gage-r-r-with-anova-xbarr-analysis

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De Anza College *

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Statistics

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Feb 20, 2024

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xlsx

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This spreadsheet is provided "as is" without warranties of any kind, either expressed or implied. When to use this spreadsheet 1) This spreadsheet allows the user to perform a complete Gage Repeatability and Reproducibility (GR&R) study. Both Analysis of Variance (ANOVA) and Xbar/Range calculations are performed. Up to three operators, ten parts and three trials can be accommodated. The GR&R is reported in terms of percent of study variation and percent of tolerance. The percentage of equipment variation, appraiser variation, part variation, and the number of distinct categories that can be distinguished are also displayed. Instructions for Data Entry 1) Generally the coloring of the cells indicate their use. White cells are for data entry, yellow cells provide instruction, turquoise cells are headings and light green cells display data that can't / shouldn't be changed. 2) Enter the part number and / or name, the characteristic of the part being measured, the tolerance specification, the gage name, the gage number, the gage type, the name of the person conducting the study, the upper specification limit and the lower specification limit. Both upper and lower specification limits are required. 3) Determine the number of parts and the number of appraisers to be used. Conduct the study and enter the data in the appropriate rows. The spreadsheet will count the number of parts and appraisers automatically. Reading the Results 1) The GR&R results are displayed as a percentage of part variation and percentage of tolerance. If no tolerance is entered, the Percent of Tolerance report will display "Enter Tol" in the data fields. Be sure to enter a value for the upper and lower specification, including zero, to ensure a proper result. 2) The percentage of equipment variation, appraiser variation, part variation, and the number of distinct categories that can be distinguished are displayed. Generally, an acceptable gage will have lower values for the equipment and the appraiser and higher values for the parts. In most industries, a GR&R less than 10% of the tolerance is considered acceptable while a GR&R greater than 30% is unacceptable. A GR&R between 10% and 30% should be investigated for improvement. The Number of Distinct Categories should be 5 or greater. 3) The Graphical Summary provides a full graphical analysis of the data. An Xbar and R chart is shown as well as Multi-vari charts showing Part Variation, Operator Variation and Part - Operator Interaction. A bar chart summarizes the total Gage R&R, Repeatability and Reproducibility for % Contribution, % Study Variation and % Tolerance. Guidance for using the Xbar and R charts follows: Xbar Chart : The area between the control limits represents the measurement uncertainty and so at least half of the points should be outside the control limits. R Chart : All points should be stable and in control. 4) The Numerical Summary displays the results of all calculations used in the ANOVA and Xbar/Range method of analysis. The Variance, Standard Deviation and Percent of Variance for each variation component are displayed. Gage R&R for Percent of Study Variation and Percent of Tolerance are displayed. The Percent of Tolerance is calculated using 5.15 standard deviations (99% of the variation) and 6.0 standard deviations (99.7% of the variation.) Both 5.15 and 6.0 are commonly used and so both are displayed. Also, the ANOVA table is displayed. A Special Note Regarding K Factors 1) All calculations are performed using the K factors outlined in revision three of the AIAG MSA manual. The new K factors are just the old factors divided by 5.15 sigma. The Percent of Tolerance report accounts for the new K factors by including 5.15 sigma in the calculations. End

