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


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


Sampling: definition

Sample

10 kg

Batch

10 t

Basic operation that involves removing a certain fraction of the batch of material.


?

? Composition

LOI

Water content

Heavy metals?Waste

Heap - Dump Treatment

Why is it important to succeed sampling?


Sampling error approach

BATCH

50 %

50 %

50 %

25 %

25 %

33.3 %

33.3 %

22.2 %

11.1 %

SAMPLES

?REAL COMPOSITION


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


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


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


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


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


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


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(


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


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)


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?


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


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


Urban waste example

progress meeting - rennes - november 2001 sampling: theory and applications progress meeting rennes,...

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