Sampling of Heterogeneous and Dynamic Material Systems: Theories of Heterogeneity, Sampling and Homogenizing

Although sampling errors inevitably lead to analytical errors, the importance of sampling is often overlooked. The main purpose of this book is to enable the reader to identify every possible source of sampling error in order to derive practical rules to (a) completely suppress avoidable errors, and (b) minimise and estimate the effect of unavoidable errors. In short, the degree of representativeness of the sample can be known by applying these rules. The scope covers the derivation of theories of probabilistic sampling and of bed-blending from a complete theory of heterogeneity which is based on an original, very thorough, qualitative and quantitative analysis of the concepts of homogeneity and heterogeneity. All sampling errors result from the existence of one form or another of heterogeneity. Sampling theory is derived from the theory of heterogeneity by application of a probabilistic operator to a material whose heterogeneity has been characterized either by a simple scalar (a variance: zero-dimensional batches) or by a function (a variogram: one-dimensional batches). A theory of bed-blending (one-dimensional homogenizing) is then easily derived from the sampling theory. The book should be of interest to all analysts and to those dealing with quality, process control and monitoring, either for technical or for commercial purposes, and mineral processing. Although this book is primarily aimed at graduates, large portions of it are suitable for teaching sampling theory to undergraduates as it contains many practical examples provided by the author's 30-year experience as an international consultant. The book also contains useful source material for short courses in Industry.

Table of Contents:
Foreword. First Part: General Introduction. 1. Basic Definitions and Notations. 2. Logical Structure of this Set of Theories. Second Part: Heterogeneity. 3. Logical Analysis of the Concepts of Homogeneity and Heterogeneity. 4. Heterogeneity of a Population of Units Composing a Zero-Dimensional Batch. 5. Heterogeneity of a Series of Units Composing a One-Dimensional Batch. Third Part: General Analysis of the Concept of Sampling. 6. Respective Roles of Sampling, Preparation and Analysis. 7. Critical Review of the Main Selection Schemes and Processes. 8. Complementary Models of the Increment Sampling Process. Fourth Part: Achievement of Sampling Correctness. 9. From Model Point-Sample to Prepared-Sample Actually Collected: Generation of Materialization Errors ME. 10. Conditions of Correct Increment Delimitation: Generation of the Delimitation Error DE. 11. Conditions of Correct Increment Extraction: Generation of the Extraction Error EE. 12. Conditions of Increment and Sample Correct Preparation: Generation of the Preparation Errors PE. Fifth Part: One-Dimensional Sampling Model. 13. One-Dimensional Sampling Model: Generation of the Integration Error IE. 14. Discontinuous Component IE1 of the Integration Error IE. 15. Continuous Component IE2 of the Integration Error. 16. Periodic Component IE3 of the Integration Error. Sixth Part: Zero-Dimensional Sampling Model. 17. Zero-Dimensional Model: General Case: Total Error TE. 18. Linking up Zero- and One-Dimensional Models. 19. Definition/Properties of Fundamental Error FE. 20. Definition and Properties of the Grouping and Segregation Error GSE. 21. Probabilistic but Incorrect Sampling: Total Error TE. Seventh Part: Sampling by Splitting. 22. Review of Main Splitting Methods and Devices. 23. Splitting Errors. Eighth Part: Resolution of Sampling Problems. 24. Properties of the Components of the Total Sampling Error: Recapitulation. 25. Solvable and Unsolvable Sampling Problems. 26. Working out a Sampling Scheme. 27. Sampling for a Moisture Analysis and for the Computation of a Dry Tonnage. 28. Sampling Particulate Solid for a Size Analysis. 29. Mass and/or Volume Estimation by Proportional Sampling. Ninth Part: Sampling for Commercial Purposes: Specific Problems. 30. Check on Sampling Correctness vs. Check on Sampling Accuracy: The Reasoning Errors. 31. Commercial Sampling and Analysis: Reflexions on the Splitting Limit Procedure. 32. Commercial Sampling and Analysis: Testing the Long-Term Agreement between Seller and Buyer. 33. Check on the Sampling Bias: Agreement between the Estimate of a Content and the True Value. Tenth Part: Homogenizing. 34. Census of the Homogenizing Processes. 35. One-Dimensional Homogenizing or Bed-Blending. Useful References. Index.