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Presentation on Measurement System Analysis
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Measurement Systems AnalysisMeasurement Systems Analysis
Define
Measure
Analyze
Improve
1ControlBy: Mahender Kumar
Learning ObjectivesLearning Objectives
• Understand the language of Measurement.• Show the importance of MeasurementShow the importance of Measurement.• Walk away knowing how to perform a Gage
R&R and how to interpret resultsR&R and how to interpret results.• Share some lessons learned.
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Since Measurement systems represent y pa sub-process within a process...
• They are subject to Variation.
• What could be the source of this variation?
• Why do Measurements Vary?• Why do Measurements Vary?
3
Sources of Measurement Variation
•Equipmentq p•Part•Operator•Operator•Environment•Procedure
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Sources of Measurement Variation
P dMenMaterialsMeasurements
Measurement System C&E Matrix
Electrical Instability
Wear
Mechanical Integrety
Corrosion
Weight
Dimension
TemperatureCleanliness
CoordinationSpeed
InterpretationCalibration Error
AttentionFatigue
Procedure
Measurement System Error
Temp Fluxctuation
Algorithm Instability
Operator Technique
Density
Conductivity
Hardness
Wear
VisionDexterity
Know ledgeCoordination
Temp Fluxctuation
Line Voltage Variation
Vibration
Cleanliness
Standard Procedure
Suff icient Work time
Maintenance StandardCalibration Frequency
StabilityResolution
Calibration
Precision
Design
Six Sigma Champion Training 5
HumidityOperator Training
Ease of useTemperature
Cleanliness
MachinesMethodsEnvironment
Possible Sources of Process VariationPossible Sources of Process VariationObserved Process Variation
Actual Process Variation Measurement Variation
Long-termProcess Variation
Short-termProcess Variation
Variationw/i sample
Variation dueto gage
Variation dueto operators
Stability LinearityRepeatability Accuracy Reproducibility
We will look at “repeatability” and “reproducibility” as these are the primary contributors to measurement error.
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ese e e p y co bu o s o e su e e e o .
Why MSAWhy MSA
RU =U : UNCERTAINITY
U =NATIONAL
STANDARD
RU = 0.0001 RANDOM UNCERTAINITY –
FOUND THRU
CALIBRATION
U = 0.0001
LABORATORY
STANDARD
RU = 0.001
CALIBRATION
SYSTEM UNCERTAINITY – OF MASTER
U = 0.001005
WORKRU = 0.01
TOTAL UNCERTAINITY –SQRT( RU*RU + SU*SU)
U = STANDARD0.01005
GAUGE FOR INSPECTION /
TESTING
RU = 0.05 U = 0.05099
Process Capability
Lower Spec. Limit Upper Spec. Limit
66 σ
Tolerance = T
Process Capability = T / 6 σ > 1.33Means, 6 σ < (0.75*T)
Impact of Uncertainty ERROR identified through Calibration Process
Lower Spec. Limit Upper Spec. Limit
Uncertainty
6 P6 σ Process
Tolerance = T
Knowledge to be obtainedKnowledge to be obtained
• How big is the measurement error?• What are the sources of measurementWhat are the sources of measurement
error?• Is the gage stable over time?• Is the gage stable over time?• Is the gage capable for this process?• How do we improve the measurement
system?
