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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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
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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
exceeded by the difference between two
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
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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)
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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
Engineering definition:
The additional spread within measurements made
under reproducibility conditions.
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Chemical definition:
Reproducibility is a number that is unlikely to be
exceeded by the difference between two
measurements made under reproducibility
conditions.
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R&R
Engineering definition:
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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