The present book is based on the experience of sampling powders and bulk materials at institute of "Mechanische Verfahrens technik " , Karlsruhe University (Germany). sampling is understood to be the taking of samples from a material in order to obtain information about the composition of the total amount in respect of one or more attributes, such as metal content, ash content, moisture, particle size, particle shape etc. In the case of granular bulk material already comminuted or not, samples from tubs, trucks, bags or barrels. As granular material has a strong tendency to segregate, portions…mehr
The present book is based on the experience of sampling powders and bulk materials at institute of "Mechanische Verfahrens technik " , Karlsruhe University (Germany). sampling is understood to be the taking of samples from a material in order to obtain information about the composition of the total amount in respect of one or more attributes, such as metal content, ash content, moisture, particle size, particle shape etc. In the case of granular bulk material already comminuted or not, samples from tubs, trucks, bags or barrels. As granular material has a strong tendency to segregate, portions must be removed form these containers at many places. The book describes the basic theory behind sampling materials in powder or granular form. In addition to providing fundamental statistical data, it also highlights the mistakes that can arise in the different types of sampling techniques, such as suspensions, pellet cross-sections, sample dividing, or sampling according to number or weight. If the samples contain individual particles, comparable in size to the size of the sample itself then in addition to the number of individual elements in the sample and the type of sampling the particle size and particle size distribution will be further variables. This book will pay special attention to this fact important for the whole of powder technology, the chemical, pharmaceutical, food and and for mineral processing industry.Hinweis: Dieser Artikel kann nur an eine deutsche Lieferadresse ausgeliefert werden.
1 Introduction.- 2 Fundamentals of Statistics.- 2.1 Frequency distribution of discrete attributes.- 2.2 Cumulative frequency of discrete attributes.- 2.3 Arithmetic mean and sample variance for discrete distributions.- 2.4 Frequency distribution of continuous attributes.- 2.5 Expectation and variance of one-dimensional probability functions.- 2.6 Two-dimensional distribution functions.- 2.7 Expectations and variances of a two-dimensional distribution function.- 2.8 Conditional expectations.- 2.9 Rules for calculating expectations and variances.- 2.9.1 One-dimensional distribution functions.- 2.9.2 Two-dimensional distribution functions.- 2.9.3 Conditional distribution functions.- 3 Random Sampling Distributions.- 3.1 Concept of the random sample.- 3.2 Sampling without replacement.- 3.3 Random sampling with replacement.- 3.3.1 Binomial replacement.- 3.3.2 Poisson distribution.- 3.3.3 Normal distribution.- 4 Sampling from a Population Having an Arbitrary Distribution of the Attribute.- 4.1 Sampling with replacement.- 4.2 Sampling without replacement.- 5 Inference from the Sample About the Population (Confidence Intervals).- 5.1 Sampling when the variance of the population is known.- 5.2 Normally distributed populations with known variance ?2.- 5.3 Sampling from normally distributed populations with unknown variance.- 5.3.1 Chi-square distribution (confidence interval for sample variances.- 5.3.2 The t distribution (confidence intervals for means when the variance is unknown.- 6 Sampling Procedures.- 6.1 Random and systematic sampling.- 6.2 Stratified sample.- 6.3 Proportional subdivision a stratified sample.- 6.4 Cost-optimizing selection for a stratified sample.- 6.5 Example of stratified sampling.- 6.6 Multi-stage sampling.- 6.7 Cost-optimizing selection in multi-stagesampling.- 6.8 Example of multi-stage sampling.- 6.9 Double sampling for bulk material.- 7 Sampling from a Random Mixture.- 7.1 Sampling with a constant number n of particles from a two-material mixture.- 7.1.1 Variance of the numerical concentration.- 7.1.2 Variance of the concentration by mass.- 7.2 Sampling with a constant sample size n from a multi-material mixture.- 7.3 Sampling with a constant mass (or volume) from a two-component mixture.- 7.3.1 The problem of a random mixture formed from two even-grained fractions of any size.- 7.3.2 Random mixture of two even-grained fractions.- 7.4 Constant sample mass and the random mixture of several components of unequal grain size.- 7.5 Random mixture of two particle-size distributions.- 7.6 Random mixture for suspensions.- 8 Sampling in a Sample Divider.- 8.1 Numerical concentration in the case of two or more components.- 8.2 Variance of the concentration by mass of two or more components having differing even-grain fractions.- 8.3 Variance of the concentrations by number and by mass for a two-material mixture.- 8.4 Experiments on a rotary sample-divider from Messrs. Retsch.- 9 Sampling for Grain-Size Analysis.- 9.1 Object and method of sampling.- 9.2 Sampling error for sampling with a constant particle number n from a numerical distribution Q0.- 9.3 Sampling error for sampling with a constant particle number n from a cumulative volume distribution Q3.- 9.4 Sampling error of a cumulative volume distribution Q3 for constant sample masses of solid in the sample.- 9.5 Sampling error of a numerical distribution Q0 or of a cumulative volume distribution Q3 in sampling with a constant suspension volume VSus from a suspension.- 9.6 Sampling error in sample-dividing.- 9.6.1 Cumulative numerical distribution Q0.- 9.6.2 Cumulativevolume distribution Q3.- 10 Sampling Error when Sampling from Ores and Fuels.- 11 Investigations of Random Packings.- 11.1 Definitions and formulation of the problem.- 11.2 Relationship between area porosity and volume porosity.- 11.3 Test for random packing.- 11.4 Grain size analysis by determination of the diameters of sectioned solid particles.- 11.4.1 Determination of all moments Mn,o of the sphere diameter distribution from the moments Mk,o of the section circle diameter distribution.- 11.4.2 Solution of the integral equation.- 11.4.3 Determination of sphere diameter distributions qo (d) with the aid of a histogram of section circle diameters.- 12 Sampling from Non-Random Mixtures.- 12.1 Systematic variance.- 12.2 Correlation length, correlogram.- 13 Sampling from a Convevor Belt.- 13.1 Variance within and between belt sections of lenght L.- 13.2 Inspection of given quantities when sampling randomly or systematically from a conveyor belt.- 14 Sampling Devices.- 14.1 Devices for sampling liquids.- 14.2 Devices for sampling gases and dusts.- 14.3 Devices for sampling granular and lumpy material.- 14.4 Sample splitters.- Notes.- Literature.
