BIS Measurement Error R Caulcutt

8/13/2019 BIS Measurement Error R Caulcutt

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Measurement error

The terminology and definitions used in different

industries

Roland Caulcutt

Caulcutt Associates


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Measurement

How do people use measurements?

People use measurements to help them:

1. Control a process

2. Assess the capability of a process

3. Improve a process

4. Classify a product or service

5. Settle customer/supplier disputes


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3

The classification of products and

services

Not

acceptable

Not

acceptableAcceptable

LSL USL Quality

When there is no measurement error we can

distinguish between good and bad products,

with confidence.


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When there is measurement error we may be left indoubt about the acceptability of the product or

service.

Not

acceptable

Not

acceptableAcceptable

Uncertainty

?????Uncertainty

?????

LSL USL Quality

Classification with measurement error


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Terminology

5

Accuracy

Bias

Trueness

Precision

RepeatabilityReproducibility

R&R

Measurement systems analysis

Measurement uncertainty

Unfortunately some of these terms have different

meanings in different organisations.


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19.5 20.0 20.5 21.0 Viscosity

19.5 20.0 20.5 21.0 Viscosity

19.5 20.0 20.5 21.0 Viscosity

19.5 20.0 20.5 21.0 Viscosity

Lab A

Lab B

Lab C

Lab D

Measurement in the chemical industry

True value

Poor precision

Bias/Trueness


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Bias and trueness

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For centuries scientists spoke of bias and precision.

BS5497:1979 used the words bias and precision.

BS5725:1994 uses the words trueness and precision.

C


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Repeatability and reproducibility

Repeatability:

Can the person producing the measurement

repeat in the future what he/she did in the past?

Reproducibility:

Can a second person reproduce the

measurement made by the first person?

Precision can be split into two components:

Repeatability

Reproducibility.


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Definitions in the chemical industry

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Repeatability is a number that is unlikely to be

exceeded by the difference between two

measurements made under repeatability conditions.

(Repeatability = 2.82sReproducibility is a number that is unlikely to be


measurements made under reproducibilityconditions.

(Reproducibility = 2.82s)

C


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Calculation of repeatability and

reproducibility

Repeatability = 2.82(Repeatability sd)

Reproducibility = 2.82(Reproducibility sd)

Reproducibility sd =

[(Repeatability sd)2+ (Between labs sd)2]

C

10


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A procedure for the chemical industry

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C

For each level:

send 2 samples

to each of 10 laboratories.

Use the 20 results to estimate repeatability and

reproducibility, at each level.


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Measurement uncertainty

Since about 1993 analytical chemists haveincreasingly used measurement uncertainty to

assess measurement error.

Measurement uncertainty is an interval within whichthe true value is believed to lie.

Measurement uncertainty = x + ks

x is the measured value, s is a standard deviationk is a coverage factor.

C

12


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19.5 20.0 20.5 21.0 Diameter

19.5 20.0 20.5 21.0 Diameter

19.5 20.0 20.5 21.0 Diameter

19.5 20.0 20.5 21.0 Diameter

Smith

Jones

Brown

Lee

Measurement in mechanical engineering

True value

Poor precision

Inaccuracy


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Repeatabilityis

the measurement variability

found

whenthe same item is measured repeatedly

with a specific gauge

by

the same operator.

Repeatability is often called Equipment variation

Repeatability in engineering E

QS9000


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R & Ris

the total measurement variability

found when

the same item is measured repeatedlywith a specific gauge

by

different operators.

R & R depends on equipment variation and

appraiser variation.

R & R E

QS9000


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Measurement variability is defined as the range within

which 99% of the repeat measurements can beexpected to lie.

Mean2.575s-2.575s

99%

99% of repeat measurements

will lie within a band, which

has a width of 5.15s.

Measurement variability E


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Repeatability = 5.15sEsE= SD of repeat measurements by a typical operator.Reproducibility= 5.15sAsA= SD of operator true mean measurements.

R&R = 5.15sTsT = SD of repeat measurements by different operators.

Calculation of R&R E

QS9000


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We can express the R&R as a percentage of the

tolerance.

%R&R=100*R&R/(USL-LSL)

%R&R should not be more than 30% of tolerance.

It is desirable that %R&R is less than 10%.

R&R and product classification E

QS9000

If the purpose of measuring is process

improvement, we should express the R&R as a

percentage of the product variation.


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LSL USL

LSL USL

LSL USL

LSL USL

R&R = 100%

R&R = 30%

R&R = 10%

R&R = 0%

Can you demonstrate your quality? E


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A procedure for engineering industry

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E

Select 10 components.

Ask assessor A to measure each component twice.

Ask assessor B to measure each component twice.

You may wish to use a third assessor.

Analyse the 40 (60) results, using MINITAB, to

estimate repeatability, reproducibility and R&R.

Express R&R as a % of:

1. Tolerance

2. Product variation


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Repeatability differences

Engineering definition:

Repeatability is the spread of measurements made

under repeatability conditions.

(Repeatability = 5.15s)

22

Chemical definition:

Repeatability is a number that is unlikely to be

exceeded by the difference between twomeasurements made under repeatability

conditions.

(Repeatability = 2.82s


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Reproducibility differences


The additional spread within measurements made

under reproducibility conditions.

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Chemical definition:

Reproducibility is a number that is unlikely to be


measurements made under reproducibility

conditions.


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R&R


The total spread of measurements made under

reproducibility conditions.

The chemical industry does not use R&R.

R&R(Engineering)

is similar to Reproducibility(Chemical)

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Variability

To understand the usefulness of your measurement process

you need to calculate the total variation and break this downas follows:

Total variation

Product variation Measurement system variation

Repeatability Reproducibility

Operator Operator bypart

interaction

Short Long

term term


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Repeatability and reproducibility have different

meanings in different industries.

R&R should be less than 30% of tolerance, and

preferably less than 10%.

Using only 2 or 3 assessors can be a weakness of the

recommended procedure in QS9000.

Graphing the results may tell you much more

about the measurement system than you would

learn from the analysis.

Summary


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Bibliography

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QS 9000 Superseded by: PD ISO/TS 16949: 2009 Quality

management systems. Particular requirements for the

application of ISO 9001:2008 for automotive production and

relevant service part organizations. (Section 8 - Measurement

Analysis and Improvement)

BS ISO 5725-2: 1994 Accuracy (trueness and precision) ofmeasurement methods and results. Basic methods for the

determination of repeatability and reproducibility of a standard

measurement method.

BS EN ISO 4259: 2006 Petroleum products. Determination andapplication of precision data in relation to methods of test.

Quantifying uncertainty in analytical measurement , Second

edition (2000) - Eurachem


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BIS Measurement Error R Caulcutt

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