1. INT 506/706: Total Quality Management Lec #8, Gauge R & R Studies

2. Outline Review Measurements Gauge R & R Repeatability Reproducibility 2

3. Measurement Your data with its subsequent analysis, is only as good as your measurement system

4. Measurement Variation found on a control chart is a combination of product variation and gauge variation

5. Measurement Is it valid? Validity –Are you measuring what you think you are measuring? Is it precise? Precision –A lack of precision = excessive variation in measurements Is it accurate? Accuracy –A lack of accuracy indicates the average measurement is off target

6. Measurement Validity: –A measurement is valid if it represents the feature or geometry of interest

7. Measurement Validity: –Fundamental in developing an effective measurement system. –Will the measurement method faithfully portray the quantity of interest.

8. Measurement Precision: –A measurement system is precise if it shows little variation when the same object or geometry is measured repeatability.

9. Measurement Precision: –Does one get essentially the same value every time a particular measurement is made? –Intrinsic property of a measurement method or device

10. Measurement Accuracy: –A measurement system is accurate (unbiased) if, on average, it produces the correct value

11. Measurement Is the average value the “true” value? This is the reason and science of calibration.

12. Precision or Accuracy? Target shooting analogy: –PRECISION: produce a tight pattern, consistency. –ACCURACY: produce a pattern centered on the bull’s eye, hitting the target

13. Low Precision/Low Accuracy

14. High Precision/Low Accuracy

15. Low Precision/High Accuracy

16. High Precision/High Accuracy

17. Summary Measurement systems should be: –Valid: measuring what you want it to measure –Accurate: centered on the target, on average –Precise: consistent with little variation

18. Gauge R & R Used to quantify the precision of gauges or other measurement devices or systems. Multiple operators using the same gauge (measurement device or system)

19. Set up How many like pieces are to be measured? How many people will be involved in taking readings? How many repeat readings will be made by each individual?

20. Set Up Several parts, n p. Several operators, n o. Each operator measures each part several times, n M.

21. Set Up Obs.Appraiser AAppraiser B Sample Trial 1 Trial 2 Trial 3 __ X A __ R A Trial 1 Trial 2 Trial 3 __ X B __ R B 1 2 3 4 5 n o – several parts n o – several operators n m – repeated measures of same part

22. Set up Minitab worksheet can be created for your gauge R&R study

23. Rule of 10 The rule of 10 states that the gauge should be at least 1/10 as accurate as the tolerance of the characteristic that is being measured

24. Rule of 10 Example: Engineering tolerance: +/- 0.005 inches Total tolerance:0.010 inches Rule of 10:.010/10 = 0.001 inches is the precision your gauge should be able to read, called the discrimination capability.

25. Repeatability Measures the consistency of readings of the same item by one person Poor repeatability reflects gauge (measuring device) problems

26. Reproducibility Variation in the average measurement when different people use the same gauge Poor reproducibility reflects an operator/training problem

27. Range Method Calculating the averages and ranges of appraisers’ trials making repeated measures

28. Example Two appraisers being studied using an outside micrometer to measure the outside diameter of a part 0.047 +/- 0.003

29. Example 5 parts, n p = 5 2 operators, n o = 2 2 repeat measurements, n M = 2 0.047 +/- 0.003

30. Example Obs.Appraiser AAppraiser B Sample Trial 1 Trial 2 Trial 3 __ X A __ R A Trial 1 Trial 2 Trial 3 __ X B __ R B 1.0473.0472-.04725.0001.0472.0469-.04705.0003 2.0468.0471-.04695.0003.0471.0469-.0470.0002 3.0472.0470-.0471.0002.0470.0471-.04705.0001 4.0471.0473-.0472.0002.0470.0471-.04705.0001 5.0468.0470-.0469.0002.0467.0469-.0468.0002

31. Example Obs.Appraiser AAppraiser B Sample Trial 1 Trial 2 Trial 3 __ X A __ R A Trial 1 Trial 2 Trial 3 __ X B __ R B 1.0473.0472-.04725.0001.0472.0469-.04705.0003 2.0468.0471-.04695.0003.0471.0469-.0470.0002 3.0472.0470-.0471.0002.0470.0471-.04705.0001 4.0471.0473-.0472.0002.0470.0471-.04705.0001 5.0468.0470-.0469.0002.0467.0469-.0468.0002 Determine: 1) Average ranges & Ranges for each sample on each operator Average Range (R o ) =.04708 -.04699 = R o =.00005

32. Example Obs.Appraiser AAppraiser B Sample Trial 1 Trial 2 Trial 3 __ X A __ R A Trial 1 Trial 2 Trial 3 __ X B __ R B 1.0473.0472-.04725.0001.0472.0469-.04705.0003 2.0468.0471-.04695.0003.0471.0469-.0470.0002 3.0472.0470-.0471.0002.0470.0471-.04705.0001 4.0471.0473-.0472.0002.0470.0471-.04705.0001 5.0468.0470-.0469.0002.0467.0469-.0468.0002 Determine: 1) Average ranges & Ranges for each sample on each operator

33. Example Determine: 2) Average for each sample… Appraiser AAppraiser B Sample Trial 1Trial 2Trial 1Trial 2 1.0473.0472.0469.047150 2.0468.0471.0469.046975 3.0472.0470.0471.047075 4.0471.0473.0470.0471.047125 5.0468.0470.0467.0469.04685 =.047035 Max Min

34. Example Determine: 3) Compute X-bar and R Charts 4 or 5 averages in x-bar chart should be outside control limits

35. Example Desirable Averages chart

36. Example Average of the averages Average ranges Range of inspector averages Range of the part averages

37. Repeatability –Compute the range for each operator/part combination. –R-bar is the average of the ranges. Appendix 11, p. 499 (3 rd edition)

38. Repeatability Variance =.0001638 2 =.00000002683044

39. Reproducibility –A measurement system is reproducible when different appraisers produce consistent results

40. Reproducibility The term includes error due to repeated measure (appraiser measuring two times)

41. Reproducibility Neg. variances impossible, Set to 0 Neg. variances impossible, Set to 0 Depending on how close to 0, Minitab will take square root of absolute value Variance =.00000000142559

42. Measurement System Variation due to Equipment Variation (Repeatability) and Appraiser Variation (Reproducibility)

43. Measurement System

45. Part-to-part All the other variation not accounted for in the measurement system

46. Part-to-part Appendix 11 m = 5 (number of parts) g = 1 (since there is only one Range calculation

47. Total Process Variation Measurement system variation plus part-to- part variation Measurement Part-to-Part Variation

48. Total Process Variation

50. Evaluate Measurement System

51. Minitab