IV.3 Designs to Minimize Variability

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IV.3 Designs to Minimize Variability

• Background
• An Example
• Design Steps
• Transformations
• The Analysis
• A Case Study

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BackgroundAccuracy/Precision

• Factors Can Affect Response Variable by Either
• Changing Its Average Value (Accuracy)
• Changing Its Variation (Precision) or
• BOTH

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BackgroundExample 4 - Example I.2.3 Revisited

• Which Factors Affect
• Accuracy?
• Precision?

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BackgroundAnalysis for Changes in Variability

• For studying Variability, we can use ALL the
  designs, ALL the ideas that we used when studying
  changes in mean response level.
• However,
• Smaller Variability is ALWAYS better
• We MUST work with replicated experiments
• We will need to transform the response s

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Example 5Mounting an Integrated Circuit on
SubstrateFigure 5 - Factor LevelLochner and
Matar - Figure 5.11

• Response bond strength

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Example 5 - Design StepsSelecting the
DesignFigure 6 - The Experimental DesignLochner
and Matar - Figure 5.12

• 1. Select an appropriate experimental design

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Example 5 - Design StepsReplication and
Randomization

• 2. Determine number of replicates to be used
• Consider at Least 5 (up to 10)
• In Example 5 5 replicates, 40 trials
• 3. Randomize order of ALL trials
• Replicates Run Sequentially Often Have Less
  Variation Than True Process Variation
• This May Be Inconvenient!

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Example 5 - Design StepsCollecting the
DataFigure 7 - The DataLochner and Matar -
Figure 5.13

• 4. Perform experiment record data
• 5. Group data for each factor level combination
  and calculate s.

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Example 5 - Design StepsThe Analysis

• 6. Calculate logarithms of standard deviations
  obtained in 5. Record these.
• 7. Analyze log s as the response.

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TransformationsWhy transform s?

• If the data follow a bell-shaped curve, then so
  do the cell means and the factor effects for the
  means. However, the cell standard deviations and
  factor effects of the standard deviations do not
  follow a bell-shaped curve.
• If we plot such data on our normal plotting
  paper, we would obtain a graph that indicates
  important or unusual factor effects in the
  absence of any real effect. The log
  transformation normalizes the data.

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TransformationsDistributions and Normal
Probability Plots of s2 and Log(s2)
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Example 5 - AnalysisFigure 8 - Response Table
for MeanLochner and Matar - Figure 5.14
  y A B C AB AC BC D
Standard Order Bond Strength Adhesive Type Conductor Material Cure Time       IC Post Coating
1 73.48 -1 -1 -1 1 1 1 -1
2 83.88 1 -1 -1 -1 -1 1 1
3 81.58 -1 1 -1 -1 1 -1 1
4 75.6 1 1 -1 1 -1 -1 -1
5 87.06 -1 -1 1 1 -1 -1 1
6 79.54 1 -1 1 -1 1 -1 -1
7 79.38 -1 1 1 -1 -1 1 -1
8 90.32 1 1 1 1 1 1 1
Sum 650.84 7.84 2.92 21.76 2.08 -1 3.28 34.84
Divisor 8 4 4 4 4 4 4 4
Effect 81.355 1.96 0.73 5.44 0.52 -0.25 0.82 8.71
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Example 5 - AnalysisFigure 9 - Response Table
for Log(s)Lochner and Matar - Figure 5.15
  y A B C AB AC BC D
Standard Order Log(s) Adhesive Type Conductor Material Cure Time       IC Post Coating
1 0.196 -1 -1 -1 1 1 1 -1
2 0.314 1 -1 -1 -1 -1 1 1
3 -0.097 -1 1 -1 -1 1 -1 1
4 0.713 1 1 -1 1 -1 -1 -1
5 -0.149 -1 -1 1 1 -1 -1 1
6 0.467 1 -1 1 -1 1 -1 -1
7 0.149 -1 1 1 -1 -1 1 -1
8 0.299 1 1 1 1 1 1 1
Sum 1.892 1.694 0.236 -0.36 0.226 -0.162 0.024 -1.158
Divisor 8 4 4 4 4 4 4 4
Effect 0.2365 0.4235 0.059 -0.09 0.0565 -0.041 0.006 -0.2895
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Example 5 - AnalysisFigure 10 - Effects Normal
Probability Plot for Mean

• What Factor Settings Favorably Affect the Mean?

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Example 5 - AnalysisFigure 11 - Effects Normal
Probability Plot for Log(s)Lochner and Matar -
Figure 5.16

• What Factor Settings Favorably Affect Variability?

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Example 5 - Interpretation

• Silver IC post coating increases bond strength
  and decreases variation in bond strength.
• Adhesive D2A decreases variation in bond
  strength.
• 120-minute cure time increases bond strength.

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Case Study 1Filling Weight of Dry Soup Mix -
Factors and Response
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Case Study 1Filling Weight of Dry Soup Mix -
Effects Table

• Interpret This Data
• Determine the Important Effects
• Do the Interaction Tables and Plots for
  Significant Interactions