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# coursehero 48 - 1 a GageR&RStudyANOVAMethod Source Parts...

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1. a) Gage R&R Study - ANOVA Method  Two-Way ANOVA Table With Interaction  Source DF SS MS F P Parts 9 96.750 10.7500 15.2362 0.000 Operators 1 0.150 0.1500 0.2126 0.656 Parts * Operators 9 6.350 0.7056 0.4922 0.871 Repeatability 40 57.333 1.4333 Total 59 160.583 α to remove interaction term = 0.05 Two-Way ANOVA Table Without Interaction  Source DF SS MS F P Parts 9 96.750 10.7500 8.27139 0.000 Operators 1 0.150 0.1500 0.11541 0.736 Repeatability 49 63.683 1.2997 Total 59 160.583 Gage R&R  %Contribution Source VarComp 95% CI (of VarComp) 95% CI Total Gage R&R 1.29966 (0.920, 6.433) 45.21 (17.35, 80.86) Repeatability 1.29966 (0.907, 2.018) 45.21 (13.81, 72.48) Reproducibility 0.00000 (0.000, 5.084) 0.00 (2.33, 61.97) Operators 0.00000 (0.000, 5.084) 0.00 (2.33, 61.97) Part-To-Part 1.57506 (0.620, 5.750) 54.79 (19.14, 82.65) Total Variation 2.87472 (1.880, 9.483) 100.00 Study Var %Study Var Source StdDev (SD) 95% CI (6 × SD) 95% CI (%SV) Total Gage R&R 1.14003 (0.959, 2.536) 6.8402 (5.755, 15.218) 67.24 Repeatability 1.14003 (0.952, 1.421) 6.8402 (5.714, 8.524) 67.24 Reproducibility 0.00000 (0.000, 2.255) 0.0000 (0.000, 13.529) 0.00 Operators 0.00000 (0.000, 2.255) 0.0000 (0.000, 13.529) 0.00 Part-To-Part 1.25501 (0.788, 2.398) 7.5301 (4.726, 14.387) 74.02 Total Variation 1.69550 (1.371, 3.079) 10.1730 (8.226, 18.477) 100.00

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Source 95% CI Total Gage R&R (41.66, 89.92) Repeatability (37.17, 85.13) Reproducibility (15.26, 78.72) Operators (15.26, 78.72) Part-To-Part (43.75, 90.91) Total Variation Number of Distinct Categories = 1 95% CI = (0.688147, 3.08645) Gage name: Date of study: Reported by: Tolerance: Misc: Part-to-Part Reprod Repeat Gage R&R 80 40 0 Percen t % Contribution % Study Var 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 4 2 0 Parts Sam p le Ran g e _ R= 1.9 UCL= 4.891 LCL=0 1 2 10 9 8 7 6 5 4 3 2 1 10 9 8 7 6 5 4 3 2 1 52 50 48 Parts Sam p le M ean _ _ X=49.917 UCL= 51.860 LCL=47.973 1 2 10 9 8 7 6 5 4 3 2 1 55 50 45 Parts 2 1 55 50 45 Operators 10 9 8 7 6 5 4 3 2 1 52 50 48 Parts A verag e 1 2 Operators Components of Variation R Chart by Operators Xbar Chart by Operators Measurement by Parts Measurement by Operators Parts * Operators Interaction Gage R&R (ANOVA) Report for Measurement
b) From ANOVA table we get that there is difference between parts not in operators, Part to part contain 74.2% of total variation in the measurements is due to the differences between parts. In other words, the system cannot distinguish between parts with low percentages.

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