Lecture 12

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# Lecture 12 - PowerPoint PPT Presentation

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
• 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
• 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 minimum aberration (MA) designs
• E=ABC; F=ABD
Example
• Results
Example
• Which effects can we estimate?
• Defining Contrast Sub-Group: I=ABCE=ABDF=CDEF
• Word-Length Patter:
• 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
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)
• 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 (4.4.2)
• 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
• 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