fulltext_019 - Chapter 20 Statistical Background Contents...

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469 H.G. Merkus, Particle Size Measurements, DOI 10.1007/978-1-4020-9015-8_20, © Springer Science+Business Media B.V. 2009 ±Abstract: Good understanding of statistics and mathematical procedures is essen- tial for proper interpretation of characterization results for particulate products and their production processes. Some basic background and some exercises are pro- vided in this chapter. ±20.1± ±Introduction± Particle size analysis is performed to obtain a quantitative answer with respect to par- ticle size, one or more characteristic parameters of a particle size distribution (PSD) or particle concentration. The measurements can be performed repeatedly on a single Chapter 20 Statistical Background Good practice requires: basic understanding of statistics statistical evaluation of measurement results attention for quality maintenance procedures Contents 20.1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469 20.2 Mean and Spread of Data; Types of Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 470 20.3 Addition of Random Errors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 473 20.4 Types of Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474 20.5 Confidence Intervals . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 479 20.6 Significance and Hypothesis Testing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480 20.7 Outlier Testing. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 483 20.8 Analysis of Variance (ANOVA) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484 20.9 Control Charts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486 20.10 Proficiency Testing Schemes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 489 20.11 Information Extraction Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 20.11.1 Regression Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 20.11.2 Auto-Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490 20.11.3 Cross-Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 20.11.4 Principal Component Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 491 20.12 Definitions and Symbols. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 492 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494 Annex 20 A: Exercises for Calculation of Mean, Standard Deviation and Variation Coefficient . . . . . . . . . . . . . . . . . . 495 Annex 20 B: Exercises for Calculation of Confidence Intervals and Producer’s Risk and Consumer’s Risk. . . . . . . . . . . . . . . . . . . . . 499
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470 20 Statistical Background particle or on a collection of particles. The result is always a set or population ±of± values having some kind of distribution, regardless whether it concerns repeated size measurements of a single particle or the sizes of particles in a mixture. It can be com- pared with the results coming from a height measurement of men. The measurement uncertainty and the large variety of factors that contribute to the genesis of particles or to the growth of men cause this. These populations are commonly represented by one or a few characteristic parameters, such as the mean or average value (measure of location), the degree of spread (or dispersion) of the distribution, the largest/smallest value, the degree of symmetry or peakedness of the distribution, the number of modes, etc. In particle technology, we must distinguish between two types of distributions: The distribution of measurement results of any characteristic parameter, such as concentration, size or shape, around the mean value, caused by random errors during measurement. The distribution of particle sizes, caused by the genesis or production process of the±particles.± The measured values for a property “ x ” coming from either type of distribution can be represented in many ways. The first way is to provide all the data in digital form. This often results in large tables with data, which offer no possibility for a quick overview. For a better overview, often the mean or the median value is calcu-
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This note was uploaded on 05/06/2010 for the course MECH. 28197 taught by Professor Dr.shafii during the Spring '10 term at Sharif University of Technology.

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fulltext_019 - Chapter 20 Statistical Background Contents...

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