In Minitab, the result of the distinct number of categories is truncated so if we’d analyzed our Gage R&R in Minitab for multiple parts, the number of distinct categories would be 5 for this example. In our example, the StDev for parts is 1.0853 and the StDev for Gage (repeatability + reproducibility) is the square root the two combined variance components which is 0.282984, so we get: (1.0853/0.282984)*1.41 = 5.4 The number of distinct categories is calculated in Minitab as: (Standard deviation for Parts/Standard deviation for Gage)*1.41 This is really useful information-if we arrange the table as above the result is a close match to what we could obtain from Minitab for a full Gage R&R.Īdditionally, we can calculate the number of distinct categories. First, we’ll need the standard deviation of the variance components, and then we can calculate the Study Variation and % Study Variation as shown below: Using the same information, we can also obtain estimates of the StudyVar and %StudyVar. In the graph above, the vertical points for each operator represent the repeatability, and the measures across operators represent the reproducibility. Here we can see that Operator A’s measures are higher than B’s, and B’s are higher than C’s. If we’d like to see a visual representation of how each of the operators measured the same part, we can create an individual scatterplot with groups to represent each of the operators, then add the mean symbol and mean connect line: Not bad! Most of our variation is attributable to the part-to-part variation, which is desirable in a good measurement system.
Now that we have an estimate of the total variance, we can estimate the %Contribution for each of the three components by dividing individual components by the total and multiplying by 100: Since we have the standard deviation for part-to-part, the first step is to square the standard deviation to calculate the variance: 1.08530 2 = 1.17788Īs the second step, we will sum the variance estimates for the three components: 1.17788 + 0.06278 + 0.01730 = 1.25796 The total variation is the sum of the variance components for the part-to-part variation, for repeatability and for reproducibility. Using Historical Part-to-Part Standard DeviationĪs a first example, let’s assume that the historical standard deviation for part to part is 1.0853. The reproducibility is 0.06278 (the variance component for Operator), and the repeatability is 0.01730 (the variance component for Error). Let’s also assume that the data are arranged in the worksheet as shown below the estimated variance components from the session window output are also shown below. Let’s assume that we’ve conducted a Gage study with one part and three operators by following the instructions in the article referenced above. The way to proceed with the estimates of the historical StDev or the Tolerance is best explained with examples. Using the tolerance, we can get an estimate of the %Tolerance for the total gage (which is interpreted using the same guidelines as %Study Variation). We can also obtain some useful information about our measurement system if we use the process tolerance. From there, we can work through a few hand calculations to obtain most of the information we would have obtained had we done a full Gage R&R. If we have a historical estimate of the standard deviation for the Part-to-Part variation, we can get an estimate of the total variation and %Contribution. So, what other information will we need to get meaningful information about our measurement system? Getting Meaningful Information about the Measurement System
We will also need to do some simple hand calculations. However, if we combine what we’ve learned about the variance for Repeatability and Reproducibility with some additional information, we can obtain a significant amount of information about our measurement system.
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