Measurement System Analysis

Measurement Systems Analysis Define Measure

Analyze

Improve

By: Mahender Kumar

Control1

Learning Objectives • Understand the language of Measurement. • Show the importance of Measurement. Measurement • Walk away knowing how to perform a Gage R&R and how to interpret results. results • Share some lessons learned.

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Since Measurement systems y represent p a sub-process within a process... • They are subject to Variation. • What could be the source of this variation? • Why do Measurements Vary?

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Sources of Measurement Variation

•Equipment q p •Part •Operator •Environment •Procedure 4

Sources of Measurement Variation Measurement System C&E Matrix Measurements

Materials

Men

Cleanliness

Mechanical Integrety

Temperature Dimension

Wear

Weight Corrosion

Electrical Instability

Hardness Algorithm Instability

Conductivity Density

Procedure P d Fatigue Attention Calibration Error Interpretation Speed Coordination Know ledge Dexterity Vision

Measurement System Error Temp Fluxctuation Line Voltage Variation Vibration Cleanliness

Standard Procedure Sufficient Work time Maintenance Standard Calibration Frequency Operator Training

Humidity

Environment

Wear

Operator Technique

Ease of use

Stability Resolution Calibration Precision Design Temperature Cleanliness

Methods Machines Six Sigma Champion Training

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Possible Sources of Process Variation Observed Process Variation

Actual Process Variation

Measurement Variation

Long-term

Short-term

Variation

Variation due

Variation due

Process Variation

Process Variation

w/i sample

to gage

to operators

Repeatability

Accuracy

Stability

Linearity

Reproducibility

We will look at “repeatability” and “reproducibility” as these ese aree thee primary p y contributors co bu o s too measurement e su e e error. e o. 6

Why MSA

RU = 0.0001

U= 0.0001

U : UNCERTAINITY NATIONAL STANDARD

RU = 0.001

U= 0.001005

RANDOM UNCERTAINITY – FOUND THRU CALIBRATION

LABORATORY STANDARD

SYSTEM UNCERTAINITY – OF MASTER TOTAL UNCERTAINITY – SQRT( RU*RU + SU*SU)

WORK

RU = 0.01

U= 0.01005

STANDARD

RU = 0.05

U= 0.05099

GAUGE FOR INSPECTION / TESTING

Process Capability Lower Spec. Limit

Upper Spec. Limit

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

> 1.33

Impact of Uncertainty

ERROR identified through Calibration Process

Lower Spec. Limit

Upper Spec. Limit

Uncertainty

6 σ Process P Tolerance = T

Knowledge to be obtained • How big is the measurement error? • What are the sources of measurement error? • Is the gage stable over time? • Is the gage capable for this process? • How do we improve the measurement system? 11

Sources of Variation P d t Variability Product V i bilit (Actual variability)

Measurement Variability

Total Variability (Observed variability)

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Effects of Measurement Error Averages

Measurement System Bias — Determined through “Accuracy Study”

µ total = µ product + µ measurement Variability

Measurement System Variability — Determined through “R&R Study” y

2 σ 2total = σ 2product + σ measurement

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

• Stability (over time) • Variation related terms – Repeatability – Reproducibility 14

Definition of Terms • Reference Value – The theoretically or agreed upon correct value 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 y (Bias) ( ) – The difference between the average of the measurement error distribution and the reference value of the specimen measured

The Nature of Process Variation 1

2

3

4

5

Precise but not Accurate

1

2

3

4

Accurate but not Precise

Rule R l off th thumb: b . . . . . .Test equipment MUST be a least 10 times more accurate t & precise i then th what’s h t’ b being i ttested t d 17

Measurement System Error

Precise but not accurate

Accurate but not precise

Not accurate or precise

Accurate and precise

Prrecision

Precision vs. vs Accuracy

Accuracy

Definition of Terms • Repeatability p y – The variation in repeated measurements of the same items with a single measurement system – Within appraiser/system variation

• Reproducibility R d ibilit – The variation in the average measurements by diff different t appraisers i or systems t measuring i th the same items – Between appraiser/system variation

Terms • Linearity – The degree to which bias changes with changes in the magnitude of the characteristic measured

• Stability y – The dependability, or consistency of the measurement p process over time

Measurement Systems 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 on a case by b case b basis i

Measurement System Studies • Potential Studies – Assess potential of a measurement system to be capable over the long term – 10 p parts measured 2–3 times byy one or more appraisers – A “quick and dirty” y studyy to find out if you y are in the ballpark – Assesses repeatability and reproducibility – Often called an R&R study

• True value: – Theoreticallyy correct value – unknown and unknowable – 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 24

BIAS Definition BIAS — Is the difference between the observed average of the measurement and the reference value. The referencevalue is the value that serves as an agreed-upon reference. The reference value can be determined by averaging several measurements with a higher level (e.g., metrology lab) of measuring equipment.