Gage Repeatability and Reproducibility Data Collection Sheet Part No. & Name: Blocks Heidenhain Gage 10/25/22 Characteristics: Aluminum Hoang,Binh,Thinh Specifications: Upper Spec 0.04 # of Trials = 3 0.5908 Xbar diff = 0.0007777 2.58 Lower Spec -0.04 # of appraisers = 3 0.5231 Rbarbar = 0.00236 2.6907222 Total Tol 0.08 # of parts = 10 0.3146 Appraiser/Trial # Part Average 1 2 3 4 5 6 7 8 9 10 Hoang 1 -0.0005 -2.4255 -1.483 -2.6845 -2.2485 -1.861 -1.802 -1.654 -2.128 -0.856 -1.7143 2 -0.001 -2.425 -1.4825 -2.6895 -2.2485 -1.862 -1.8045 -1.655 -2.1305 -0.8615 -1.716 3 -0.001 -2.425 -1.4815 -2.69 -2.245 -1.8615 -1.803 -1.654 -2.127 -0.857 -1.7145 Average -0.000833 -2.425167 -1.482333 -2.688 -2.247333 -1.8615 -1.803167 -1.654333 -2.1285 -0.858167 -1.714933 Range 0.0005 0.0005 0.0015 0.0055 0.0035 0.001 0.0025 0.001 0.0035 0.0055 0.0025 Binh 1 0 -2.43 -1.4815 -2.6885 -2.2488 -1.8615 -1.8025 -1.654 -2.131 -0.85553 -1.715333 2 0.001 -2.435 -1.4825 -2.692 -2.2485 -1.86 -1.8015 -1.654 -2.1305 -0.855 -1.7158 3 0.001 -2.4365 -1.4825 -2.6855 -2.2475 -1.86 -1.802 -1.6545 -2.1325 -0.86 -1.716 Average 0.0006667 -2.433833 -1.482167 -2.688667 -2.248267 -1.8605 -1.802 -1.654167 -2.131333 -0.856843 -1.715711 Range 0.001 0.0065 0.001 0.0065 0.0013 0.0015 0.001 0.0005 0.002 0.005 0.00263 Thinh 1 0.0015 -2.427 -1.4825 -2.695 -2.248 -1.86 -1.804 -1.654 -2.131 -0.855 -1.7155 2 0.0015 -2.4295 -1.482 -2.692 -2.247 -1.86 -1.8005 -1.6535 -2.13 -0.857 -1.715 3 0.002 -2.425 -1.483 -2.695 -2.2475 -1.8605 -1.801 -1.654 -2.131 -0.853 -1.7148 Average 0.0016667 -2.427167 -1.4825 -2.694 -2.2475 -1.860167 -1.801833 -1.653833 -2.130667 -0.855 -1.7151 Range 0.0005 0.0045 0.001 0.003 0.001 0.0005 0.0035 0.0005 0.001 0.004 0.00195 Part Average 0.0005 -2.428722 -1.482333 -2.690222 -2.2477 -1.860722 -1.802333 -1.654111 -2.130167 -0.85667 Xbarbar = -1.715248 2.6907222 [(Rbar a = 0.00250000000000006 + Rbar b = 0.00262999999999995 + Rbar c = 0.00195000000000001) / # of appraisers = 3] = Rbarb Rbarbar = 0.00236 (Max Xbar = -1.71493333333333) - Min Xbar = -1.715711) = Xbar diff Xbar diff = 0.0007777 K 1 = D 4 = K 2 = R p = K 3 = Xbar a = Rbar a = Xbar b = Rbar b = Xbar c = Rbar c = R p = Gage Name: Gage Number: Gage Type: Date: Performed by:

(Rbarbar = 0.00236000000000001) x (D4 = 2.58) = UCL R UCL R = 0.0060888 Gage Repeatability and Reproducibility Report - % VARIATION Part No. & Name: Blocks Gage Name: Heidenhain Gage Date: 10/25/2022 Characteristics: Aluminum Gage Number: Performed by: Hoang,Binh,Thinh Specifications: Gage Type: Upper Spec 0.04 # of Trials = 3 0.5908 Xbar diff = 0.0007777 2.58 Lower Spec -0.04 # of appraisers = 3 0.5231 Rbarbar = 0.00236 2.6907222 Total Tol 0.08 # of parts = 10 0.3146 Measurement Unit Analysis % Total Variation Repeatability - Equipment Variation (EV) Percent Equipment Variation EV = %EV = 100 [ EV / TV ] = (0.00236000000000001) x (0.5908) Trials = 100 [0.0014 / 0.8465 ] = 0.0014 2 0.8862 = 0.165 % 3 0.5908 Reproducibility - Appraiser Variation (AV) Percent Appraiser Variation AV = SQRT{(Xbar diff x K 2)^2 - (EV/[(# parts) x (# trials)])} %AV = 100 [ AV / TV ] = SQRT(0 - 0) = 100 [0.0003 / 0.8465 ] = 0.0003 Appraisers 2 3 = 0.035 % K2 0.7071 0.5231 Repeatability & Reproducibility (GRR) Percent Gage Repeatability & Reproducibility Variation GRR = SQRT[ (EV^2) + (AV^2) ] %GRR = 100 [ GRR / TV ] = SQRT [ 0 + 0 ] = 100 [0.0014 / 0.8465 ] = 0.0014 = 0.165 % Part Variation (PV) Parts Percent Part Variation PV = 2 0.7071 %PV = 100 [ PV / TV ] = 0.8465 3 0.5231 = 100 [0.8465 / 0.8465 ] 4 0.4467 = 100.000 % Total Variation (TV) 5 0.403 TV = SQRT[ (GRR^2) + (PV^2) ] 6 0.3742 Number of Distinct Categories that can be Distinguished = SQRT [0 + 0.7166 ] 7 0.3534 ndc = 1.41( PV / GRR ) K 1 = D 4 = K 2 = R p = K 3 = (Rbarbar) x (K 1 ) K 1 K 3 R p x K 3

