Dec
21
Tools You should Know - Measurement Systems Formulas
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These are fairly simple relationships. With the exception of %Tolerance, all the other metrics are just different manipulations of the same numbers.
s2Total = s2parts + s2Measurement System
s2Measurement System = s2Repeatibility + s2Reproducibility
s2Reproducibility = s2Operator + s2Operator*Part
P/T = %Tolerance = 6* sMeasurement System / (USL-LSL)
P/TV = %Study Variation = sMeasurement System / sTotal
%Contribution = s2Measurement System / s2Total
Distinct Categories = Round-down ((sMeasurement System / sparts) * 1.41)
And for Don Wheeler fans -
Discrimination Ratio = Square Root ((s2Measurement System / s2parts) * 2 – 1)
Look at the table showing how the numbers change depending on how much variation the measurement system is contributing and the tolerance. Distinct Categories and Discrimination Ratio are basically the same number. %Study Variation is simply the square root of %Contribution.
| s2Parts | s2MS | Tol | Cp | %Tol | %Study Variation | %Contribution | Distinct Categories | Discrimination Ratio |
| 0.99 | 0.01 | 6 | 1 | 10.0% | 10.0% | 1.0% | 14 | 14.04 |
| 0.97 | 0.03 | 6 | 1 | 17.3% | 17.3% | 3.0% | 8 | 7.98 |
| 0.95 | 0.05 | 6 | 1 | 22.4% | 22.4% | 5.0% | 6 | 6.08 |
| 0.93 | 0.07 | 6 | 1 | 26.5% | 26.5% | 7.0% | 5 | 5.06 |
| 0.91 | 0.09 | 6 | 1 | 30.0% | 30.0% | 9.0% | 4 | 4.38 |
| 0.89 | 0.11 | 6 | 1 | 33.2% | 33.2% | 11.0% | 4 | 3.90 |
| 0.87 | 0.13 | 6 | 1 | 36.1% | 36.1% | 13.0% | 3 | 3.52 |
| 0.85 | 0.15 | 6 | 1 | 38.7% | 38.7% | 15.0% | 3 | 3.21 |
| 0.83 | 0.17 | 6 | 1 | 41.2% | 41.2% | 17.0% | 3 | 2.96 |
| 0.81 | 0.19 | 6 | 1 | 43.6% | 43.6% | 19.0% | 2 | 2.74 |
| 0.79 | 0.21 | 6 | 1 | 45.8% | 45.8% | 21.0% | 2 | 2.55 |
| 0.77 | 0.23 | 6 | 1 | 48.0% | 48.0% | 23.0% | 2 | 2.39 |
| 0.75 | 0.25 | 6 | 1 | 50.0% | 50.0% | 25.0% | 2 | 2.24 |
| 0.73 | 0.27 | 6 | 1 | 52.0% | 52.0% | 27.0% | 2 | 2.10 |
| 0.71 | 0.29 | 6 | 1 | 53.9% | 53.9% | 29.0% | 2 | 1.97 |
| 0.99 | 0.01 | 12 | 2 | 5.0% | 10.0% | 1.0% | 14 | 14.04 |
| 0.97 | 0.03 | 12 | 2 | 8.7% | 17.3% | 3.0% | 8 | 7.98 |
| 0.95 | 0.05 | 12 | 2 | 11.2% | 22.4% | 5.0% | 6 | 6.08 |
| 0.93 | 0.07 | 12 | 2 | 13.2% | 26.5% | 7.0% | 5 | 5.06 |
| 0.91 | 0.09 | 12 | 2 | 15.0% | 30.0% | 9.0% | 4 | 4.38 |
| 0.89 | 0.11 | 12 | 2 | 16.6% | 33.2% | 11.0% | 4 | 3.90 |
| 0.87 | 0.13 | 12 | 2 | 18.0% | 36.1% | 13.0% | 3 | 3.52 |
| 0.85 | 0.15 | 12 | 2 | 19.4% | 38.7% | 15.0% | 3 | 3.21 |
| 0.83 | 0.17 | 12 | 2 | 20.6% | 41.2% | 17.0% | 3 | 2.96 |
| 0.81 | 0.19 | 12 | 2 | 21.8% | 43.6% | 19.0% | 2 | 2.74 |
| 0.79 | 0.21 | 12 | 2 | 22.9% | 45.8% | 21.0% | 2 | 2.55 |
| 0.77 | 0.23 | 12 | 2 | 24.0% | 48.0% | 23.0% | 2 | 2.39 |
| 0.75 | 0.25 | 12 | 2 | 25.0% | 50.0% | 25.0% | 2 | 2.24 |
| 0.73 | 0.27 | 12 | 2 | 26.0% | 52.0% | 27.0% | 2 | 2.10 |
| 0.71 | 0.29 | 12 | 2 | 26.9% | 53.9% | 29.0% | 2 | 1.97 |
| 0.99 | 0.01 | 3 | 0.5 | 20.0% | 10.0% | 1.0% | 14 | 14.04 |
| 0.97 | 0.03 | 3 | 0.5 | 34.6% | 17.3% | 3.0% | 8 | 7.98 |
| 0.95 | 0.05 | 3 | 0.5 | 44.7% | 22.4% | 5.0% | 6 | 6.08 |
| 0.93 | 0.07 | 3 | 0.5 | 52.9% | 26.5% | 7.0% | 5 | 5.06 |
| 0.91 | 0.09 | 3 | 0.5 | 60.0% | 30.0% | 9.0% | 4 | 4.38 |
| 0.89 | 0.11 | 3 | 0.5 | 66.3% | 33.2% | 11.0% | 4 | 3.90 |
| 0.87 | 0.13 | 3 | 0.5 | 72.1% | 36.1% | 13.0% | 3 | 3.52 |
| 0.85 | 0.15 | 3 | 0.5 | 77.5% | 38.7% | 15.0% | 3 | 3.21 |
| 0.83 | 0.17 | 3 | 0.5 | 82.5% | 41.2% | 17.0% | 3 | 2.96 |
| 0.81 | 0.19 | 3 | 0.5 | 87.2% | 43.6% | 19.0% | 2 | 2.74 |
| 0.79 | 0.21 | 3 | 0.5 | 91.7% | 45.8% | 21.0% | 2 | 2.55 |
| 0.77 | 0.23 | 3 | 0.5 | 95.9% | 48.0% | 23.0% | 2 | 2.39 |
| 0.75 | 0.25 | 3 | 0.5 | 100.0% | 50.0% | 25.0% | 2 | 2.24 |
| 0.73 | 0.27 | 3 | 0.5 | 103.9% | 52.0% | 27.0% | 2 | 2.10 |
| 0.71 | 0.29 | 3 | 0.5 | 107.7% | 53.9% | 29.0% | 2 | 1.97 |