ARTICLES
# Gauge R&R (One Equipment, multiple Part, multiple Appraisers)

### Dart Board

### Reproducibility Chart

### Probability Plot

### Interaction Effects

### Tabular output

A Gauge R&R (GRR), is used to study repeatability (by the same operator) and reproducibility (by different operators). For this application, consisting of multiple parts an Analysis of Variance is required to extract as much information as possible. Notably the ANOVA method, as opposed to the historical control chart methods, can detect interaction effects between appraisers and parts (items) measured.

For this type of study each appraiser must test the same part at least twice. At least two parts must be measured, and all appraisers must test the same number of parts the same number of times. Each part has a different Reference value.

BIS.Net Analyst recommends a Gauge Bias (One Equipment, multiple Parts, multiple Appraisers) analysis instead, which provides information on bias variation, similar in principle to a Bias Linearity Analysis

An example of input is shown below.

Appraisers in this instance are coded as A, B, C. Parts are coded as 1,2,3.

The BIS.Net MSA APP provides the following output.

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 combined.

The circles are placed at 1 standard deviation (green), 2 standard deviations (yellow), 3 standard deviations (orange) and beyond (red) around zero. The standard deviation is the total standard deviation.

Each of the small circles correspond to the recorded measurements (in this case difference between actual and reference value).

Using a sophisticated algorithm, 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.

Coloured clusters reflect reproducibility. A perfectly reproducible gauge will not be clustered by colour.

The reproducibility chart is used to identify appraisers that differ significantly from expectation. All appraisers should fall inside the two red limits. Those that fall outside the limits may need to be retrained. The red limits are based on the total equipment variation and take into account part to part to part variation.

The above instance shows that there is a reproducibility problem as two appraisers fall outside the red limits.

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.

The Appraiser-Part interaction charts is used to visually detect if there are interactions. An appraiser – part interaction means that the measurements obtained by each appraiser depend on the part measured. The above example shows that the measurements for all 3 appraisers follow the same pattern over all parts. For example, all 3 appraisers obtain lower values for part 2, compared to part 1 and 3. The relative gap between appraisers is relatively constant over all parts meaning that there is no interaction.

The Analysis of Variation table is included for completeness. If a result is significant than there is statistical evidence that the differences are not due to chance alone. In this instance there is significant part variation in parts, which is not explained by chance alone. As mentioned above this is expected. There is also significant variation between appraiser, taking account of the part variation, also not explained by chance alone. The interaction between part and appraiser is insignificant and may thus be due to chance.

If there is no interaction effect the ANOVA pools the variation due to error and interaction for significance testing. 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 how much the percentage of the various components of variation, (all measured by Sd) takes up relative to the total study variation (or process variation if chosen as an option). The last column uses variance instead of standard deviation. A zero value is used if there is no statistical significant interaction effect.

Gauge R&R is the total variation due to appraisers, equipment variation and interaction, but not parts.

AV is the abbreviation for Appraiser variation and EV for equipment (instrument variation).

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