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