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Sources of VariationSources of Variation
P d t V i bilitProduct Variability(Actual variability)
MeasurementVariability
Total Variability(Observed variability)
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Effects of Measurement ErrorEffects of Measurement Error
AveragesMeasurement
System Bias —Averages
µ µ µ= +
Determined through “Accuracy Study”
µ µ µtotal product measurement= +
VariabilityMeasurement System
Variability —Determined through
“R&R Study”
σ σ σtotal product measurement2 2 2= +
y
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TerminologyTerminology
• Location related terms:– True value– Bias– Linearity
• Stability (over time)• Variation related terms
– Repeatability– Reproducibility
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Definition of Terms
Reference Value• Reference Value– The theoretically or agreed upon correct
value of the characteristic beingvalue of the characteristic being measured, traceable to some standard
• Resolution– The smallest increment, or unit of ,
measure, available from a measurement process
– Generally at least 1/10th of the specification range
Definition of Terms
• Precision– The degree of agreement (or variability)
between individual measurements or test results from measuring the same specimen(s)
• Accuracy (Bias)y ( )– The difference between the average of the
measurement error distribution and the reference value of the specimen measured
The Nature of Process Variation
54321
Precise but not Accurate
4321 4321
Accurate but not Precise
R l f th b. . . . . .Test equipment MUST be a least 10 times
t & i th h t’ b i t t d
Rule of thumb:
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more accurate & precise then what’s being tested
Measurement System ErrorMeasurement System Error
Precise but Accurate but Not accurate Accurate not accurate not precise or precise and
precise
Precision vs AccuracyPrecision vs. Accuracyre
cisi
on
Pr
AccuracyAccuracy
Definition of Terms
• Repeatabilityp y– The variation in repeated measurements of the
same items with a single measurement system– Within appraiser/system variation
R d ibilit• Reproducibility– The variation in the average measurements by
diff t i t i thdifferent appraisers or systems measuring the same itemsBetween appraiser/system variation– Between appraiser/system variation
TermsTerms
• Linearity– The degree to which bias changes withThe degree to which bias changes with
changes in the magnitude of the characteristic measured
• Stabilityy– The dependability, or consistency of the
measurement process over timep
MeasurementSystems Capability
• The variability resulting from measurement error must not exceed a significant proportion of the intended specifications said to be capable
• In addition, it is not desirable for measurement error to exceed a significant proportion of the total process variability
• Capability is not the same as acceptability, acceptability must be determined
b b ion a case by case basis
Measurement System StudiesMeasurement System Studies
• Potential Studies– Assess potential of a measurement system toAssess potential of a measurement system to
be capable over the long term– 10 parts measured 2–3 times by one or more p y
appraisers– A “quick and dirty” study to find out if you are in y y y
the ballpark– Assesses repeatability and reproducibility– Often called an R&R study
• True value:– Theoretically correct value – unknown and unknowabley– Reference standards– NIST standards
• Bias– Distance between average value of all measurements
and true value– Amount gage is consistently off target
Systematic error or offset
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– Systematic error or offset
BIAS Definition
BIAS Is the difference between the
BIAS Definition
BIAS — Is the difference between the observed average of the measurement and the reference value. The reference-value is the value that serves as an
ReferenceValuevalue is the value that serves as an
agreed-upon reference. The reference value can be determined by averaging several measurements with a higher levelseveral measurements with a higher level (e.g., metrology lab) of measuring equipment.
ObservedA V l
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Average ValueACCURACY IS THE SAME AS BIAS
LinearityDifference in the accuracy values of a gage through the expected operating range of the gage
Regression Plot Linearity is Not Good
Good Linearity Bad Linearity
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45
55
4545
35
25
Trial
s
R-Squared = 0.981
Y = 0.934227 + 0.994959X
45
35
25
Trial
s
R-Squared = 0.982
Y = 0.245295 + 0.99505X
5040302010
15
5
Standard5040302010
15
5
Standard
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Standard Standard
StabilityStability
• The distribution of measurements remains constant and predictable over time for both mean and standard deviation
• Total variation in the measurements obtained with th t t ta gage, on the same master or master parts,
when measuring a single characteristic over an extended time periodextended time period.
• Evaluated using a trend chart or multiple measurement analysis studies over time
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measurement analysis studies over time
Stability (drift) DefinitionStability (drift) Definition
Stability — Is the total variation in Time-2Stability Is the total variation in the measurement obtained with a measurement system (test / gage ) on the same master parts when measuring p ga single characteristic over an extended time period.
Ti 1Magnitude Time-1g
timeStabilityPoints to the frequency of Mean center Calibration
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StabilityPoints to the frequency of Mean center Calibration
• Total variation in the measurement system• Measure of natural variation of repeated p
measurements• Terms: Random Error, Spread, Test/Retest
error• Repeatability and Reproducibility
σ σ σMS G O2 2 2= +
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RepeatabilityσG
p y
• The inherent variability of the measurement system• Variation in measurements obtained with a gage when
d l ti b t hil iused several times by one operator while measuring a characteristic on one part.
