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

2. Background Accuracy/Precision
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
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.
However,
Smaller Variability is ALWAYS better
We MUST work with replicated experiments
We will need to transform the response s
Actually, we don’t always need replicated experiments

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

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

7. Example 5 - Design Steps Replication and Randomization
2. Determine number of replicates to be used
Consider at Least 5 (up to 10)
In Example 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 Steps Collecting the Data Figure 7 - The Data Lochner and Matar - Figure 5.13
4. Perform experiment; record data
5. Group data for each factor level combination and calculate s.
SO is actually 1,5,3,7,2,6,4,8 (this is reverse standard order)

9. Example 5 - Design Steps The Analysis
6. Calculate logarithms of standard deviations obtained in 5. Record these.
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 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.
The calculation of factor effects actually helps to correct for non-normality. Log transformation isn’t ideal, so difficult-to-interpret patterns result.

11. Transformations Distributions and Normal Probability Plots of s2 and Log(s2)
Effects in lower end of lower left panel are too small, not too large. The lower right panel is better, but still a little tricky to interpret.

12. Example 5 - Analysis Figure 8 - Response Table for Mean Lochner and Matar - Figure 5.14y A B C AB AC BC D
Standard
Order
Bond
Strength
Adhesive
Type
Conductor
Material
Cure
Time
IC Post
Coating 1
73.48 -1 2
83.88 3
81.58 4
75.6 5
87.06 6
79.54 7
79.38 8
90.32
Sum
650.84
7.84
2.92
21.76
2.08
3.28
34.84
Divisor
Effect
81.355
1.96
0.73
5.44
0.52
-0.25
0.82
8.71

13. Example 5 - Analysis Figure 9 - Response Table for Log(s) Lochner and Matar - Figure 5.15y A B C AB AC BC D
Standard
Order
Log(s)
Adhesive
Type
Conductor
Material
Cure
Time
IC Post
Coating 1
0.196 -1 2
0.314 3
-0.097 4
0.713 5
-0.149 6
0.467 7
0.149 8
0.299
Sum
1.892
1.694
0.236
-0.36
0.226
-0.162
0.024
-1.158
Divisor
Effect
0.2365
0.4235
0.059
-0.09
0.0565
-0.041
0.006

14. Example 5 - Analysis Figure 10 - Effects Normal Probability Plot for 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?

16. 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.
It’s rare to have a factor increase the mean and reduce variation.

17. Case Study 1 Filling Weight of Dry Soup Mix - Factors and Response
Refer to gelatin and panna cotta. It’s not clear how many reps were used. An MIS student worked for a company that produced gourmet brownie and cookie mixes. Design generator is E=ABCD

18. Case Study 1 Filling Weight of Dry Soup Mix - Effects Table
Interpret This Data
Determine the Important Effects
Do the Interaction Tables and Plots for Significant Interactions
As an exercise, plot effects, and look at two-way tables.