IV.4 Signal-to-Noise Ratios

1
IV.4 Signal-to-Noise Ratios

• Background
• Example

2
BackgroundMotivation

• Wouldnt 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
  Taguchis 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 Taguchis 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 ATT 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 WafersInterpretati
on

• 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 WafersInterpretati
on

• Conclusions
• Set nozzle position at 6
• Use continuous susceptor rotation method
• Use deposition time to adjust mean to target