• Estimated by the pooled standard deviation of the
σ GRd
=2*
Estimated by the pooled standard deviation of the distribution of repeated measurements
• Repeatability is less than the total variation of the measurement system
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R t bilit D fi itiRepeatability Definition
Repeatability — The variation in measurementsobtained with one measurement instrument when used several times by one appraiser whilewhen used several times by one appraiser whilemeasuring the identical characteristic onsame part.
REPEATABILITY
31
σOReproducibility σOp y
• Operator variability of the measurement system• Variation in the average of the measurements
d b diff i hmade by different operators using the same gage when measuring a characteristic on one partM t b dj t d f i ti• Must be adjusted for gage variation
• Reproducibility is less than the total variation of the measurement system
R
the measurement system
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σ ORd
=2*
Reproducibility DefinitionOperator-B
Reproducibility Definition
Reproducibility — Is the variation in the average of the measurements made by different
Operator-B
measurements made by different appraisers using the same measuring instrument when measuring the identical characteristic on the same Operator-Cidentical characteristic on the same part.
Ope ato C
d ibili
Operator-A
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Reproducibility
Accuracy of MeasurementAccuracy of Measurement
• Broken down into three components:1. Stability: the consistency of y ymeasurements over time.2. Accuracy: a measure of the amount of ybias in the system.3. Linearity: a measure of the bias values ythrough the expected range of measurements.
Precision of MeasurementPrecision of Measurement
• Precision, Measurement Variation, can be broken down into two components:p1. Repeatability (Equipment variation): variation in measurements under exact conditions.2. Reproducibility (Appraiser variation): variation in the average of measurements when different operators measure the same part.
Measurement System DiscriminationyLeast count should be at most one-tenth of the total process capability or tolerance (6 sigma)process capability or tolerance (6 sigma)
– Process capability 10 Max Least count 1Part to Part variation must be greater than the smallest
it funit of measure
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Types of R&R Studies
• Variable Gage R&R– NumbersNumbers– Units of measure
• Attribute Gage R&R• Attribute Gage R&R– Subjective (cosmetic defects)
Scatter of defects– Scatter of defects– feel/visual
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Basic TermsBasic Terms
EV= Equipment Variation (Repeatability)
AV= Appraiser Variation (Reproducibility)AV Appraiser Variation (Reproducibility)
R&R= Repeatability & Reproducibility
PV= Part Variation
TV= Total Variation of R&R and PV
K1-Trial, K2-Operator, & K3-Part Constants
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Gage R&R studyGage R&R study
Generally two or three operators
Generally 10 units to measureGenerally 10 units to measure
Each unit is measured 2-3 times by each operatoroperator
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Preparation for a Measurement pStudy
• Determine if reproducibility is an issue. If it is, select the number of operators to participate.
• Operators selected should normally use the measurement• Operators selected should normally use the measurement system.
• Select samples that represent the entire operating range.• Gage must have graduations that allow at least one-tenth
of the expected process variation.• Insure defined gaging procedures are followedInsure defined gaging procedures are followed.• Measurements should be made in random order.• Study must be observed by someone who recognizes the
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importance of conducting a reliable study.
Procedure for Performing R&R gStudy
• Calibrate the gage, or assure that it has been calibrated.• Have the first operator measure all the samples once in random
order.• Have the second operator measure all the samples once in
random order.• Continue until all operators have measured the samples once p p
(this is Trial 1).• Repeat above steps for the required number of trials.• Use GR&R form to determine the statistics of the study.y
– Repeatability, Reproducibility & %GR&R– Standard deviations of each of the above– % Tolerance analysis
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• Analyze results and determine action, if any.
Variable Gage R&Rg
Guidelines% R&R Results% R&R Results
≤ 10% Gage is OK
10% – 30% Maybe acceptable based upon importanceof application, and cost factor
Over 30% Gage system needs improvement/correctiveOver 30% Gage system needs improvement/correctiveaction
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Xbar Chart by Operator Operator*Part No. Interaction
30
35
40
n 30
35
40
A - B - C -
10
15
20
25
Sam
ple
Mea
n
10
15
20
25
Aver
age
0
5
10
0
5
10
1 2 3 4 5 6 7 8 9 10
Part No.
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Thanks
For any query pl mail me at mahender kumar@yahoo co inFor any query pl. mail me at mahender.kumar@yahoo.co.in
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