Czaplicki J.M. Statistics for Mining Engineering

CRC Press/Balkema, 2014. VIV, 272 p. — ISBN: 978-1-138-00113-8 (Hbk), ISBN: 978-1-315-81503-9 (eBook PDF).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.Fundamentals
Goal and task of statistics
Basic terms of probability theory
Basic terms of statistical inferenceSome areas of application of mathematical statistics in miningAnalysis of data
Testing of sample randomness
An outlier in a sample
Stationarity testing of sequences
Outcome dispersion testing
Cyclic component tracing
Autocorrelation analysis
Homogeneity of dataSynthesis of data
Estimation of the parameters of a random variable
Probability distribution description
An example of empirical–theoretical inference about the distribution of a random variableRelationships between random variables
The chi-square test of independence
The Pearson’s linear correlation coefficient
al correlation coefficient and multiple correlation coefficient
Non-linear correlation measuresSynthesis of data—regression analysis
Preliminary remarks
Linear regression
Linear transformations and multidimensional models
Autocorrelation and autoregression models
Classical linear regression for many variables
Regression with errors in values of random variables
Linear regression with additional informationSpecial topic: Prediction
Introduction and basic terms
Subject of prediction
ExamplesExplanations of some important termsStatistical tables
Distribution function Φ(z) of standardised normal distribution N(0, 1).
Quantiles of the standardised normal distribution N(0, 1)
Critical values of the Student’s t-distribution
Critical values of the Chi-squared distribution
Critical values of the Snedecor’s F distribution for α = 0.10
Critical values of the Snedecor’s F distribution for α = 0.05
Critical values of the Snedecor’s F distribution for α = 0.025
Critical values of the series distribution
Critical values of the Cochran statistic for α = 0.05
Critical values of the Hartley statistic for α = 0.05
Quantiles of the Poisson distribution
Critical values in Kolmogorov test of goodness-of-fit
Critical values of a linear correlation coefficient and a partial correlation coefficient
Critical values of the Spearman’s rank correlation coefficient
Critical values of a multiple correlation coefficient
a. Critical values Dn,m(α) in the Smirnov test of goodness-of-fit for two empirical distributions
b.Distribution of the Smirnov statistic Dn,m P{Dn,m ≤ k/n}
Critical values α(2n, 2m) of the distributionSubject index