Progress Meeting - Rennes - November 2001 Sampling: Theory and applications Progress meeting Rennes,...
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Transcript of Progress Meeting - Rennes - November 2001 Sampling: Theory and applications Progress meeting Rennes,...
Progress Meeting - Rennes - November 2001
Sampling: Theory and applications
Progress meetingRennes, November 28-30, 2001
Progress meetingRennes, November 28-30, 2001
Fifth Framework Program
Progress Meeting - Rennes - November 2001
The 3 types of the overall measurement error
Scientific error
Sampling Error
Analysis Error
1
2
3
Surfaces
Pb or
ClGrinding? Insufficient control of the concept involved
Heterogeneity of the object to be measured
Imperfections in protocols or analysis tools
Progress Meeting - Rennes - November 2001
Sampling: definition
Sample
10 kg
Batch
10 t
Basic operation that involves removing a certain fraction of the batch of material.
Progress Meeting - Rennes - November 2001
?
? Composition
LOI
Water content
Heavy metals?Waste
Heap - Dump Treatment
Why is it important to succeed sampling?
Progress Meeting - Rennes - November 2001
Sampling error approach
BATCH
50 %
50 %
50 %
25 %
25 %
33.3 %
33.3 %
22.2 %
11.1 %
SAMPLES
?REAL COMPOSITION
Progress Meeting - Rennes - November 2001
The a priori qualities of sampling
Probabilistic: when the selection is based on the notion of selection probability.
Correct: when being probabilistic, the selection chances are uniformly distributed
Uncorrect: when the latter condition is not fulfilled
Non-probabilistic: When the selection is not based on the notion of selection probability.
Deterministic: when the selection is founded on the implementation of a rigid system, without intervention of a random element
Purposive: when the selection is founded on the choice by the sampling operator of the elements of the batch to be retained as a sample
Progress Meeting - Rennes - November 2001
The a posteriori qualities of sampling
They are dependent on the results of the selection (i.e. the Sampling Error SE)
Unbiased: when the mean of SE is 0 Biased: when the mean of SE is not 0 Accurate: when the absolute value of the bias (m(SE)) is not larger than a
certain standard of accuracy m0(SE)
Reproducible or precise: when the variance of SE is not larger than a certain standard of reproducibility
Representative: when sampling is both accurate and reproducible Exact: when SE is identically 0 (m(SE) and (SE) = 0) Equitable: when the commercial value of the batch calculated on the basis of
the sample is a random variable with an average equal to the commercial value calculated on the basis of the true content
Progress Meeting - Rennes - November 2001
Heterogeneity of materials
The heterogeneity is responsible for the generation of sampling errors
Homogeneity of constitution and distribution
Heterogeneity of constitution
Perfect heterogeneityof distribution
Heterogeneityof constitution
Homogeneityof distribution
Progress Meeting - Rennes - November 2001
DISTRIBUTIONDISTRIBUTIONCONSTITUTIONCONSTITUTION
HETEROGENEITYHETEROGENEITY
Technics &Technics &
ProceduresProcedures
Fondamental Sampling Error
Fondamental Sampling Error
Segregation errorSegregation error
Preparation, weighting analytical errors
Preparation, weighting analytical errors
Heterogeneity and sampling error
Progress Meeting - Rennes - November 2001
Heterogeneity and sampling error
CONSTITUTION
HETEROGENEITY
can be minimized by physical homogenization of the batch to be analyzedDifficult to estimate
responsible of thefundamental
sampling errorCan be estimated
DISTRIBUTION
Progress Meeting - Rennes - November 2001
Fundamental Error of sampling
One of the component of the total sampling error. Defined as the error related to the constitution heterogeneity of the
batch, which results from frequencies and physicochemical particularities of the particles.
Irreducible without modifying the state of the material. Optimal limit ideally reached when conditions of equiprobability of
sampling particles are respected.
MINIMAL Error
CORRECT sampling
HOMOGENISED batch
Progress Meeting - Rennes - November 2001
As for: cardboard or glass (i.e. MODECOM categories) in MSW
c2(SE): relative variance of the fundamental error of sampling for family c
Ms: mass of the sample
M: mass of the initial batch material to sample
ti: mass proportion of family i in sample
tc: mass proportion of family c in the sample; this is the parameter that attempt to determine through sampling
mi: mean unit mass of one particle in family i
mc: mean unit mass of particle in family c.
From P. Gy
Estimation of the Fundamental Error
n
1iii
c
cc
s
2c mt
t
t21.m.
M
1
M
1)SE(
Progress Meeting - Rennes - November 2001
Complementarity sampling - analysis
Decomposition of a processus to estimate the quality : batch material that we want to evaluate (unknown real content aL)
primary sample in industrial medium (unknown real content aS1)
secondary sample at the laboratory (unknown real content aS2)
analysis result of the analysis: ar= estimation of aS2 = estimation of aL
Additivity of the sampling and analysis error
Additivity of means and variances due to independance in probability
EG ET ET AE 1 2
Consequency : the work of analist has no meaning if sampling is biased
Progress Meeting - Rennes - November 2001
Sample preparation
Primary sample Several kgwithout any transformationRepresentative of the batch
Sample for analysis A few gPowder
Preparation operations:Separation (stratification)Size reduction (Mixing)Secondary sampling (splitting)...
Sampling plan = Operation succession
Each step of the sampling plan is source of error
Total sampling error = Sum of the errors at each step of the plan (linked to the variance additivity)
Progress Meeting - Rennes - November 2001
MSW Sampling
?
Aim: To determine the composition of MSW, in terms of:
MODECOM© categories,size distribution,NSOM and inerts grades,Etc.
Problem: Several samples and sub-samples are taken and measurements are
made on different masses. What is the accuracy of the sample and what is the signification of a value
when such a sampling plan is made?
Progress Meeting - Rennes - November 2001
MSW caracterisation methodology
> 100 mm 20-100 mm 8-20 mm < 8 mm
500 kg500 kg
Rest
1/4
Heterogeneous
1/4 1/4 1/4
~ 20 kg~ 20 kg
~ 120 kg~ 120 kg
Size sorting(>100 mm ; 20-100 mm ; 8-20 mm ; < 8 mm)
Manual Sorting LOI
The wholeThe whole ~ 500 g~ 500 g~ 5 kg~ 5 kg ~ 50 g~ 50 g
Drying
Progress Meeting - Rennes - November 2001
Different sources for the sampling error
500 kg500 kgMSWMSW
~ 120 kg ~ 120 kg
(> 100 mm) (20-100 mm) (8-20 mm) (< 8 mm)
5 kg5 kg 500 g500 g 50 g50 g
Potential source of sampling error
Progress Meeting - Rennes - November 2001
Urban waste example