1. IV.4.1 IV.4 Signal-to-Noise Ratios o Background o Example

2. IV.4.2 Background Motivation o Wouldn’t it be Nice to Have a Single Performance Measure that Simultaneously Identified Factor Settings that – Optimally target the mean – Reduce variation o This is the Major Motivation Underlying Taguchi’s Use of Signal-to-Noise Ratios.

3. IV.4.3 Background Some Popular S/N Ratios o Taguchi proposed OVER 80 signal-to-noise (S/N) ratios. The following three are among his most widely applicable. Our goal is to MAXIMIZE all three.  SN s = -10 log(  y 2 /n) – What are the optimal values for y i ? – Used when “smaller is better”  SN L = -10 log(  y 2 )/n) – What are the optimal values for y i ? – Used when “larger is better” o SN T = 10 log(y 2 /s 2 ) – Ostensibly used when “target is better” – How does SN T measure proximity to target?

4. IV.4.4 Background Criticisms of Taguchi’s S/N Ratios o SN s and SN L – y will almost always be a more sensitive measure of the size of effects on the mean o SN T – If y and s are independent, we can look at them separately to make better decisions – y and s are frequently directly related, a situation SN T will not detect

5. IV.4.5 Example 6 Growing an Epitaxial Layer on Silicon Wafers Figure 12 - Wafers Mounted on Susceptor Kacker, R. N. and Shoemaker, A. C. (1986). “Robust Design: A Cost-Effective Method for Improving Manufacturing Processes” AT&T Technical Journal 65, pp.311-342.

6. IV.4.6 Example 6 Growing an Epitaxial Layer on Silicon Wafers Figure 13 - Initial and Test Settings  The response variable is thickness of epitaxial layer in  m with a target of 14.5  m. Which factors will affect – mean? – variation?

7. IV.4.7 Example 6 Growing an Epitaxial Layer on Silicon Wafers Figure 14 - The Experimental Design o Each experimental run results in 70 observations on the response!

8. IV.4.8 Example 6 Growing an Epitaxial Layer on Silicon Wafers Figure 14 - The Experimental Design o Note that the design here is “non-standard” o Can you assign factors to columns A, B, C, and D in the 16-run signs table? – Hint: the original factors A, B, C and D cannot be used to generate the design o Which columns would the other 4 factors be assigned to in the 16-run signs table?

9. IV.4.9 Example 6 - Analysis Using Only SN T Growing an Epitaxial Layer on Silicon Wafers Figure 16a - Completed Response Table

10. IV.4.10 Example 6 - Analysis Using Only SN T Growing an Epitaxial Layer on Silicon Wafers Figure 17 - Effects Normal Probability Plot

11. IV.4.11 Example 6 - Analysis Using Only SN T Growing an Epitaxial Layer on Silicon Wafers Interpretation o What factors favorable affect SN T ? – A (susceptor rotation method) set at continuous – H (nozzle position) set at 6.

12. IV.4.12 Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Figure 18a - Response Table for Mean

13. IV.4.13 Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Figure 19a - Response Table for Log(s)

14. IV.4.14 Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Figure 20 - Effects Normal Probability Plot for Mean

15. IV.4.15 Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Figure 21 - Effects Normal Probability Plot for Log(s)

16. IV.4.16 Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Interpretation o What factors affect the mean? – D (deposition time) set at high level increases the mean. o What factor settings favorably affect variability? – A (susceptor rotation method) set at continuous. – H (nozzle position) set at 6. – D (deposition time) set at low.

17. IV.4.17 Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Interpretation o Conclusions: – Set nozzle position at 6 – Use continuous susceptor rotation method – Use deposition time to adjust mean to target