IV.3 Designs to Minimize Variability

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# IV.3 Designs to Minimize Variability - PowerPoint PPT Presentation

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
• Background
• An Example
• Design Steps
• Transformations
• The Analysis
• A Case Study
BackgroundAccuracy/Precision
• Factors Can Affect Response Variable by Either
• Changing Its Average Value (Accuracy)
• Changing Its Variation (Precision) or
• BOTH
BackgroundExample 4 - Example I.2.3 Revisited
• Which Factors Affect
• Accuracy?
• Precision?
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
Example 5Mounting an Integrated Circuit on SubstrateFigure 5 - Factor LevelLochner and Matar - Figure 5.11
• Response: bond strength
Example 5 - Design StepsSelecting the DesignFigure 6 - The Experimental DesignLochner and Matar - Figure 5.12
• 1. Select an appropriate experimental design
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 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 StepsThe Analysis
• 6. Calculate logarithms of standard deviations obtained in 5. Record these.
• 7. Analyze log s as the response.
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 - AnalysisFigure 8 - Response Table for MeanLochner and Matar - Figure 5.14
Example 5 - AnalysisFigure 9 - Response Table for Log(s)Lochner and Matar - Figure 5.15
• What Factor Settings Favorably Affect the Mean?
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
• 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 1Filling Weight of Dry Soup Mix - Effects Table
• Interpret This Data
• Determine the Important Effects
• Do the Interaction Tables and Plots for Significant Interactions