2. Measurement Process Characterization
2.4. Gauge R & R studies
2.4.5. Analysis of bias

2.4.5.5.

Geometry/configuration differences

How to deal with configuration differences

The mechanism for identifying and/or dealing with differences among geometries or configurations in an instrument is basically the same as dealing with differences among the gauges themselves.

Example of differences among wiring configurations

An example is given of a study of configuration differences for a single gauge. The gauge, a 4-point probe for measuring resistivity of silicon wafers, can be wired in several ways. Because it was not possible to test all wiring configurations during the gauge study, measurements were made in only two configurations as a way of identifying possible problems.

Data on wiring configurations and a plot of differences between the 2 wiring configurations

Measurements were made on six wafers over six days (except for 5 measurements on wafer 39) with probe #2062 wired in two configurations. This sequence of measurements was repeated after about a month resulting in two runs. Differences between measurements in the two configurations on the same day are shown in the following table.

Differences between wiring configurations

  Wafer Day     Probe    Run 1     Run 2

   17.   1      2062.   -0.0108    0.0088
   17.   2      2062.   -0.0111    0.0062
   17.   3      2062.   -0.0062    0.0074
   17.   4      2062.    0.0020    0.0047
   17.   5      2062.    0.0018    0.0049
   17.   6      2062.    0.0002    0.0000

   39.   1      2062.   -0.0089    0.0075
   39.   3      2062.   -0.0040   -0.0016
   39.   4      2062.   -0.0022    0.0052
   39.   5      2062.   -0.0012    0.0085
   39.   6      2062.   -0.0034   -0.0018

   63.   1      2062.   -0.0016    0.0092
   63.   2      2062.   -0.0111    0.0040
   63.   3      2062.   -0.0059    0.0067
   63.   4      2062.   -0.0078    0.0016
   63.   5      2062.   -0.0007    0.0020
   63.   6      2062.    0.0006    0.0017

  103.   1      2062.   -0.0050    0.0076
  103.   2      2062.   -0.0140    0.0002
  103.   3      2062.   -0.0048    0.0025
  103.   4      2062.    0.0018    0.0045
  103.   5      2062.    0.0016   -0.0025
  103.   6      2062.    0.0044    0.0035

  125.   1      2062.   -0.0056    0.0099
  125.   2      2062.   -0.0155    0.0123
  125.   3      2062.   -0.0010    0.0042
  125.   4      2062.   -0.0014    0.0098
  125.   5      2062.    0.0003    0.0032
  125.   6      2062.   -0.0017    0.0115

Test of difference between configurations

Because there are only two configurations, a t-test is used to decide if there is a difference. If $$ {\large t} = \left| \frac{\sqrt{N}}{{\large s}_{diff}} \mbox{Avg}_{\, diff} \right| > 2 $$ the difference between the two configurations is statistically significant.

The average and standard deviation computed from the 29 differences in each run are shown in the table below along with the t-values which confirm that the differences are significant for both runs.

Average differences between wiring configurations

 Run  Probe     Average       Std dev    N      t 

  1    2062   - 0.00383       0.00514    29   -4.0
  2    2062   + 0.00489       0.00400    29   +6.6

Unexpected result

The data reveal a wiring bias for both runs that changes direction between runs. This is a somewhat disturbing finding, and further study of the gauges is needed. Because neither wiring configuration is preferred or known to give the 'correct' result, the differences are treated as a component of the measurement uncertainty.