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IV.3 Designs to Minimize Variability. Background An Example Design Steps Transformations The Analysis A Case Study. Background Accuracy/Precision. Factors Can Affect Response Variable by Either Changing Its Average Value (Accuracy) Changing Its Variation (Precision) or BOTH.

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iv 3 designs to minimize variability
IV.3 Designs to Minimize Variability
  • Background
  • An Example
    • Design Steps
    • Transformations
    • The Analysis
  • A Case Study
background accuracy precision
BackgroundAccuracy/Precision
  • Factors Can Affect Response Variable by Either
    • Changing Its Average Value (Accuracy)
    • Changing Its Variation (Precision) or
    • BOTH
background example 4 example i 2 3 revisited
BackgroundExample 4 - Example I.2.3 Revisited
  • Which Factors Affect
    • Accuracy?
    • Precision?
background analysis for changes in variability
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
slide5
Example 5Mounting an Integrated Circuit on SubstrateFigure 5 - Factor LevelLochner and Matar - Figure 5.11
  • Response: bond strength
slide6
Example 5 - Design StepsSelecting the DesignFigure 6 - The Experimental DesignLochner and Matar - Figure 5.12
  • 1. Select an appropriate experimental design
example 5 design steps replication and randomization
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!
example 5 design steps collecting the data figure 7 the data lochner and matar figure 5 13
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.
example 5 design steps the analysis
Example 5 - Design StepsThe Analysis
  • 6. Calculate logarithms of standard deviations obtained in 5. Record these.
  • 7. Analyze log s as the response.
transformations why transform s
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.
example 5 analysis figure 8 response table for mean lochner and matar figure 5 14
Example 5 - AnalysisFigure 8 - Response Table for MeanLochner and Matar - Figure 5.14
example 5 analysis figure 9 response table for log s lochner and matar figure 5 15
Example 5 - AnalysisFigure 9 - Response Table for Log(s)Lochner and Matar - Figure 5.15
example 5 analysis figure 10 effects normal probability plot for mean
Example 5 - AnalysisFigure 10 - Effects Normal Probability Plot for Mean
  • What Factor Settings Favorably Affect the Mean?
slide15
Example 5 - AnalysisFigure 11 - Effects Normal Probability Plot for Log(s)Lochner and Matar - Figure 5.16
  • What Factor Settings Favorably Affect Variability?
example 5 interpretation
Example 5 - Interpretation
  • Silver IC post coating increases bond strength anddecreases variation in bond strength.
  • Adhesive D2A decreases variation in bond strength.
  • 120-minute cure time increases bond strength.
case study 1 filling weight of dry soup mix effects table
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