chapter 21 measurement analysis. measurement it is important to define and validate the measurement...
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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.
• 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.
Measurement
222tmeasuremenitemtotal
2222othersprocessindividualtmeasuremen
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
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.
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
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 = 2
product + 2measurement system
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.
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
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.
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)
Example 21.6
Opt1-Rep1 Opt1-Rep2 Opt2-Rep1 Opt2-Rep 2 Part Operator Measurement9011.60 9011.40 9011.40 9011.50 1 1 9011.69012.40 9012.20 9012.20 9012.10 2 1 9012.49013.00 9012.80 9012.80 9012.80 3 1 9013.09012.60 9012.40 9012.40 9012.50 4 1 9012.69009.80 9009.80 9009.60 9009.80 5 1 9009.89013.20 9013.20 9013.20 9013.00 6 1 9013.29013.40 9013.20 9013.20 9013.20 7 1 9013.49012.20 9013.20 9012.20 9012.30 8 1 9012.29014.00 9013.80 9013.80 9013.80 9 1 9013.89011.60 9011.40 9011.40 9011.60 1 1 9011.49012.40 9012.20 9012.20 9012.10 2 1 9012.29013.00 9012.80 9012.80 9012.80 3 1 9012.89012.60 9012.40 9012.50 9012.50 4 1 9012.49009.80 9009.80 9009.80 9009.80 5 1 9009.89013.20 9013.20 9013.00 9013.00 6 1 9013.29013.40 9013.20 9013.20 9013.20 7 1 9013.29012.20 9012.00 9012.30 9012.30 8 1 9012.09014.00 9013.80 9013.80 9013.80 9 1 9014.09011.60 9011.40 9011.50 9011.50 1 2 9011.69012.40 9012.20 9012.10 9012.10 2 2 9012.49013.00 9012.80 9012.80 9012.80 3 2 9013.09012.60 9012.40 9012.50 9012.50 4 2 9012.69009.80 9009.80 9009.80 9009.80 5 2 9000.89013.20 9013.20 9013.00 9013.00 6 2 9013.29013.40 9013.20 9013.20 9013.20 7 2 9013.49012.20 9012.00 9012.30 9012.30 8 2 9012.29014.00 9013.80 9013.80 9013.80 9 2 9013.89011.60 9011.40 9011.50 9011.50 1 2 9011.49012.40 9012.20 9012.10 9012.10 2 2 9012.29013.00 9012.80 9012.80 9012.80 3 2 9012.89012.60 9012.40 9012.50 9012.50 4 2 9012.49006.80 9009.80 9009.80 9009.80 5 2 9009.89013.20 9013.20 9013.00 9013.00 6 2 9013.29013.40 9013.20 9013.20 9013.20 7 2 9013.29012.20 9012.00 9012.30 9012.30 8 2 9012.09012.20 9012.20 9012.30 9012.30 9 2 9012.0
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.
Sample Number Attribute
Op1 Try1
Op1 Try2
Op2 Try1
Opt2 Try2
Op3 Try1
Op3 Try2
Agree Y/N
Agree2 Y/N
1 Pass Pass Pass Pass Pass Fail Fail n n2 Pass Pass Pass Pass Pass Fail Fail n n3 Fail Fail Fail Fail Pass Fail Fail n n4 Fail Fail Fail Fail Fail Fail Fail y y5 Fail Fail Fail Pass Fail Fail Fail n n6 Pass Pass Pass Pass Pass Pass Pass y y7 Pass Fail Fail Fail Fail Fail Fail y n8 Pass Pass Pass Pass Pass Pass Pass y y9 Fail Pass Pass Pass Pass Pass Pass y n
10 Fail Pass Pass Fail Fail Fail Fail n n11 Pass Pass Pass Pass Pass Pass Pass y y12 Pass Pass Pass Pass Pass Pass Pass y y13 Fail Fail Fail Fail Fail Fail Fail y y14 Fail Fail Fail Pass Fail Fail Fail n n15 Pass Pass Pass Pass Pass Fail Fail n n16 Pass Pass Pass Pass Pass Fail Fail n n17 Fail Fail Fail Fail Pass Fail Fail n n18 Fail Fail Fail Fail Fail Fail Fail y y19 Fail Fail Fail Pass Fail Fail Fail n n20 Pass Pass Pass Pass Pass Pass Pass y y21 Pass Fail Fail Fail Fail Fail Fail y n22 Pass Pass Pass Pass Pass Pass Pass y y23 Fail Pass Pass Pass Pass Pass Pass y n24 Fail Pass Pass Fail Fail Fail Fail n n25 Pass Pass Pass Pass Pass Pass Pass y y26 Pass Pass Pass Pass Pass Pass Pass y y27 Fail Fail Fail Fail Fail Fail Fail y y28 Fail Fail Fail Pass Fail Fail Fail n n29 Pass Pass Pass Pass Pass Fail Fail n n30 Pass Pass Pass Pass Pass Fail Fail n n
Test Parts
Master Expert
1 Good2 Bad3 Good4 Good5 Good6 Good7 Good8 Good9 Bad
10 Bad11 Good12 Bad13 Bad14 Bad15 Bad16 Good17 Bad18 Bad19 Good20 Bad21 Good22 Bad23 Bad24 Bad25 Good26 Good27 Bad28 Good29 Good30 Good
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 contributesvariation Total
variationity Repeatabil
variation Total
variationility Reproducib
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