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Chapter 21 Measurement Analysis

Chapter 21 Measurement Analysis. 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.

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Chapter 21 Measurement Analysis

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  1. Chapter 21Measurement 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 2total= 2product+ 2measurement 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&RExample 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

  13. Attribute Gage R&R StudyExample 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. 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

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