Representative Sampling
30 min crash course
Peter Paasch Mortensen (MSc. Chem. Eng, Ph.D.)
Senior Project Manager
Global Categories & Operation – Supply Chain Development
Initial questions one could ask
Why do we sample?
• Proces control,
• Quality,
• Legal,
• Economics,
• Mass Balances
What characteristics do we want the sample to
have?
• Easy to extract,
• Composite sample,
• Representative,
• ......
• ......
Who is sampling?
Machines
Operators
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Which characteristics are most important?
Representative Sampling ”Take home messages”
In general:
• Focus on representative sampling first and worry about the rest (e.g. sample size) afterwards.
But ask yourself:
Why do you want a sample?
• Proces control/adjustment, Quality, Legal, .....
(different effort might be needed)
How to sample?
• At what frequency?
• Random, Systematic , Stratified?
• Instrumentation: In/On/At/Off-line evaluation?
Is the sample representative?
• This can (and should) be evaluated
Representative sampling – 30 min crash course
Outline:
• What is representative sampling
• Correct sampling
• 0-D and 1-D lots
• Sampling errors
• Correct sampling errors
• Incorrect sampling errors
• How to evaluate a sampling procedure
Representative sampling
• The overall driver for sampling:
• Analysis is only performed on a fraction of the complex material
(the lot).
• But:
• If the sample does not truly represent the lot, erroneous deductions and conclusions will invariably follow – no
matter how precise the actual analysis
• So:
• There has to be a balance between the sampling accuracy & precision and the assaying technique imposed on the
sample.
When is a sample correctly extracted?
Basic requirements
1.
ALL elements in a batch must have equal probability of being selected by the sampling tool.
2.
All elements NOT part of the sample/increment defined by the sampling tool must have zero
probability of ending up in the sample (e.g. no leftovers in sampling tool).
3.
And that the sample is not altered after extraction.
Correct sampling
Basic rule:
All elements in the lot must have equal probability of being selected.
Why are ”samples” not always representative ?
Sample tools are not designed properly
The effect of incorrect sample delimination
Incorrect sample profile
Minkkinen 2006
The effect of correct sample delimination
Correct sample profiles
Minkkinen 2006
Why are ”samples” not always representative ?
Sample tools are not designed properly continued
Theory of Sampling (TOS)
The global estimation error is made up of the total sampling error and the total analystical error
Total sampling error prior to Laboratory
Incorrect sampling errors (ICS)
IDE
IWE
IEE
IPE
FSE
GSE
Correct sampling errors (CSE)
FSE: Fundamental Sampling
Error originates from differences
between fragments – crush
material to minimize.
Total Analytical Error
IDE: Incorrect Delimination Error is
related to the shape of the sampling
tool
IWE: Relatates to weighing errors
IEE: Incorrect Extraction Error is related
to the material extracted by the
sampling tool
IPE: Incorrect Preparation Error relates
to all alterations of the sample after
the sample has been taken
TFE
CFE
Process sampling errors (PSE)
GSE: Grouping and Segregation
Error originates from particles
tendency to segregate within
the lot – blend material to
minimize.
CFE: Cyclic Fluctuation Error
originates from periodic
changes over time. Do
varigraphic analysis to
determine sampling frequency.
TFE: Time Fluctuation Error
originates from long term
trends. Do varigraphic analysis
to determine sampling
frequency.
Why should I care about sampling errors?
Because - There is no point in being precisely wrong!
How do we measure representativeness?
First let us define the relative sampling error from
the analytical grade a in the lot L and the sample s:
• A sampling process is said to be accurate when the
average error me is practically zero
𝑒=
𝑎𝑠 −𝑎𝐿
𝑎𝐿
• A sampling process is said to be reproducible if the
variance of the relative error se2 is small.
Representativeness re2 is a composite property of
the relative error
• Only a correct sampling procedure secures that
samples are both accurate and reproducible
• The random component of re2 tend to reduce when
averaging over a large number of sample.
• This is not the case with the systematic part and
this is why a sampling bias is problematic.
𝑟𝑒 2 = 𝑚𝑒 2 +𝑠𝑒 2
Sampling Unit Operations
1.
Always perform a heterogeneity characterization of new materials
2.
Mix (homogenize) well before all further sampling steps.
3.
Use composite sampling.
4.
Only use representative mass reduction.
5.
