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IV.4 Signal-to-Noise Ratios

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Title: 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
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