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= 0.8465 8 0.3375 = 1.41 (0.8465 / 0.0014 ) 9 0.3249 = 852.546 or approximately: 852 10 0.3146 Gage Repeatability and Reproducibility Report - % TOLERANCE (5.15 Sigma) Part No. & Name: Blocks Gage Name: Heidenhain Gage Date: 10/25/2022 Characteristics: Aluminum Gage Number: Performed by: Hoang,Binh,Thinh Specifications: Gage Type: Upper Spec 0.04 # of Trials = 3 0.5908 Xbar diff = 0.0007777 2.58 Lower Spec -0.04 # of appraisers = 3 0.5231 Rbarbar = 0.00236 2.6907222 Total Tol 0.08 # of parts = 10 0.3146 Measurement Unit Analysis % Total Tolerance Repeatability - Equipment Variation (EV) Percent Equipment Variation EV = %EV = 100 [ EV / Total Tol ] = (0.00236000000000001) x (0.5908) x (5.1) Trials = 100 [0.0071 / 0.08 ] = 0.0071 2 0.8862 = 8.875 % 3 0.5908 Reproducibility - Appraiser Variation (AV) Percent Appraiser Variation AV = (5.1 Sigma) x SQRT{(Xbar diff x K 2)^2 - (EV/[(# parts) x (# trials)])} %AV = 100 [ AV / Total Tol ] = (5.1) x SQRT(0 - 0) = 100 [0.0016 / 0.08 ] = 0.0016 Appraisers 2 3 = 2.000 % K2 0.7071 0.5231 Repeatability & Reproducibility (GRR) Percent Gage Repeatability & Reproducibility Variation GRR = SQRT[ (EV^2) + (AV^2) ] %GRR = 100 [ GRR / Total Tol ] = SQRT [ 0.0001 + 0 ] = 100 [0.0073 / 0.08 ] = 0.0073 = 9.125 % Part Variation (PV) Parts Percent Part Variation PV = 2 0.7071 %PV = 100 [ PV / Total Tol ] = (2.69072222222222) x (0.3146) x (5.1) 3 0.5231 = 100 [4.31715 / 0.08 ] = 4.31715 4 0.4467 = 5396.438 % 5 0.403 K 1 = D 4 = K 2 = R p = K 3 = (Rbarbar) x (K 1 ) x (5.1 Sigma) K 1 K 3 (R p) x (K 3 ) x (5.1 Sigma)

Total Tolerance (Total Tol) 6 0.3742 Number of Distinct Categories that can be Distinguished TV = Upper Spec - Lower Spec 7 0.3534 ndc = 1.41( PV / GRR ) = 0.04 - -0.04 8 0.3375 = 1.41 (4.31715 / 0.0073 ) = 0.08 9 0.3249 = 833.860 or approximately: 833 10 0.3146

Gage R&R for Aluminum Gage Name: Heidenhain Gage Part No. & Name: Blocks Upper Tolerance: 0.04 Date: 10/25/2022 Gage No. Lower Tolerance: -0.04 Performed by: Hoang,Binh,Thinh Gage Type: Total Tolerance: 0.08 0% 1000% 2000% 3000% 4000% 5000% 6000% 7000% Components of Variation, ANOVA % Contribution % Study Variation % Tol (5.15 SD) % Tol (6.0 SD) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 Xbar Chart by Operator Op. A Op. B Op. C Av- er- age UCL X LCL X Ser 0 0.001 0.002 0.003 0.004 0.005 0.006 0.007 Range Chart by Operator Op. A Op. B Op. C Av- er- age UCL R 1 2 3 4 5 6 7 8 9 10 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 Operator - Part Interaction Op A Op B Op C 1 2 3 4 5 6 7 8 9 10 -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 Part Op A Op B Op C -3 -2.5 -2 -1.5 -1 -0.5 0 0.5 Operator Gage R&R Repeat Reprod Part-Part 0% 1000% 2000% 3000% 4000% 5000% 6000% 7000% Components of Variation, Xbar/Range

