The author of this book earned a Master of Science degree in Mine Mechanization and a Doctor of Science degree in Mining and Geological Engineering with a specialization in Mine Machinery from the Silesian University of Technology, Gliwice, Poland. His areas of specialization include mine transport, reliability of mine machinery systems, and reliability of hoist head ropes. The preface acknowledges that a wide variety of technical devices are available to realize specific objectives, and that commonly several devices are linked, creating systems of devices to carry out complex functions that, in mining engineering, include excavating rock, hauling broken material, dumping waste, storing ore, and treating ore with mechanical, chemical or thermal processes.

Basic knowledge of probability theory and some idea of the theory of reliability and of operation (also called exploitation in this book) are presumed. The book has nine chapters, with nine pages of references and a two-page subject index. The last two chapters are a four-page ‘explanation of some important terms’ and a 29-page collection of 18 statistical tables.

Chapter 1, on fundamentals (48 pages, three sections), describes the goal and task of statistics, and provides basic terms of probability theory statistical inference. Readers who are intimidated by statistics and probability will find this book to be challenging to more or less the same degree. Readers will find the guidance and applications to be helpful. For example, the mathematical use of a ‘sample’ of a ‘general population’ is put into context by the practical decision to take only a sample because (1) testing all elements of a nearly infinite population is not possible, (2) collecting samples may be destructive and it would be senseless to destroy the whole population, (3) testing large numbers of samples has high cost, and (4) testing many samples is not sensible if the interest is in estimating selected properties within some range of certainty. Mathematical statistics tasks are (1) estimating unknown parameters of a feature by treating it as a random variable, (2) verifying statistical hypotheses about the feature, (3) identifying random processes, and (4) making decisions in the case of uncertainty about features. Some areas of mathematical statistics applied in mining are mentioned in Chapter 2 (five pages).

Chapter 3, on analysis of data (55 pages), consists of seven sections. An example of the useful guidance in Chapter 3 relates to non-randomness being a signal that something is untypical and ‘finding the reasons for this untypical regularity is by all means recommended. It may be the source of significant information on the object being investigated and it does not matter whether it is a technical item, a process, or a property of the surrounding rocks. Sometimes, the reason can be prosaic—an informatics error in the system that is collecting the data.’ Another example of useful guidance relates to the importance of an outlier in a sample. In terms of equipment reliability, repair times for some extreme damaging events should not be combined with repair times of regular or routine failures. Over-winding by a hoist conveyance can induce a rupture of the hoist head wire rope; the repair time to replace the rope because of over-winding should not be combined with routine-wear repair times.

A useful comment regarding stationarity relates to an unusual repair-time situation in which a sudden failure occurs to a critical machine for which no spare part is readily available. The critical nature of this machine resulted in making use of a similar machine that subsequently put additional stress on other machines in the production process. Repair-event durations would be influenced by such repair practices. A footnote in Chapter 3 indicates that assessing a newly installed hoist head rope is not sensible because it operates for a period of time without any wire cracks developing.

Dr. Czaplicki provides additional practical guidance in the section on cyclic component of tracing (Section 3.5). If several events exceed some threshold level, the nature of the events should be assessed. If the reasons that the events occurred are repeated, then they are not entirely random and a recommendation may be formulated to eliminate them from further operation of the system. If the reasons that the events occurred are all different, then they can be evaluated as purely random regardless of how rare they were. Application of statistical procedures can provide information that indicates which events should have further comprehensive consideration, but that is all; advanced analyses, including physical aspects, must proceed outside the area of mathematics.

Chapter 4, on synthesis of data (28 pages), consists of three sections and includes estimates of one or more random variables, the probability distribution that describes measured data, and an example of an empirical–theoretical inference about the distribution of a random variable. One example in this chapter is a follow-on from an example in Chapter 3, which stopped at a test of stationarity that concluded no basis existed to reject the hypothesis that stated that the sequence of measured values met the condition of stationarity. The follow-on example works through the process to identify a theoretical probability distribution that satisfactorily describes the measured data.

Relationships between random variables is the subject of Chapter 5, which consists of four sections (14 pages) addressing different tests of independence or correlation. It is relatively common that a random variable is suspected of having an influence on one or more different random variables. Theoretical models are developed between random variables with relative ease, but all models have assumptions that must be fulfilled to validate applicability. A common assumption is that the variables are, in fact, independent. If variable independence cannot be demonstrated, then additional questions arise regarding how strongly dependent the variables are and what the character (linear, nonlinear) of dependence may be. The chi-squared test for two random variables is a basic test for categorical data (i.e. values that are names or labels, such as colour or type) as opposed to quantitative data (i.e. values that are numerical quantities). The bias for type I error (rejecting a true hypothesis) in the chi-squared test is recognized and approaches are presented for removing the bias. If independence between the variables must be rejected, then evaluation of the nature of the interdependence or correlation is appropriate. Linear, partial and multiple correlation coefficients and nonlinear correlation measures are discussed in Chapter 5.

Chapter 6 is the second part of synthesis of data, focusing on regression analysis and consisting of seven sections (48 pages). The author uses ‘explanatory variable’ in lieu of ‘independent variable’ (denoted by *X*) and ‘variable being explained’ in lieu of ‘dependent variable’ (denoted by *Y*) because in some cases the variables that are treated statistically as independent may be dependent on each other. Relations between variables have different natures, such as cause-and-effect, symptomatic, tendency-to-a-trend, autoregressive, memory-in-a-process and adaptive-character. The process of linear transformation is discussed to allow linear regression calculations to be performed on the transformed variables. An important 11-page section in Chapter 6 (Section 6.6) addresses regression in which values of random variables have errors. The methods presented in this section allow variables to be treated as (1) correct and without errors (absolute), (2) correct but with random errors (deterministic), or (3) randomly inaccurate. An eight-page section in Chapter 6 (Section 6.7) addresses linear regression with additional information from outside the sample that is suitable for statistical calculations. Such information can originate from theoretical considerations, results from earlier investigations and analyses, or previously obtained samples of similar nature.

Chapter 7 is a special topic on prediction comprising three sections (23 pages). Basic terms are introduced, such as anticipation, predicting and forecasting. A rational forecast is an inference based on a logical process that runs from a set of facts that belong to the past along with proper interpretation towards their conclusions. Scientific prediction requires that the process of inference is based on the rules of science. Among the problems connected with general prediction is the use of logical tools for forecasting. It is characterized by an approach that is based on a research process that comprises collecting data about the past and diagnosing them by applying an appropriate method to infer future events. This research process usually is expressed by a suitable mathematical component that changes with time because of increasing uncertainty and decreasing precision further into the future. Dr. Czaplicki notes that a degenerated approach to prediction exists in some engineering areas that ‘relies on the assumption that what has happened in the past will be repeated unchanged in the future’. This approach is not forecasting future events; nonetheless, such an approach can be found in some reliability books to which the term ‘prediction’ is attached. Chapter 7 concludes with three examples of prediction.

*Statistics for Mining Engineering* may use examples of mine machinery to explain relevant statistics and probability, but it is a valuable reference, rich with guidance, for engineers and scientists alike.

Jeffrey R. Keaton

Amec Foster Wheeler, Los Angeles, CA, USA

Jeff.Keaton@amecfw.com

- © 2015 The Authors