1. R&R Homework Statgraphics “Range Method”

2. DATA OperatorPartTrialMeasure B117.75 B218.813 B316.875 B127.813 B228.25 B326.5 B137.375 B239.188 B336.75 C117.125

3. Analysis Summary Operators: OPERATORS Parts: PARTS Trials: TRIALS Measurements: MEASURE 5 operators 3 parts 3 trials Average range = 1.165 Range of x-bars = 2.14856 Estimated Estimated Percent Sigma Variance of Total -------------------------------------------------------------------------- Repeatability 0.68193 0.465029 39.88 Reproducibility 0.837196 0.700897 60.12 -------------------------------------------------------------------------- R & R 1.07978 1.16593 100.00 Parts 0.915393 0.837944 -------------------------------------------------------------------------- Total 1.41558 2.00387 The StatAdvisor --------------- Based on a study involving 5 operators, each measuring 3 parts 3 times, the estimated standard deviation of the measurement process for MEASURE equals 1.07978. Of the total variance, 60.1151% is due to differences between operators (Reproducibility) while 39.8849% is due to the instrument (Repeatability). To estimate the range of error this implies, select Gage Report from the list of Tabular Options.

4. Gage Report 5 operators 3 parts 3 trials Measurement Unit Analysis and Study Variation ---------------------------------------------------------------------- 6.0 Percent Study Percent Std. dev. Variation Contribution Repeatability 4.09158 48.17 23.21 Reproducibility 5.02318 59.14 34.98 ---------------------------------------------------------------------- R & R 6.47868 76.28 58.18 Parts 5.49236 64.67 41.82 95.0 Confidence Intervals ---------------------------------------------------------------------- Lower 6.0 Upper Limit Std. dev. Limit Repeatability 3.24112 4.09158 5.55081 Reproducibility 2.9891 5.02318 14.8558 R & R 5.19998 6.47868 8.59681 Parts 2.85964 5.49236 34.518 Tolerance Analysis ---------------------------- Percent of Tolerance Repeatability 34.0965 Reproducibility 41.8598 R & R 53.989 Parts 45.7696 Tolerance = 12.0

5. Gage Report Summary The StatAdvisor --------------- This table shows intervals equal to 6.0 times the standard deviations due to Repeatability, Reproducibility, combined R&R, and variability between parts. These intervals can be expected to contain 99.73% percent of the errors attributed to each source. For example, we would expect the measurements of MEASURE to deviate from the true values by +/-3.23934 due to combined R&R, an interval 6.47868 units wide. Comparing the variability of the measurement process to the overall variability in MEASURE, the measurement process contributes 58.1837% with the remaining 41.8163% attributable to differences amongst the parts. Since the estimates of variability are subject to sampling error, the confidence intervals show how precise these estimates are. Given a tolerance or specification 12.0 units wide (+/-6.0), the variability from the measurement process can be expected to cover 53.989% of that range. This would normally be unacceptable precision for a measurement process.

6. Operator Averages by Part

7. Range of Parts by Operator

8. Range of Operators by Part

9. Operator Box and Whisker Plots

10. R&R Plot

11. Operator Run Charts by Part