Progress Meeting - Rennes - November 2001 Sampling: Theory and applications Progress meeting Rennes, November 28-30, 2001 Progress meeting Rennes, 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 Surfaces Pb or Cl Grinding ?  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 % 25 % 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 m 0 (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 heterogeneity of distribution Heterogeneity of constitution Homogeneity of distribution

Progress Meeting - Rennes - November 2001 DISTRIBUTIONCONSTITUTION HETEROGENEITY Technics & Procedures Procedures Fondamental Sampling Error Segregation error 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 analyzed Difficult to estimate responsible of the fundamental sampling error Can 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  c 2 (SE): relative variance of the fundamental error of sampling for family c M s : mass of the sample M: mass of the initial batch material to sample t i : mass proportion of family i in sample t c : mass proportion of family c in the sample; this is the parameter that attempt to determine through sampling m i : mean unit mass of one particle in family i m c : mean unit mass of particle in family c. From P. Gy Estimation of the Fundamental Error

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 a L ) ë primary sample in industrial medium (unknown real content a S1 ) ë secondary sample at the laboratory (unknown real content a S2 ) ë analysis ë result of the analysis: a r = estimation of a S2 = estimation of a L Additivity of the sampling and analysis error Additivity of means and variances due to independance in probability Consequency : the work of analist has no meaning if sampling is biased

Progress Meeting - Rennes - November 2001 Sample preparation Primary sampleSeveral kg  without any transformation  Representative of the batch Sample for analysisA few g  Powder 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 mm8-20 mm < 8 mm 500 kg Rest 1/4 Heterogeneous 1/4 ~ 20 kg ~ 120 kg Size sorting (>100 mm ; mm ; 8-20 mm ; < 8 mm) Manual SortingLOI The whole ~ 500 g ~ 5 kg ~ 50 g Drying

Progress Meeting - Rennes - November 2001 Different sources for the sampling error 500 kg MSW ~ 120 kg (> 100 mm)( mm)(8-20 mm)(< 8 mm) 5 kg 500 g 50 g Potential source of sampling error

Progress Meeting - Rennes - November 2001 Urban waste example