Comminute (chrush) whenever neccesary.
6.
Perform a varigraphic characterization of 1-D heterogeneity
7.
Whenever possible turn 0-D, 2-D and 3-D lots into 1-D equivalents
LDT: Lot Dimensionality Transformation
How to take a representative sample of the curd in a cheese VAT?
By transforming 0-dimensional lot to a 1-dimensional lot
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How to evaluate a sampling process?
The Replication Experiment (0-D case)
Primary sampling
Secondary sampling / Mass Reduction
Tertiary sampling / Sub-sampling
Analysis s.s.
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The Replication Experiment (0-D case)
Primary Sampling Error (PSE)
..…
- extract a primary sample (e.g. 20 kg)
- extract a secondary sample, e.g. 1 kg (mass reduction)
- extract a tertiary sample, e.g. 2 g (mass reduction)
Repeat e.g. 10 times
- perform analysis
𝑠𝑃𝑆𝐸 2
𝑚𝑃𝑆𝐸 2
The Replication Experiment (0-D case)
Secondary Sampling Error (SSE)
Now: select a single of the primary samples
..…
Repeat sub-sampling (mass reduction) from the same
primary sample 10 times
𝑠𝑆𝑆𝐸 2
𝑚𝑆𝑆𝐸 2
The Replication Experiment (0-D case)
Tertiary Sampling Error (TSE)
Now select a single of the secondary samples
Perform tertiary sampling 10 times from the
same secondary sample
..…
𝑠𝑇𝑆𝐸 2
𝑚 𝑇𝑆𝐸 2
The Replication Experiment (0-D case)
Total Analytical Error (TAE)
At the bottom line:
Repeat only the analysis 10 times
“Press the button” 10 times! (if analysis is non-destructive)
..…
𝑠𝑇𝐴𝐸 2
𝑚 𝑇𝐴𝐸 2
The Replication Experiment (0-D case)
Comparison of sampling stages
PSE
Typical relative magnitude of sampling
variances:
SSE
TSE
var(PSE),var(SSE),var(TSE),var (TAE)
TAE
PSE
SSE
TSE
TAE
Something is clearly WRONG regarding
the third sampling level - we may want to
have a closer look at the third stage in our
sub-sampling procedure …
The Replication Experiment (0-D case)
Now was the sampling procedure correct ? The averages will tell
𝑚 𝑇𝐴𝐸 ≈ 𝑚 𝑇𝑆𝐸 ≈ 𝑚𝑆𝑆𝐸 ≈ 𝑚𝑃𝑆𝐸
1-D sampling
Q
1 estimation (A) 2
v( j ) On-line

 (hq  j  hq ) 
2(Q  j )
q 1
1
2(Q  j )a L2
Activity
0.6
0.5
Systematic selection
0.4
Random selection
Stratified random selection
0.3
Minimal Practical Error
0(0-D case)
20
40
60
80
100
120
# measurements
-3
2
x 10
Va riogra m a nd a uxila ry functions ( A)
Variogram
1.5
Wstratif ied
Q
 (a
q 1
q j

0.3
Variography
2
0.3
0
20
40
60
80
100
120
0
# measurements
-3
x 10
-3
Va riogra m a nd a uxila ry functions ( A)
2
x 10
Variogram
On-line estimation (A)
Wstratif ied
1.5
1.5
0.5
0.5
0
v(j)
1
0.6
Wrandom
1
0.5
0
10
20
30
40
50
60
0
70
0
Lag (j)
0.4
Total sampling error (A)
0.02
0.02
Stratif ied selection mode
Systematic selection mode
Random selection mode
0.015
0
0.01 20
2
0
60
80
120
0.01
0.005
Va riogra m a nd a uxila ry functions ( A)
0
10
20
30
# increments
1.5
100
# measurements
0.005
-3
x 10
40
0.015
Activity
0.3
Activity
Activity
v(j)
Wsystematic
40
50
Variogram
Wstratif ied
0
0
2
In conclusion
• Representative sampling is crucial for data reliability and the conclusions that follows.
• Theory of samling offers guidance on how to characterize materials and sampling procedures.
• By simple tests you can get an idea of how representative your sampling procedure is – its not rocket
science.
Slide
No.
27
• 21. oktober 2015
Thank you for your attention
Contact information: pemoe@arlafoods.com
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21 October 2015