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AIAG MSA gauge R&R study: three appraisers, ten parts, three trials by the Average and Range method and by ANOVA

ToolGauge R&R
SourceAutomotive Industry Action Group (2010). Measurement Systems Analysis Reference Manual, 4th ed. AIAG, Southfield, MI. Chapter III Section B, Tables III-B 6a (data), 6b (Average and Range report), 7 and 8 (ANOVA), as reproduced by Minitab's Example of Crossed Gage R&R Study (GageData.MWX).
LevelProfessional

Problem

Three appraisers each measure the same ten parts three times in random order with one gauge (90 readings, grand mean 0.0014). Find the repeatability (equipment variation), reproducibility (appraiser variation), gauge R&R, part-to-part and total variation, their percentages of the study variation and of a tolerance of 8, and the number of distinct categories, by the AIAG Average and Range report and by the two-way ANOVA with the appraiser × part interaction; judge the measurement system against the AIAG bands.

Inputs to Enter

  • Study: Average and Range (AIAG report); data in the data-sheet layout, one line per appraiser and part with the three trials across (A 1 0.29 0.41 0.64 … C 10 −1.49 −1.77 −2.16)
  • Tolerance 8 (Minitab's process tolerance for the example), study variation 6σ, K1 from the report form (1/d2), interaction rule 0.25
Open the Gauge R&R tool (loaded with this example)

Answers

  • R̿ = 0.3417, X̄diff = 0.4447, Rp = 3.511; K1 = 0.5908, K2 = 0.5231, K3 = 0.3146 (d2* = 1.69257, 1.91155, 3.17905)
  • EV = 0.2019 (book 0.20188), AV = 0.2297 (0.22963), GRR = 0.3058 (0.30575), PV = 1.1045 (1.10456), TV = 1.1460 (1.14610)
  • %EV 17.61, %AV 20.04, %GRR 26.68, %PV 96.37 (book 17.62 / 20.04 / 26.68 / 96.38); %GRR of tolerance 22.9; ndc = 1.41 PV/GRR = 5.09 → 5: marginal (10 to 30 %)
  • ANOVA: SS appraiser 3.1673, part 88.3619, interaction 0.3590 (F 0.434, p 0.974, pooled), error 2.7589; pooled MS 0.03997; components GRR 0.09143, repeatability 0.03997, reproducibility 0.05146, part 1.08645, total 1.17788; %Study Variation 27.86, %Tolerance 22.68, ndc 4

Notes

The tool's default inputs are this study; press Submit. Switch the study select to ANOVA for the second table. Every printed value above is checked in test_gauge_rr.php together with the AIAG linearity study (bias = 0.7367 − 0.1317 × reference, t 10.158 and −12.043), the AIAG bias study (σr 0.22514, t 0.1153, interval −0.1185 to 0.1319 with ν = 10.8), the Appendix C d2* table, Montgomery Example 8.7, Fleiss' worked κ = 0.210 and the numpy/scipy script References/Gauge-RR/gaugerr_check.py.