ARTICLES

# Gauge R&R (One Equipment, one part, multiple Appraisers)

A Gauge R&R (GRR), is used to study repeatability (by the same operator) and reproducibility (by different operators). Historically control charts were used for this type of analysis. With modern computing power the Analysis of Variance (ANOVA) method is the recommended option. BIS.Net MSA hence uses the ANOVA method.

There are several types of Gauge R&R analysis that can be performed. This option is applicable when one reference part is used for the study. For the study each operator will perform n repeat tests on the same part. At the conclusion of the study the analyst will have an estimate of the repeatability and reproducibility and can compare these with the process variation.

Input consists of one column of measurements for each appraiser, such as

 27.64 28.4 28.01 27.48 28.24 27.86 26.82 28.54 28.44 27.42 28.61 28.69 27.2 27.82 28.32 27.91 27.93 27.75 28.2 28.45 28.21

The BIS.Net App provides the following output, each of which are now explained.

### Dart Board

The dart board is a visual tool which enables the analyst to see at a glance how reproducible the measurements are and how good or bad the repeatability is.

The circles are placed at 1 standard deviation (green), 2 standard deviations (yellow), 3 standard deviations (orange) and beyond (red) around the reference value (white). If a reference value has not been entered, then the average is used.

Each of the small circles correspond to the recorded measurements. The difference between the white circle and small circle is equal to the measurement.

The circles have been randomly placed around the centre just as if they were thrown darts. This is an effective way for visualizing repeatability and reproducibility. Each coloured point corresponds to a different appraiser.

The horizontal line is a more conventional, but less effective way of showing the scatter

The large black circles are the average measurements for each appraiser, highlighting reproducibility problems, if they exist.

If a reference (true ) value of the part has been entered then this powerful tool will show if there is a bias, evidenced by measurements not clustering around the white circle.

Bias Evident

### Reproducibility Chart

The reproducibility chart is used to identify appraisers that differ significantly from expectation. All appraisers should fall inside the two red bands. Those that fall outside the bands may need to be retrained.

### Probability Plot

The probability plot is used to establish normality of the measurement error (residuals) . BIS.Net MSA uses the Anderson Darling Statistic and will advise if the if there is evidence of non-normality. The ANOVA method does assume normality. Fortunately, measurement error tends to follow a normal distribution.

### Tabular output

The Analysis of Variation table is included for completeness. If the result is significant than there is statistical evidence that the differences by the appraisers is not due to chance alone. In this instance the conclusion is confirmed by the Reproducibility Chart.

The approximate confidence intervals are the intervals within which the reproducibility and repeatability, measured by standard deviation, are likely to fall, at the chosen level of significance. If the default of .05 has been used, then the confidence coefficient is equal to 100-.05 *100=95

The measurement system performance table shows the percentage of variation reproducibility and repeatability (both measured by Sd) taken up relative to either the total study variation, or process variation if entered. The last column uses variance instead of standard deviation.

If study variation is used i.e. process variation is not entered than the cells in the Gauge R&R row are blank because Gauge R&R is the total variation compared against, instead of process variation. Process variation is the preferred option.

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