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.

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.