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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. 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

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  1. IV.3 Designs to Minimize Variability • Background • An Example • Design Steps • Transformations • The Analysis • A Case Study

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

  3. BackgroundExample 4 - Example I.2.3 Revisited • Which Factors Affect • Accuracy? • Precision?

  4. 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

  5. Example 5Mounting an Integrated Circuit on SubstrateFigure 5 - Factor LevelLochner and Matar - Figure 5.11 • Response: bond strength

  6. Example 5 - Design StepsSelecting the DesignFigure 6 - The Experimental DesignLochner and Matar - Figure 5.12 • 1. Select an appropriate experimental design

  7. 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!

  8. 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.

  9. Example 5 - Design StepsThe Analysis • 6. Calculate logarithms of standard deviations obtained in 5. Record these. • 7. Analyze log s as the response.

  10. 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.

  11. TransformationsDistributions and Normal Probability Plots of s2 and Log(s2)

  12. Example 5 - AnalysisFigure 8 - Response Table for MeanLochner and Matar - Figure 5.14

  13. Example 5 - AnalysisFigure 9 - Response Table for Log(s)Lochner and Matar - Figure 5.15

  14. Example 5 - AnalysisFigure 10 - Effects Normal Probability Plot for Mean • What Factor Settings Favorably Affect the Mean?

  15. Example 5 - AnalysisFigure 11 - Effects Normal Probability Plot for Log(s)Lochner and Matar - Figure 5.16 • What Factor Settings Favorably Affect Variability?

  16. 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.

  17. Case Study 1Filling Weight of Dry Soup Mix - Factors and Response

  18. 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

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