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

## 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.