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Gage R&R for Aluminum Gage Name: Heidenhain Gage Part No. & Name: Blocks Upper Tolerance: 0.04 Date: 10/25/2022 Gage No. Lower Tolerance: -0.04 Performed by: Hoang,Binh,Thinh Gage Type: Total Tolerance: 0.08 Gage R&R Study - ANOVA Method Gage R&R Study - Xbar/Range Method Variance and Standard Deviation Components Variance and Standard Deviation Components Source St. Dev. Variance Source St. Dev. Variance Total Gage R&R 0.0023741 5.636E-06 0.00% Total Gage R&R 0.0014 1.96E-06 0.00% Repeatability 0.0016108 2.595E-06 0.00% Repeatability 0.0014 1.96E-06 0.00% Reproducibility 0.001744 3.042E-06 0.00% Reproducibility 0.0003 9E-08 0.00% Operator 0 0 0.00% Part to Part 0.8465 0.7165623 100.00% Operator*Part 0.0018136 3.289E-06 0.00% Total Variation 0.8465 0.7165623 100.00% Part to Part 0.7946314 0.631439 100.00% Total Variation 0.7946349 0.6314447 100.00% Process Tolerance = 0.08 Process Tolerance = 0.08 Gage R&R Using 5.15 Standard Deviations (99%) Gage R&R Using 5.15 Standard Deviations (99%) Source Source Total Gage R&R 0.0122265 0.30% 15.28% Total Gage R&R 0.00721 0.17% 9.01% Repeatability 0.0082956 0.20% 10.37% Repeatability 0.00721 0.17% 9.01% Reproducibility 0.0089816 0.22% 11.23% Reproducibility 0.001545 0.04% 1.93% Operator 0 0.00% 0.00% Part to Part 4.359475 100.00% 5449.34% Operator*Part 0.0093403 0.23% 11.68% Total Variation 4.359475 100.00% 5449.34% Part to Part 4.0923516 100.00% 5115.44% Total Variation 4.0923699 100.00% 5115.46% Gage R&R Using 6.0 Standard Deviations (99.7%) Gage R&R Using 6.0 Standard Deviations (99.7%) Source Source Total Gage R&R 0.0142444 0.30% 17.81% Total Gage R&R 0.0084 0.17% 10.50% Repeatability 0.0096648 0.20% 12.08% Repeatability 0.0084 0.17% 10.50% Reproducibility 0.010464 0.22% 13.08% Reproducibility 0.0018 0.04% 2.25% Operator 0 0.00% 0.00% Part to Part 5.079 100.00% 6348.75% Operator*Part 0.0108819 0.23% 13.60% Total Variation 5.079 100.00% 6348.75% Part to Part 4.7677883 100.00% 5959.74% Total Variation 4.7678096 100.00% 5959.76% Number of Distinct Categories = 852 Number of Distinct Categories = 471 Analysis of Variance (ANOVA) Table Source DF SS MS F p Part 9 51.146674 5.6829638 ### 0.000 Operator 2 1.006E-05 5.029E-06 0.404 0.674 Op.x Part Interaction 18 0.0002243 1.246E-05 4.803 0.000 Gage (error) 60 0.0001557 2.595E-06 Total 89 51.147064 p value for Op. x Part Interaction as error term = 0.25 % of Variance % of Variance Study Variation % Study Variation % of Tolerance Study Variation % Study Variation % of Tolerance Study Variation % Study Variation % of Tolerance Study Variation % Study Variation % of Tolerance

