “de-alias” the AC and BE interaction, but what treatments should be run?
  • Would like to estimate the model with all potentially significant effects
    • A, E, AC, BE
  • The experiment is not completely randomized since the follow-up runs are performed only after original experiment
    • Include a block effect
  • Model:
optimal design approach 4 4 21
Optimal Design Approach (4.4.2)
  • The best set of new trials should optimize some design criterion
  • Should estimate the model of interest in best possible manner
  • Already have initial (say 16) trials, so design criterion is driven by original experiment and the model
  • D-optimality:
  • Motivation:
assignment question
Assignment Question
  • Suppose in the cable shrinkage example, effects A, E and AC=BE are identified as signifincat
  • To resolve the aliasing of the interaction effects, a follow-up experiment with 4 trials is to be performed
  • What 4 trails should be performed?
  • Use the D-optimality criterion and report the value of Dmax