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The GAGE Application |
All calculations described here are based upon a specified multiple of , where the multiple can be 4, 5.15, or 6. Figure A.3 shows a sample gage report created with the GAGE application using the average and range method.
The measure of repeatability (or equipment variation), denoted by EV, is calculated as
Average and Range Method Test ID: Gasket Performed By: Date: 09/18/98 John Smith Part No. & Name: Gasket Characteristics: Specification: 0.6-1.0 mm Gage Name: Thickness Gage No.: X-2034 Gage Type: 0-10 mm MEASUREMENT UNIT ANALYSIS % PROCESS VARIATION Repeatability EV = 0.1443 % EV = 15.33 % Reproducibility AV = 0.1516 % AV = 16.11 % Gage R&R R&R = 0.2093 % R&R = 22.24 % Part Variation PV = 0.9177 % PV = 97.50 % Total Variation TV = 0.9413 Results are based upon predicting 5.15 sigma. (99.0% of the area under the normal distribution curve) |
The quantity d_{2} (Duncan 1974, Table M) depends on the number of trials used to calculate a single range. In the GAGE application, the number of trials can vary from 2 to 4. Use of d_{2} is valid when ; otherwise, the GAGE application uses d_{2}^{*} (Duncan 1974, Table D3), which is based on the number of ranges calculated from #operators ×#parts and on the number of trials.
The measure of reproducibility (or appraiser variation), denoted by AV, is calculated as
The measure of repeatability and reproducibility, denoted by R&R, is calculated as
Part-to-part variation, denoted by PV, is calculated as
Here the quantity d_{2}^{*} (Duncan 1974, Table D3) depends on the number of parts used to calculate a single range. In the GAGE application, the number of parts can vary from 2 to 15.
Total variation, denoted by TV, is based on gage R&R and part-to-part variation.
The measures of repeatability, reproducibility, gage R&R, part variation, and total variation are shown in Figure A.3 under the heading "MEASUREMENT UNIT ANALYSIS." The right-hand side of the report shows the "% PROCESS VARIATION" analysis, which compares the gage factors to total variation. The percent of total variation accounted for by each factor is calculated as follows:
Instead of percent of process variation, your analysis may be based on percent of tolerance. For this you must specify a tolerance value. Then %EV, %AV, %R&R, and %PV are calculated by substituting the tolerance value for TV (the denominator) in the preceding formulas. A sample report with "% TOLERANCE ANALYSIS" is shown in Figure A.4.
What is considered acceptable for %R&R?
Barrentine (1991) gives the following guidelines:
10% or less | excellent |
11% to 20% | adequate |
21% to 30% | marginally acceptable |
over 30% | unacceptable |
In general, interpretation may be guided by local standards.
Average and Range Method Test ID: Gasket Performed By: Date: 09/18/98 John Smith Part No. & Name: Gasket Characteristics: Specification: 0.6-1.0 mm Gage Name: Thickness Gage No.: X-2034 Gage Type: 0-10 mm Tolerance: 0.4 MEASUREMENT UNIT ANALYSIS % TOLERANCE ANALYSIS Repeatability EV = 0.1443 % EV = 36.08 % Reproducibility AV = 0.1516 % AV = 37.91 % Gage R&R R&R = 0.2093 % R&R = 52.34 % Part Variation PV = 0.9177 % PV = 229.43 % Total Variation TV = 0.9413 Results are based upon predicting 5.15 sigma. (99.0% of the area under the normal distribution curve) |
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