Chapter 12

1. Chapter 12

2. Initial thoughts Success depends upon the ability to measure performance. Rule #1: A process is only as good as the ability to reliably measure. Rule #2: A process is only as good as the ability to repeat. Gordy Skattum, CQE

3. Initial thoughts • It is impossible for us to improve our processes if our gaging system cannot discriminate between parts or if we cannot repeat our measurement values. • Every day we ask “Show me the data” - yet we rarely ask is the data accurate and how do you know?

4. Purpose of measurement • Product Control • Detection, conformance to a design specification • Process Control • Prevention, real-time control, assessing a feature to its natural process variation What is a gage used for?

5. Gage R&R is… • Gage Repeatability and Reproducibility • A study to understand the within-system and between-system variation in a measurement system. • A comparison of standard deviation • A part of MSA – Measurement System Analysis • Bias • Linearity • Stability • Repeatability • Reproducibility

6. Impact on SPC and 6s • Difficult/impossible to make process improvements • Causes quality / cost / delivery / responsiveness problems • False alarm signals, increases process variation, loss of process stability • Improperly calculated control limits • Can make our processes worse!

7. AIAG/MSA • AIAG – Automotive Industry Action Group • Collaboration between “Big 3” to create one set of guidelines for all suppliers • MSA reference manual– Measurement System Analysis • Introduction to MSA • Covers normally occurring measurement situations • Developed to meet specific needs of the automotive industry

8. Measurement Terms • Discrimination • In selecting or analyzing a measurement system, we are concerned about the system’s discrimination, or the capability of the system to detect and faithfully indicate even small changes of the measured characteristic • also known as resolution.

9. Measurement Terms • Randomness • A condition in which any individual item in a set has the same mathematical probability of occurrence as all other items within the specified set, i.e., individual events are not predictable even though they may collectively belong to a definable distribution. • Random Sample • One or more samples randomly selected from the population.

10. Measurement Terms • Bias • The difference between the observed average of measurements and the reference value. • Bias is measured as “accuracy” or as “accuracy shift.” • Choices for addressing bias error • Calibrate the gage; adjust, correct, or apply an offset • Change the system (instrument, condition, masters, …)

11. Measurement Terms Accuracy vs. Precision Precise Yes No No Accurate Yes

12. Measurement Terms • Linearity • Linearity is the bias over the operating range of a measurement system. This, along with bias, is checked as part of the calibration procedure. Choices for addressing linearity • Calibrate, adjust the gage or build offset table • Change the system (condition, masters, …)

13. Measurement Terms • Stability • Stability (or drift) is the total variation in the measurements obtained with a measurement system on the same master or parts when measuring a single characteristic over an extended time period. Stability Time 2 Time 1

14. Repeatability Measurement Terms • Repeatability (EV) • Repeatability is the variation in measurements obtained with one measurement instrument when used several times by one appraiser while measuring the identical characteristics on the same part. Includes all within-system variation.

15. Measurement Terms • Repeatability • Two common sources of repeatability error are measurement variations due to the instrument itself and positional variation of the part in the instrument. Since both variations are represented by the subgroup ranges, the study range chart will show the consistency of the process. Any point out of control on the study Range chart should be investigated for its assignable cause and corrected.

16. Operator B Operator C Operator A Repeatability Measurement Terms • Reproducibility (AV) • Reproducibility is the variation in the average of the measurements made by different appraisers using the same measuring instrument when measuring the identical characteristics on the same part. Includes all between-system variation.

17. Measurement Terms • Reproducibility • Reproducibility implies that the variability among appraisers will be consistent. If variability does exist, the appraisers overall averages will differ. This is shown by comparing each appraisers average on the study Xbar chart.

18. Measurement Terms • Part-To-Part Variation (look for >50% out of control) • Part-to-part variation is also displayed on the study Xbar chart. For each appraiser, the subgroup averages reflect the part-to-part differences. Adequate part-to-part variation will display data points beyond the control limits. The more out of control, the better.

