measurement system analysis

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Measurement Systems Analysis Measurement Systems Analysis Define Measure Analyze Improve Control By: Mahender Kumar

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Page 1: Measurement System Analysis

Measurement Systems AnalysisMeasurement Systems Analysis

Define

Measure

Analyze

Improve

1ControlBy: Mahender Kumar

Page 2: Measurement System Analysis

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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Page 3: Measurement System Analysis

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?

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Page 4: Measurement System Analysis

Sources of Measurement Variation

•Equipmentq p•Part•Operator•Operator•Environment•Procedure

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Page 5: Measurement System Analysis

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

Page 6: Measurement System Analysis

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 .

Page 7: Measurement System Analysis

Why MSAWhy MSA

Page 8: Measurement System Analysis

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

Page 9: Measurement System Analysis

Process Capability

Lower Spec. Limit Upper Spec. Limit

66 σ

Tolerance = T

Process Capability = T / 6 σ > 1.33Means, 6 σ < (0.75*T)

Page 10: Measurement System Analysis

Impact of Uncertainty ERROR identified through Calibration Process

Lower Spec. Limit Upper Spec. Limit

Uncertainty

6 P6 σ Process

Tolerance = T

Page 11: Measurement System Analysis

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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Page 12: Measurement System Analysis

Sources of VariationSources of Variation

P d t V i bilitProduct Variability(Actual variability)

MeasurementVariability

Total Variability(Observed variability)

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Page 13: Measurement System Analysis

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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Page 14: Measurement System Analysis

TerminologyTerminology

• Location related terms:– True value– Bias– Linearity

• Stability (over time)• Variation related terms

– Repeatability– Reproducibility

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Page 15: Measurement System Analysis

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

Page 16: Measurement System Analysis

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

Page 17: Measurement System Analysis

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

Page 18: Measurement System Analysis

Measurement System ErrorMeasurement System Error

Precise but Accurate but Not accurate Accurate not accurate not precise or precise and

precise

Page 19: Measurement System Analysis

Precision vs AccuracyPrecision vs. Accuracyre

cisi

on

Pr

AccuracyAccuracy

Page 20: Measurement System Analysis

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

Page 21: Measurement System Analysis

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

Page 22: Measurement System Analysis

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

Page 23: Measurement System Analysis

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

Page 24: Measurement System Analysis

• 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

Page 25: Measurement System Analysis

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

Page 26: Measurement System Analysis

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

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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

Page 27: Measurement System Analysis

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

Page 28: Measurement System Analysis

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

Page 29: Measurement System Analysis

• 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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Page 30: Measurement System Analysis

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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Page 31: Measurement System Analysis

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

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Page 32: Measurement System Analysis

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*

Page 33: Measurement System Analysis

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

Page 34: Measurement System Analysis

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.

Page 35: Measurement System Analysis

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.

Page 36: Measurement System Analysis

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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Page 37: Measurement System Analysis

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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Page 38: Measurement System Analysis

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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Page 39: Measurement System Analysis

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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Page 40: Measurement System Analysis

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.

Page 41: Measurement System Analysis

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.

Page 42: Measurement System Analysis

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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Page 43: Measurement System Analysis

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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Page 44: Measurement System Analysis

Thanks

For any query pl mail me at mahender kumar@yahoo co inFor any query pl. mail me at [email protected]

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