IV.4 Signal-to-Noise Ratios Background Example

Background Motivation 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.

Background Some 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) Used when “larger is better” SNT = 10 log(y2/s2) Ostensibly used when “target is better” How does SNT measure proximity to target? Skim for now

Background Criticisms 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 Instead of SN(T), could also use (ybar-t)^2 + s^2 (quadratic loss function)

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.

Example 6 Growing an Epitaxial Layer on Silicon Wafers Figure 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?

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

Example 6 Growing an Epitaxial Layer on Silicon Wafers 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? Show 16-run signs table. Assign A to D, B to C, and C to B, E to D. D=-ABC, F=ABD, G=ACD and H=BCD. This is still a Resolution IV design.

Example 6 - Analysis Using Only SNT Growing an Epitaxial Layer on Silicon Wafers Figure 16a - Completed Response Table Doesn’t show entire table. Open Excel sheet.

Example 6 - Analysis Using Only SNT Growing an Epitaxial Layer on Silicon Wafers Figure 17 - Effects Normal Probability Plot

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

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

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

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

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

Example 6 Analysis Using Mean and Log(s) Growing an Epitaxial Layer on Silicon Wafers Interpretation 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. Why did SN(T) miss D?

Example 6 Analysis Growing an Epitaxial Layer on Silicon Wafers Interpretation Conclusions: Set nozzle position at 6 Use continuous susceptor rotation method Use deposition time to adjust mean to target