19. Measurement Terms • Effective resolution • Having adequate discrimination • Rules for determining effective resolution • Count the number of “0” plot points on the process range (R) control chart. If >25%, then the gage lacks effective resolution • Count the discrimination levels between the UCL and the LCL of the process average control chart. If <5 levels, gage lacks effective resolution

20. Effective resolution rules Levels between UCL-LCL? Number of zeros?

21. 10:1 rule • “Old rule” • The measuring device must be able to read at least 1/10th of the tolerance width • “New rule” • The measuring device must be able to read at least 1/10th of the process width

22. Gage R&R levels • A capability measure • Typically we compare • Gage R&R to tolerance • Gage R&R to process • Three levels of results • 0-10%  • 10-30%  • +30%

23. Gage R&R for Height • Let’s try something. Let’s take 2 people, a tape measure and measure their heights.

24. So… How do we do a study?

25. Initial control chart analysis • Our first concerns are about the measurements systems discrimination (10:1 rule) • We can determine if the measurement system has adequate discrimination by reviewing the control charts for the process ahead of time. (effective resolution) • We need to make sure we study parts over the total range for the process or tolerance, whichever is greater • Is the process stable?

26. Preparation for Conducting a GR&R Study • The approach to be used should be well planned out. • Determine the number of appraisers (3), sample parts (10), and trials (3) in advance. • Criticality of dimension (location) • Part configuration • The appraisers chosen should be selected from those who normally operate the instrument. • The sample parts selected must represent at least the entire range of the process. • Each part will be marked for identification.

27. Preparation (cont.) • Use the 10:1 rule. • Assure that the appraisers method of measuring the characteristics feature is following the defined measurement procedure. Each should use the same technique.*

28. Preparation (cont.) • To minimize the likelihood of misleading results, the following steps should be taken: • The measurements should be made in a random order. The appraisers should be unaware of which numbered part is being checked in order to avoid any possible knowledge bias. • In reading the equipment, the readings should be estimated to the nearest resolution that can be obtained. If possible, readings should be made to one-half of the smallest resolution. • YOU must oversee the entire study.

29. Guidelines for determining a Gage R&R • Since the purpose of the analysis of a measurement system is to understand the systems variation, the use of graphical tools is very important. • Personal investigations have unveiled 3 powerful gage analysis software packages. • SPCXL (Sigma Zone) • Minitab • MeasurLink (Mitutoyo) • All will deliver identical results* • SPCXL is easy to use and inexpensive. • Minitab is a complete statistical analysis package which requires a lot of training. • MeasurLink was originally designed specifically for GR&R’s, and is easy to use.

30. Guidelines (cont.) • The four standard methods for analyzing measurement systems are: • Range method (short form) • Average and Range (long form) • ANOVA (Analysis of Variance) • Attribute gage study (both short and long form methods) • Each method has its advantages and disadvantages as well as limitations. • Refer to the MSA reference manual (Measurement Systems Analysis) for additional information.

31. Excel sheet available on website

32. Analysis of Results Following are examples of gage analysis charts one would find using SPCXL.

33. Results (cont)

34. Class Exercise

35. Class Exercise

36. Maximum Deflection • Is one-half the Gage R&R plus any bias in the gage Maximum Possible one-way deflection

37. Maximum Deflection Example • You did a gage study and found the R&R to be .048. The average measured value of a 2.00” standard is 2.01. Find the maximum deflection. So what does this mean?

38. 99% of the data* Accuracy shift .01 2.034 1.986 R&R 2 R&R = .024 2 True value 2.00 Average 2.01 *if R&R is based on 5.15s Answer

39. Total variance • The total amount of variance in the gage and in the process

40. Total variance example • A control chart with tolerance limits from 5.00.025 is created with sample sizes of 4 and an average range of .008. A gage study was done where the average range was .00287 with each part measured 3 times. What is the true process capability ratio? Did the gage have much of an effect on the process capability?