IV.4 Signal-to-Noise Ratios

1. IV.4 Signal-to-Noise Ratios • Background • Example

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

3. BackgroundSome Popular S/N Ratios • 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. • SNs = -10 log(Sy2/n) • What are the optimal values for yi? • Used when “smaller is better” • SNL = -10 log(S(1/y2)/n) • What are the optimal values for yi? • Used when “larger is better” • SNT = 10 log(y2/s2) • Ostensibly used when “target is better” • How does SNT measure proximity to target?

4. BackgroundCriticisms of Taguchi’s S/N Ratios • SNs and SNL • y will almost always be a more sensitive measure of the size of effects on the mean • SNT • 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 SNT will not detect

5. Example 6Growing an Epitaxial Layer on Silicon WafersFigure 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. Example 6Growing an Epitaxial Layer on Silicon WafersFigure 13 - Initial and Test Settings • The response variable is thickness of epitaxial layer in mm with a target of 14.5 mm. Which factors will affect • mean? • variation?

7. Example 6Growing an Epitaxial Layer on Silicon WafersFigure 14 - The Experimental Design • Each experimental run results in 70 observations on the response!

8. Example 6Growing an Epitaxial Layer on Silicon WafersFigure 14 - The Experimental Design • Note that the design here is “non-standard” • 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 • Which columns would the other 4 factors be assigned to in the 16-run signs table?

9. Example 6 - Analysis Using Only SNTGrowing an Epitaxial Layer on Silicon WafersFigure 16a - Completed Response Table

10. Example 6 - Analysis Using Only SNTGrowing an Epitaxial Layer on Silicon WafersFigure 17 - Effects Normal Probability Plot

11. Example 6 - Analysis Using Only SNTGrowing an Epitaxial Layer on Silicon WafersInterpretation • What factors favorable affect SNT? • A (susceptor rotation method) set at continuous • H (nozzle position) set at 6.

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

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

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

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

16. Example 6 Analysis Using Mean and Log(s)Growing an Epitaxial Layer on Silicon WafersInterpretation • What factors affect the mean? • D (deposition time) set at high level increases the mean. • 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. Example 6 Analysis Using Mean and Log(s)Growing an Epitaxial Layer on Silicon WafersInterpretation • Conclusions: • Set nozzle position at 6 • Use continuous susceptor rotation method • Use deposition time to adjust mean to target