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Statistics for Mining EngineeringBy Jacek M. Czaplicki
M00001552
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Many areas of mining engineering gather and use statistical information, provided by observing the actual operation of equipment, their systems, the development of mining works, surface subsidence that accompanies underground mining, displacement of rocks surrounding surface pits and underground drives and longwalls, amongst others. In addition, the actual modern machines used in surface mining are equipped with diagnostic systems that automatically trace all important machine parameters and send this information to the main producer’s computer. Such data not only provide information on the technical properties of the machine but they also have a statistical character. Furthermore, all information gathered during stand and lab investigations where parts, assemblies and whole devices are tested in order to prove their usefulness, have a stochastic character. All of these materials need to be developed statistically and, more importantly, based on these results mining engineers must make decisions whether to undertake actions, connected with the further operation of the machines, the further development of the works, etc. For these reasons, knowledge of modern statistics is necessary for mining engineers; not only as to how statistical analysis of data should be conducted and statistical synthesis should be done, but also as to understanding the results obtained and how to use them to make appropriate decisions in relation to the mining operation.
This book on statistical analysis and synthesis starts with a short repetition of probability theory and also includes a special section on statistical prediction. The text is illustrated with many examples taken from mining practice; moreover the tables required to conduct statistical inference are included.
Table of Contents
Fundamentals
1.1. Goal and task of statistics
1.2. Basic terms of probability theory
1.3. Basic terms of statistical inference
Some areas of application of mathematical statistics in mining
Analysis of data
3.1. Testing of sample randomness
3.2. An outlier in a sample
3.3. Stationarity testing of sequences
3.4. Outcome dispersion testing
3.5. Cyclic component tracing
3.6. Autocorrelation analysis
3.7. Homogeneity of data
Synthesis of data
4.1. Estimation of the parameters of a random variable
4.2. Probability distribution description
4.3. An example of empirical–theoretical inference about the distribution of a random variable
Relationships between random variables
5.1. The chi-square test of independence
5.2. The Pearson’s linear correlation coefficient
5.3. Partial correlation coefficient and multiple correlation coefficient
5.4. Non-linear correlation measures
Synthesis of data—regression analysis
6.1. Preliminary remarks
6.2. Linear regression
6.3. Linear transformations and multidimensional models
6.4. Autocorrelation and autoregression models
6.5. Classical linear regression for many variables
6.6. Regression with errors in values of random variables
6.7. Linear regression with additional information
Special topic: Prediction
7.1. Introduction and basic terms
7.2. Subject of prediction
7.3. Examples
Explanations of some important terms
Statistical tables
9.1. Distribution function Φ(z) of standardised normal distribution N(0, 1).
9.2. Quantiles of the standardised normal distribution N(0, 1)
9.3. Critical values of the Student’s t-distribution
9.4. Critical values of the Chi-squared distribution
9.5. Critical values of the Snedecor’s F distribution for α = 0.10
9.6. Critical values of the Snedecor’s F distribution for α = 0.05
9.7. Critical values of the Snedecor’s F distribution for α = 0.025
9.8. Critical values of the series distribution
9.9. Critical values of the Cochran statistic for α = 0.05
9.10. Critical values of the Hartley statistic for α = 0.05
9.11. Quantiles of the Poisson distribution
9.12. Critical values in Kolmogorov test of goodness-of-fit
9.13. Critical values of a linear correlation coefficient and a partial correlation coefficient
9.14. Critical values of the Spearman’s rank correlation coefficient
9.15. Critical values of a multiple correlation coefficient
9.16a. Critical values Dn,m(α) in the Smirnov test of goodness-of-fit for two empirical distributions
9.16b.Distribution of the Smirnov statistic Dn,m P{Dn,m ≤ k/n}
9.17. Critical values α(2n, 2m) of the distribution
References
Subject index
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Author(s)
Biography
Jacek M. Czaplicki (Mining Mechanization Institute, Silesian University of Technology, Gliwice, Poland) has been an academic lecturer for forty years and is continuously associated with his home University. He did, however, leave his school for a couple of years’ lecturing in African universities.
He worked for three years at the School of Mines of the Kwara State College of Technology, Ilorin, Nigeria on a UNESCO project. A few years later, he was appointed to Zambia Consolidated Copper Mines Ltd for three years and worked as a lecturer at the School of Mines of the University of Zambia, Lusaka as part of a World Bank project.
Jacek Czaplicki received a Master of Science in Mine Mechanization from the Silesian University of Technology, Gliwice, Poland. He also obtained a Doctorate degree in Technical Sciences. Later, he submitted a dissertation and passed all of the requirements and was awarded a D.Sc. degree in Mining and Geological Engineering with a specialisation in Mine Machinery at the same home University. Currently, he is a Professor of Mining Engineering.
He has published about a hundred and forty papers and ten books in Poland and abroad. His specialization comprises mine transport, the reliability and computation of mine machinery systems and the reliability of hoist head ropes. In his research, he applies methods and models from mathematical statistics. He is an internationally recognized specialist in mine mechanization.