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Part (P) Technician (T) Cell Interaction Squares ANOVA Table No. A B C Sum n Avg RowSqs A B C Source DF SS MS F P 1 -0.0005 0 0.0015 2.5E-07 0 2.25E-06 Part 9 51.14667 5.682964 456000.8 0.000 1 2 -0.001 0.001 0.0015 0.0045 9 0.0005 2.25E-06 2.0833333E-06 1.333E-06 8.333E-06 1E-06 1E-06 2.25E-06 Operator 2 1.006E-05 5.029E-06 0.403553 0.674 3 -0.001 0.001 0.002 1E-06 1E-06 4E-06 Op.x Part Interaction 18 0.000224 1.246E-05 4.803149 0.000 1 -2.4255 -2.43 -2.427 5.88305 5.9049 5.890329 Gage (error) 60 0.000156 2.595E-06 2 2 -2.425 -2.435 -2.4295 -21.8585 9 -2.428722 53.08822 17.6443000833 17.77063 17.67341 5.880625 5.929225 5.9024703 Total 89 51.14706 3 -2.425 -2.4365 -2.425 5.880625 5.9365323 5.880625 1 -1.483 -1.4815 -1.4825 2.199289 2.1948423 2.1978063 3 2 -1.4825 -1.4825 -1.482 -13.341 9 -1.482333 19.77581 6.59193633333 6.590454 6.593419 2.197806 2.1978063 2.196324 3 -1.4815 -1.4825 -1.483 2.194842 2.1978063 2.199289 Gage R&RRepeat Reprod Part-Part 1 -2.6845 -2.6885 -2.695 7.20654 7.2280323 7.263025 % Contribution 0.00% 0.00% 0.00% 100.00% 4 2 -2.6895 -2.692 -2.692 -24.212 9 -2.690222 65.13566 21.676032 21.68679 21.77291 7.23341 7.246864 7.246864 % Study Variation 0.17% 0.17% 0.04% 100.00% 3 -2.69 -2.6855 -2.695 7.2361 7.2119103 7.263025 % Tol (5.15 SD) 9.01% 9.01% 1.93% 5449.34% 1 -2.2485 -2.2488 -2.248 5.055752 5.0571014 5.053504 % Tol (6.0 SD) 10.50% 10.50% 2.25% 6348.75% 5 2 -2.2485 -2.2485 -2.247 -20.2293 9 -2.2477 45.4694 15.1515213333 15.16411 15.15377 5.055752 5.0557523 5.049009 3 -2.245 -2.2475 -2.2475 5.040025 5.0512563 5.0512563 1 -1.861 -1.8615 -1.86 3.463321 3.4651823 3.4596 % Contribution 0.00% 0.00% 0.00% 100.00% 6 2 -1.862 -1.86 -1.86 -16.7465 9 -1.860722 31.16058 10.39554675 10.38438 10.38066 3.467044 3.4596 3.4596 % Study Variation 0.30% 0.20% 0.22% 100.00% 3 -1.8615 -1.86 -1.8605 3.465182 3.4596 3.4614603 % Tol (5.15 SD) 15.28% 10.37% 11.23% 5115.44% 1 -1.802 -1.8025 -1.804 3.247204 3.2490063 3.254416 % Tol (6.0 SD) 17.81% 12.08% 13.08% 5959.74% 7 2 -1.8045 -1.8015 -1.8005 -16.221 9 -1.802333 29.23565 9.75423008333 9.741612 9.73981 3.25622 3.2454023 3.2418003 3 -1.803 -1.802 -1.801 3.250809 3.247204 3.243601 1 -1.654 -1.654 -1.654 2.735716 2.735716 2.735716 8 2 -1.655 -1.654 -1.6535 -14.887 9 -1.654111 24.62475 8.21045633333 8.208802 8.205494 2.739025 2.735716 2.7340623 3 -1.654 -1.6545 -1.654 2.735716 2.7373703 2.735716 1 -2.128 -2.131 -2.131 4.528384 4.541161 4.541161 9 2 -2.1305 -2.1305 -2.13 -19.1715 9 -2.130167 40.83849 13.59153675 13.62775 13.61922 4.53903 4.5390303 4.5369 3 -2.127 -2.1325 -2.131 4.524129 4.5475563 4.541161 1 -0.856 -0.85553 -0.855 0.732736 0.7319316 0.731025 10 2 -0.8615 -0.855 -0.857 -7.71003 9 -0.85667 6.604951 2.20935008333 2.202541 2.193075 0.742182 0.731025 0.734449 3 -0.857 -0.86 -0.853 0.734449 0.7396 0.727609 Sum -51.448 -51.47133 -51.453 -154.3723 n 30 30 30 90 Avg -1.714933 -1.715711 -1.7151 315.9335 315.9338 ColSqs 88.22989 88.30993 88.24704 264.7869 Sum T Sqs Sum P Sqs Sum Cell Sqs -154.3723 315.9339 10 9 n 90 Ten CM 264.7868 Part 1 2 3 Xbar R Average Range TotSS 51.14706 Op. A 1 -0.0005 -0.001 -0.001 Op. A & Op. B -0.000833 0.0005 Op. A 1 -0.000833 #N/A #N/A 0.0005 #N/A #N/A Op. A 1 -0.0008333 TechSS 1.006E-05 2 -2.4255 -2.425 -2.425 Op. A & Op. C -2.425167 0.0005 2 -2.425167 #N/A #N/A 0.0005 #N/A #N/A 2 -2.4251667 PartSS 51.14667 3 -1.483 -1.4825 -1.4815 Op. B & Op. C -1.482333 0.0015 3 -1.482333 #N/A #N/A 0.0015 #N/A #N/A 3 -1.4823333 InterSS 0.000224 4 -2.6845 -2.6895 -2.69 -2.688 0.0055 4 -2.688 #N/A #N/A 0.0055 #N/A #N/A 4 -2.688 ErrorSS 0.000156 5 -2.2485 -2.2485 -2.245 -2.247333 0.0035 5 -2.247333 #N/A #N/A 0.0035 #N/A #N/A 5 -2.2473333 X 2 Sum X Sum X 2 Gage R&R Repeat Reprod Part-Part 0% 1000% 2000% 3000% 4000% 5000% 6000% 7000% % Contribution % Study Variation % Tol (5.15 SD) % Tol (6.0 SD)

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