2.
Measurement Process Characterization
2.4. Gauge R & R studies 2.4.5. Analysis of bias
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Purpose | A gauge study should address whether gauges agree with one another and whether the agreement (or disagreement) is consistent over artifacts and time. | ||
Data collection |
For each gauge in the study, the analysis requires measurements on
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Data reduction | The steps in the analysis are:
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Data from a gauge study | The data in the table below come from resistivity (ohm.cm) measurements on Q = 5 artifacts on K = 6 days. Two runs were made which were separated by about a month's time. The artifacts are silicon wafers and the gauges are four-point probes specifically designed for measuring resistivity of silicon wafers. Differences from the wafer means are shown in the table. | ||
Biases for 5 probes from a gauge study with 5 artifacts on 6 days |
Table of biases for probes and silicon wafers (ohm.cm) Wafers Probe 138 139 140 141 142 --------------------------------------------------------- 1 0.02476 -0.00356 0.04002 0.03938 0.00620 181 0.01076 0.03944 0.01871 -0.01072 0.03761 182 0.01926 0.00574 -0.02008 0.02458 -0.00439 2062 -0.01754 -0.03226 -0.01258 -0.02802 -0.00110 2362 -0.03725 -0.00936 -0.02608 -0.02522 -0.03830 |
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Plot of differences among probes | A graphical analysis can be more effective for detecting differences among gauges than a table of differences. The differences are plotted versus artifact identification with each gauge identified by a separate plotting symbol. For ease of interpretation, the symbols for any one gauge can be connected by dotted lines. | ||
Interpretation | Because the plots show differences from the average by artifact, the center line is the zero-line, and the differences are estimates of bias. Gauges that are consistently above or below the other gauges are biased high or low, respectively, relative to the average. The best estimate of bias for a particular gauge is its average bias over the Q artifacts. For this data set, notice that probe #2362 is consistently biased low relative to the other probes. | ||
Strategies for dealing with differences among gauges |
Given that the gauges are a random sample of like-kind gauges, the
best estimate in any situation is an average over all gauges. In
the usual production or metrology setting, however, it may only be
feasible to make the measurements on a particular piece with one gauge.
Then, there are two methods of dealing with the differences among
gauges.
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