1. Chapter 21 Measurement Analysis

2. Measurement It is important to define and validate the measurement system before collecting data. –Without measurement we only have opinions The measurement system is the complete process used to obtain measurements. Measurement error is inevitable. We must identify, evaluate, and control the sources of measurement error. –Any variation can be attributed to either the characteristic that is being measured, or the way the measurements are being taken.

3. Measurement

4. Sources of error Measurement error = the effect of all sources of measurement variability that cause an observed value to deviate from the true value being measured. Measuring instrument errors: –Accuracy –Linearity –Stability –Precision Measuring system errors –Repeatability –Reproducibility

5. Defining Error Accuracy = difference between the observed average and reference value. Linearity = change in accuracy across the expected operating range of the measuring instrument Stability = consistency in the measurement over time Precision = standard deviation between measurements Repeatability = variation obtained by one operator measuring the same characteristic with the same instrument Reproducibility = variation in the average of measurements taken by different operators using the same instrument.

6. How to measure error? Multiple measurements of one single characteristic –Precision: Standard deviation among measurements –Accuracy: Difference between the observed average and the reference value –Measurement System Analysis (MSA) =when precision and accuracy measurements are assed in combination Attribute and Variable Gage studies –Reproducibility –Repeatability Transactions –Measurement evaluation studies can apply… however it may not be economically viable

7. How to measure error? Measurement system bias: assessed via the calibration program Observed value = master value + measurement offset  total =  product +  measurement system Measurement system variability: assessed via the variable R&R study Observed variability = product variability+ measurement variability  2 total =  2 product +  2 measurement system

8. Defining sources of error CE (fishbone) diagram can be helpful in representing potential causes of measurement error (so they can be addressed) –Measurement, material, manpower, mother nature, methods and machines Think of a process (MSA) for measuring a part. What are some of the causes of measurement error that you can think of? –Define the variables that can influence the measurement system.

9. MINITAB Output of analysis Control charts (X-Bar and R) –Show discrimination, stability and variation in the range of measurements for each part ANOVA –For estimating error source and their contribution to overall variability Linear Regression –Estimate the linearity of system response Charts and Scatterplots –Used to study variation between and across operators and parts

10. Gage R&R Attribute Gage R&R –At least 2 operators measure 20 parts at random (twice each). –If there is little consistency between operators then the measurement system must be improved. Variable Gage R&R –Three operators measure 10 parts with the same nominal dimension in a random order, 3 times each. –Can by analyzed by X-Bar and R charts or with ANOVA method.

11. Crossed Gage R&R Example 21.6 Used for determining which portion of the variability in measurements may be due to the measurement system. –n=units; 2≤ n ≤ 10 –m= appraisers; 2 ≤m ≤3 –w= trials; 2 ≤w ≤3 –Total should be ≥20 Use the MINITAB function: –Stat>Quality tools>Gage Study>Gage R&R Study (crossed) –Examine the Xbar / R charts, what do they tell us –Examine the AVONA results (DATA set in appendix)

12. Example 21.6 Opt1-Rep1Opt1-Rep2Opt2-Rep1Opt2-Rep 2PartOperatorMeasurement 9011.609011.40 9011.50119011.6 9012.409012.20 9012.10219012.4 9013.009012.80 319013.0 9012.609012.40 9012.50419012.6 9009.80 9009.609009.80519009.8 9013.20 9013.00619013.2 9013.409013.20 719013.4 9012.209013.209012.209012.30819012.2 9014.009013.80 919013.8 9011.609011.40 9011.60119011.4 9012.409012.20 9012.10219012.2 9013.009012.80 319012.8 9012.609012.409012.50 419012.4 9009.80 519009.8 9013.20 9013.00 619013.2 9013.409013.20 719013.2 9012.209012.009012.30 819012.0 9014.009013.80 919014.0 9011.609011.409011.50 129011.6 9012.409012.209012.10 229012.4 9013.009012.80 329013.0 9012.609012.409012.50 429012.6 9009.80 529000.8 9013.20 9013.00 629013.2 9013.409013.20 729013.4 9012.209012.009012.30 829012.2 9014.009013.80 929013.8 9011.609011.409011.50 129011.4 9012.409012.209012.10 229012.2 9013.009012.80 329012.8 9012.609012.409012.50 429012.4 9006.809009.80 529009.8 9013.20 9013.00 629013.2 9013.409013.20 729013.2 9012.209012.009012.30 829012.0 9012.20 9012.30 929012.0

13. Attribute Gage R&R Study Example 21.7 Evaluates the consistency between measurement decisions to accept or reject. Use the MINITAB function: –Attribute agreement analysis –What does the data tell us? (DATA set in appendix) Remember that attribute-based measurement system cannot indicated how good or how bad a part is, only if it was rejected or accepted.

14. Sample NumberAttribute Op1 Try1 Op1 Try2 Op2 Try1 Opt2 Try2 Op3 Try1 Op3 Try2 Agree Y/N Agree2 Y/N 1Pass Fail nn 2Pass Fail nn 3 PassFail nn 4 yy 5 PassFail nn 6Pass yy 7 Fail yn 8Pass yy 9FailPass yn 10FailPass Fail nn 11Pass yy 12Pass yy 13Fail yy 14Fail PassFail nn 15Pass Fail nn 16Pass Fail nn 17Fail PassFail nn 18Fail yy 19Fail PassFail nn 20Pass yy 21PassFail yn 22Pass yy 23FailPass yn 24FailPass Fail nn 25Pass yy 26Pass yy 27Fail yy 28Fail PassFail nn 29Pass Fail nn 30Pass Fail nn Test Parts Master Expert 1Good 2Bad 3Good 4 5 6 7 8 9Bad 10Bad 11Good 12Bad 13Bad 14Bad 15Bad 16Good 17Bad 18Bad 19Good 20Bad 21Good 22Bad 23Bad 24Bad 25Good 26Good 27Bad 28Good 29Good 30Good

15. What do the numbers tell us? As a general rule of thumb: –R&R indices > 30% are considered unacceptable –Number of distinct categories indices<5 are considered unacceptable % Variation that Gage R&R contributes: % Variation that operator contributes