ARTICLES
# Bias (Multiple Parts, One Equipment, Multiple Appraisers)

### Dart Board

### Reproducibility Chart

### Probability Plot

### Interaction Effects

### Tabular output

This model has been applied to Gauge R & R studies to obtain information about repeatability (same operator) and reproducibility (different operators). However, it is an inefficient use of technology if applied directly on measurements taken from multiple variable parts. An obvious conclusion will be that there is significant part to part variation, which is already known by the nature of the design. The only useful information provided is knowledge of interactions or the absence of; which is the only reason this model is provided under Classical Analysis. Reproducibility of measurement values alone can be determined with a simpler design.

A better application for this study is to study bias. Normally a linearity study is performed to determine if bias varies linearly with part reference values. However, this assumes that bias increases or decreases with magnitude of the reference values. This is not always a valid assumption. Sometimes bias varies randomly, or at least unpredictably over the range of measurement values. This model will identify bias inconsistency without regard to linearity.

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 which appears in the first column.

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 the centre point. The standard deviation, depending on your choice, is the total study standard deviation or process variation.

Each of the small circles correspond to the individual bias measurements.

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 black circles correspond to the average Appraiser values. The greater the spread the poorer the reproducibility.

If the black circles fall on one side of the centre then there is a significant overall bias, such as shown below.

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 above instance shows that there is a reproducibility problem as two appraisers fall outside the red limits. A reproducibility problem means that there is a bias problem that depends on the appraisers, which can be a training problem.

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 bias 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 a significant reproducibility problem, confirming the reproducibility chart above. As is normally the case there is a zero-interaction effect. There is also a significant part effect. This means that the instrument has a problem with bias for different parts. A linearity study should be conducted to establish linearity. If so, it may be possible to apply a correction formula.

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 same applies to the variation in bias from part to part.

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 statistically significant interaction effect.

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

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