Mining Equipment and Systems ─ Theory and Practice of Exploitation and Reliability

It has been almost fifty years since the first papers on the application of reliability theory to mining problems were published in the United States. Developing rapidly in the late 1950s and 1960s, reliability theory quickly found a wide application in mining engineering. Ten years later "Terotechnology" became popular in the UK and at the same time its counterpart "Theory of Exploitation" was introduced in Central Europe. Similar to reliability theory, they both found wide application in mining. Since then a lot of articles have been published in many countries concerning these scopes of considerations but a wider elaboration on this topic was still lacking. This book gives an explanation of the mutual relationships between terotechnology and the theory of exploitation, and presents the fundamentals of the theory of exploitation and its role in relation to mining engineering where mine machines and machinery systems are concerned. Further, statistical diagnostics, exploitation processes of machines, reliability and its models, and the methods of modelling and analysis of the processes of changes of states are treated.
A significant part of the book deals with cyclical systems that are in common use. A variety of models are considered supported by many case studies. The last chapter deals with combined systems operating in a mixed manner. Finally, an analyses of the influence of the inhomogeneity of a different nature in a shovel-truck type system is given.The examples presented in the book are based on the data coming from operation of pieces of equipment from different mines and different countries.
This book will be of particular interest to students, academics and lecturers of mining faculties and schools of mining. Mining Engineers and other professionals in the mining industry will also find this book of interest. Finally, students in mathematics will find practical applications and problem solving in this book.

Jacek Czaplicki received his Master of Science in Mine Mechanization from the Silesian University of Technology, Gliwice, Poland. He also obtained a Doctorate degree in Technical Sciences and his Doctor in Science degree in Mining and Geological Engineering with a specialization in Mine Machinery at the same University.
He worked for three years at 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 and worked as a lecturer at the School of Mines at the University of Zambia as part of a World Bank project.
He has published more than a hundred and twenty papers. His specialization comprises mine transport, reliability and computation of mine machinery and their systems and reliability of hoist head ropes. He is an internationally recognized specialist in mine mechanization.

ContentsPreface and acknowledgements List of major notations


Introduction: Terotechnology and Theory of exploitation 1


Exploitation theory 9



Fundamentals 9


Exploitation theory in mining – preliminaries 13


Statistical diagnostics 17



Randomness of a sample 19


Outliers analysis 22


Stationarity testing of sequences 29


Stationarity testing of variance in sequences 34


Cyclical component tracing 38


Autocorrelation analysis 47


Homogeneity of data 50


Mutual independence of random variables 54


Mutual dependence of random variables 56


Exploitation process – Cases of study 65



An exploitation process of an underground monorail suspended loco 66


An exploitation process of a truck in a shovel-truck system 75


An exploitation process of a power shovel 82


Exploitation processes of a continuous miner and a shuttle car 85


Reliability and its models applied for a single piece of equipment 95



Belt conveyors 95

5.1.1. Stream of failures model 96
5.1.2. Process of changes of states: work-repair type 100

Hoisting installations 105


Hoist head ropes 110

5.3.1. A model of the hoist head rope wear process of a fatigue type 110
5.3.2. Approximation functions applied 115
5.3.3. Memory in the wearing process of ropes – further approximation functions 119
5.3.4. Rope reliability 128

System of machines operating in parallel 141


Systems of machines of continuous operation 147



Introduction 147


Principles of reduction of series systems 151


Cases of study 154


Calculation of systems 172


Quick approximation of system output 174


Semi-Markov systems 176


Cyclical systems – selected problems 197



A general model of queue theory 197


Mathematical classification of cyclical systems 201


The repairman problem 202


The Palm model 203


A system without losses 207


Erlangian systems 210


The Takács model 216


The Maryanovitch model 222


The randomised Maryanovitch model 227

8.10. The G/G/k/r model for heavy traffic situation 236

Combined systems 247



A shovel-truck system and in-pit crushing 247


A shovel-truck system and an inclined hoist of the TruckLift type 266


A stream of extracted rock– shaft bin – hoist 288


Special topic: Homogeneity of a shovel-truck system 313

References 319