1 Introduction.- 2 Fundamentals of Statistics.- 2.1 Frequency distribution of discrete attributes.- 2.2 Cumulative frequency of discrete attributes.- 2.3 Arithmetic mean and sample variance for discrete distributions.- 2.4 Frequency distribution of continuous attributes.- 2.5 Expectation and variance of one-dimensional probability functions.- 2.6 Two-dimensional distribution functions.- 2.7 Expectations and variances of a two-dimensional distribution function.- 2.8 Conditional expectations.- 2.9 Rules for calculating expectations and variances.- 2.9.1 One-dimensional distribution functions.- 2.9.2 Two-dimensional distribution functions.- 2.9.3 Conditional distribution functions.- 3 Random Sampling Distributions.- 3.1 Concept of the random sample.- 3.2 Sampling without replacement.- 3.3 Random sampling with replacement.- 3.3.1 Binomial replacement.- 3.3.2 Poisson distribution.- 3.3.3 Normal distribution.- 4 Sampling from a Population Having an Arbitrary Distribution of the Attribute.- 4.1 Sampling with replacement.- 4.2 Sampling without replacement.- 5 Inference from the Sample About the Population (Confidence Intervals).- 5.1 Sampling when the variance of the population is known.- 5.2 Normally distributed populations with known variance ?2.- 5.3 Sampling from normally distributed populations with unknown variance.- 5.3.1 Chi-square distribution (confidence interval for sample variances.- 5.3.2 The t distribution (confidence intervals for means when the variance is unknown.- 6 Sampling Procedures.- 6.1 Random and systematic sampling.- 6.2 Stratified sample.- 6.3 Proportional subdivision a stratified sample.- 6.4 Cost-optimizing selection for a stratified sample.- 6.5 Example of stratified sampling.- 6.6 Multi-stage sampling.- 6.7 Cost-optimizing selection in multi-stagesampling.- 6.8 Example of multi-stage sampling.- 6.9 Double sampling for bulk material.- 7 Sampling from a Random Mixture.- 7.1 Sampling with a constant number n of particles from a two-material mixture.- 7.1.1 Variance of the numerical concentration.- 7.1.2 Variance of the concentration by mass.- 7.2 Sampling with a constant sample size n from a multi-material mixture.- 7.3 Sampling with a constant mass (or volume) from a two-component mixture.- 7.3.1 The problem of a random mixture formed from two even-grained fractions of any size.- 7.3.2 Random mixture of two even-grained fractions.- 7.4 Constant sample mass and the random mixture of several components of unequal grain size.- 7.5 Random mixture of two particle-size distributions.- 7.6 Random mixture for suspensions.- 8 Sampling in a Sample Divider.- 8.1 Numerical concentration in the case of two or more components.- 8.2 Variance of the concentration by mass of two or more components having differing even-grain fractions.- 8.3 Variance of the concentrations by number and by mass for a two-material mixture.- 8.4 Experiments on a rotary sample-divider from Messrs. Retsch.- 9 Sampling for Grain-Size Analysis.- 9.1 Object and method of sampling.- 9.2 Sampling error for sampling with a constant particle number n from a numerical distribution Q0.- 9.3 Sampling error for sampling with a constant particle number n from a cumulative volume distribution Q3.- 9.4 Sampling error of a cumulative volume distribution Q3 for constant sample masses of solid in the sample.- 9.5 Sampling error of a numerical distribution Q0 or of a cumulative volume distribution Q3 in sampling with a constant suspension volume VSus from a suspension.- 9.6 Sampling error in sample-dividing.- 9.6.1 Cumulative numerical distribution Q0.- 9.6.2 Cumulativevolume distribution Q3.- 10 Sampling Error when Sampling from Ores and Fuels.- 11 Investigations of Random Packings.- 11.1 Definitions and formulation of the problem.- 11.2 Relationship between area porosity and volume porosity.- 11.3 Test for random packing.- 11.4 Grain size analysis by determination of the diameters of sectioned solid particles.- 11.4.1 Determination of all moments Mn,o of the sphere diameter distribution from the moments Mk,o of the section circle diameter distribution.- 11.4.2 Solution of the integral equation.- 11.4.3 Determination of sphere diameter distributions qo (d) with the aid of a histogram of section circle diameters.- 12 Sampling from Non-Random Mixtures.- 12.1 Systematic variance.- 12.2 Correlation length, correlogram.- 13 Sampling from a Convevor Belt.- 13.1 Variance within and between belt sections of lenght L.- 13.2 Inspection of given quantities when sampling randomly or systematically from a conveyor belt.- 14 Sampling Devices.- 14.1 Devices for sampling liquids.- 14.2 Devices for sampling gases and dusts.- 14.3 Devices for sampling granular and lumpy material.- 14.4 Sample splitters.- Notes.- Literature.
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