ARTICLES
# Gauge Capability and Repeatability

Gauge repeatability is a measure in terms of standard deviations of how close repeated measurements on the same part, by the same operator are. Gauge reproducibility is about close clustering of repeat measurements, not closeness to the target. Closeness to target is about bias, for which the bias module should be used. The first two images below show similar close clustering, but even though one is off-target, the repeatability is similar. The third image shows bad repeatability.

A type I study is a preliminary study of the repeatability, performed by a single appraiser taking repeated measurements on the same part with the same gauge (or instrument, or device). Ideally at least 30 measurements should be taken, but even this may be insufficient. Sample size for repeatability standard deviation can be determined with the BISNET Sample Size app.

The more comprehensive Gauge R&R analysis will provide confidence intervals on repeatability (and reproducibility)

To place perspective of the outcome of the study BISNet MSA provides the following output.

The first table is self-explanatory, consisting of summary statistics. The most important column is 6*Sd which is the spread of measurements by the same appraiser on the same part, using the same ‘gauge’.

%EV is the % Equipment variation calculated from

%EV=100*Repeatability/Process Variation where Repeatability is the study standard deviation reported in the first table. Process Variation is the standard deviation of the items/features produced as measured from a stable in-control process.

%BV is the percent bias variation calculated from

%BV=100*Bias/Process Variation where bias is the difference between observed average and the reference value. Process Variation is the standard deviation of the items/features produced as measured from a stable in-control process.

Cg and Cgk are similar to Cp and Cpk. Both values should thus be greater than 1, preferably 1.5

For the Cp and Cpk the process variation is compared to the tolerance range. For Cg and Cgk the repeatability spread is compared to a percentage of the tolerance range. This percentage is commonly 20%, meaning that measurement error should be no greater than 20% of the tolerance

Cg = percent of tolerance * tolerance/(100*6* Sd) where Sd is the Repeatability

Cgk= ((percent of tolerance*tolerance/200)-bias)/(3*Sd)

BIS.Net MSA presents the repeatability graphically in a chart such as shown below.

The measurement system has been centered between the two outer limits, the width being equal to the specified tolerance width. The inner orange limits are limits obtained from the specified percentage of the process tolerance limits (usually 20%). Clearly this measurement system is not capable, and hence the low Cg above.

**Note:**

The Cg and Cgk are dependent on an arbitrary specified tolerance percentage and will hence change if different tolerance percentages are specified. The EV% some argue is a better statistic as this is based only on the tolerance range, not arbitrary percentage of. The above image shows that the reproducibility is poor in relation to the tolerance range, requiring multiple measurements in practice which are averaged.

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