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

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

3. Background Example 4 - Example I.2.3 Revisited Which Factors Affect Which Factors Affect –Accuracy? –Precision?

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

5. Example 5 Mounting an Integrated Circuit on Substrate Figure 5 - Factor Level Lochner and Matar - Figure 5.11 Response: bond strength Response: bond strength

6. Example 5 - Design Steps Selecting the Design Figure 6 - The Experimental Design Lochner and Matar - Figure 5.12 1. Select an appropriate experimental design 1. Select an appropriate experimental design

7. Example 5 - Design Steps Replication and Randomization 2. Determine number of replicates to be used 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 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 Steps Collecting the Data Figure 7 - The Data Lochner and Matar - Figure 5.13 4. Perform experiment; record data 4. Perform experiment; record data 5. Group data for each factor level combination and calculate s. 5. Group data for each factor level combination and calculate s.

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

10. Transformations Why 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 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. 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. Transformations Distributions and Normal Probability Plots of s 2 and Log(s 2 )

12. Example 5 - Analysis Figure 8 - Response Table for Mean Lochner and Matar - Figure 5.14 yABCABACBCD Standard Order Bond Strength Adhesive Type Conductor Material Cure Time IC Post Coating 173.48 111 283.881 11 381.581 1 1 475.6111 587.06 11 1 679.5411 1 779.3811 1 890.321111111 Sum650.847.842.9221.762.083.2834.84 Divisor84444444 Effect81.3551.960.735.440.52-0.250.828.71

13. Example 5 - Analysis Figure 9 - Response Table for Log(s) Lochner and Matar - Figure 5.15 yABCABACBCD Standard OrderLog(s) Adhesive Type Conductor Material Cure Time IC Post Coating 10.196 111 20.3141 11 3-0.0971 1 1 40.713111 5-0.149 11 1 60.46711 1 70.14911 1 80.2991111111 Sum1.8921.6940.236-0.360.226-0.1620.024-1.158 Divisor84444444 Effect0.23650.42350.059-0.090.0565-0.0410.006-0.2895

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

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

16. Example 5 - Interpretation Silver IC post coating increases bond strength and decreases variation in bond strength. Silver IC post coating increases bond strength and decreases variation in bond strength. Adhesive D2A decreases variation in bond strength. Adhesive D2A decreases variation in bond strength. 120-minute cure time increases bond strength. 120-minute cure time increases bond strength.

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

18. Case Study 1 Filling Weight of Dry Soup Mix - Effects Table Interpret This Data Interpret This Data –Determine the Important Effects –Do the Interaction Tables and Plots for Significant Interactions Interpret This Data Interpret This Data –Determine the Important Effects –Do the Interaction Tables and Plots for Significant Interactions