ACCURACY IS THE SAME AS BIAS

Reference Value

Observed A Average V Value l 25

Linearity Good Linearity

Bad Linearity

Regression Plot

Linearity is Not Good

55

55

45

45

35

35

Y=0.934227+0.994959X

25

R-Squared=0.981

Trials

Trials

Difference in the accuracy values of a gage through the expected operating range of the gage

15

15

5

5 10

20

30

Standard

40

50

Y=0.245295+0.99505X

25

R-Squared=0.982

10

20

30

40

50

Standard

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Stability • The distribution of measurements remains constant and predictable over time for both mean and standard deviation • Total variation in the measurements obtained with a gage, on the th same master t or master t parts, t when measuring a single characteristic over an extended time period period. • Evaluated using a trend chart or multiple measurement analysis studies over time 27

Stability (drift) Definition Time-2

Stability — Is the total variation in the measurement obtained with a measurement system (test / gage ) on the same master pparts when measuringg a single characteristic over an extended time period. Magnitude g

Points to the frequency of Mean center Calibration

Ti Time-1 1

time Stability 28

• Total variation in the measurement system p • Measure of natural variation of repeated measurements • Terms: Random Error, Spread, Test/Retest error • Repeatability and Reproducibility

σ

2 MS

=σ +σ 2 G

2 O 29

Repeatability p y

σG

• The inherent variability of the measurement system • Variation in measurements obtained with a gage when used d severall titimes b by one operator t while hil measuring i a characteristic on one part. • Estimated by the pooled standard deviation of the distribution of repeated measurements R σG =

d 2*

• Repeatability is less than the total variation of the measurement system

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R Repeatability t bilit Definition D fi iti Repeatability — The variation in measurements obtained with one measurement instrument when used several times by one appraiser while measuring the identical characteristic on same part.

REPEATABILITY

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Reproducibility p y

σO

• Operator variability of the measurement system • Variation in the average of the measurements made d b by diff different operators using i the h same gage when measuring a characteristic on one part • Must M t be b adjusted dj t d ffor gage variation i ti • Reproducibility is less than the total variation of the measurement system σ

O

R = * d2

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Reproducibility Definition Operator-B

Reproducibility — Is the variation in the average of the measurements made by different appraisers using the same measuring instrument when measuring the identical characteristic on the same part.

Operator-C Ope ato C

Operator-A Reproducibility d ibili 33

Accuracy of Measurement • Broken down into three components: 1. Stability: y the consistency y of measurements over time. 2. Accuracy: y a measure of the amount of bias in the system. 3. Linearity: y a measure of the bias values through the expected range of measurements.

Precision of Measurement • Precision, Measurement Variation, can be broken down into two components: p 1. 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 y Discrimination zLeast count should be at most one-tenth of the total process capability or tolerance (6 sigma) – Process capability 10 Max Least count 1 zPart to Part variation must be greater than the smallest unit it off measure

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Types of R&R Studies

• Variable Gage R&R – Numbers – Units of measure

• Attribute Gage R&R – Subjective (cosmetic defects) – Scatter of defects – feel/visual 37

Basic Terms zEV= Equipment Variation (Repeatability) zAV= Appraiser Variation (Reproducibility) zAV zR&R= Repeatability & Reproducibility zPV= Part Variation zTV= Total Variation of R&R and PV zK1-Trial, K2-Operator, & K3-Part Constants

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Gage R&R study z Generally two or three operators z Generally 10 units to measure z Each unit is measured 2-3 times by each operator

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Preparation p for a Measurement Study • Determine if reproducibility is an issue. If it is, select the number of operators to participate. • 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 followed followed. • Measurements should be made in random order. • Study must be observed by someone who recognizes the importance of conducting a reliable study. 40

Procedure for Performing g R&R Study • 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 p have measured the samples p once (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

• Analyze results and determine action, if any. 41

Variable Gage g R&R

Guidelines % R&R

Results

≤ 10%

Gage is OK

10% – 30%

Maybe acceptable based upon importance of application, and cost factor

Over 30%

Gage system needs improvement/corrective action

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Xbar Chart by Operator

Operator*Part No. Interaction A-

40

35

15 10 5

30

Average

Sample Mean n

30

20

C-

40

35

25

B-

25 20 15 10 5 0

0

1

2

3

4

5

6

7

8

9

10

Part No.

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Thanks

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

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