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During 1995 a catastrophic accident took place at the No 2 Vaal Reefs shaft in South Africa, when a locomotive fell onto a cage, causing the death of 104 people. The subsequent Commission of Enquiry found that the safety detaching hook had opened when hit by parts of the falling locomotive, detaching the cage from the rope and allowing the cage to drop 400 m down the shaft. It was believed that had the hook not detached, the rope would have been sufficiently elastic not to have failed, implying that many fatalities may have been avoided. In addition, the risk of accidental opening of hooks due to impact with smaller falling objects in shafts became a concern. This paper deals with a comprehensive statistical investigation that was performed to quantify this risk, establish acceptable levels of such risks and to derive criteria for the resistance of detachment hooks against accidental opening caused by impacts. The investigation involved a survey, dynamic finite element analyses and Monte Carlo simulations.

Jan 1, 2005

By John A. Patterson

There are certain data handling techniques used by statisticans that can help one to calculate the size of an orebody and to develop some of the relationships between size, cutoff grade, average grade, mining cost, and profit. Knowing the relationships amongst these factors can help determine the most desirable operating conditions. A statistical technique that we will use is data grouping. This allows us to work with relatively few groups instead of many samples, If we were able to segregate the ore in an orebody into grade groups, add the amounts in each group, and plot the sums as a curve, we would get something like Figure 1. A smooth curve develops when the grade classes are small enough, otherwise a "stair step? histogram results. The area under the curve, being the sum of the tonnages in all of the grade classes, is proportional to the total number of tons in the orebody. If we take the data of a distribution such as Figure 1 and add the tonnages above a specific grade we have in effect a cutoff grade

Jan 1, 1958

By Milton Barbosa Landim, Denise de La Corte Bacci

Statistical methods of multiple regression analysis, trend surface analysis and principal components analysis were applied to seismographic data recorded during production blasting at a diabase quarry in the urban area of Campinas (SP), Brazil. The purpose of these analyses was to determine the influence of the following variables: distance @), charge weight per delay (W), and scaled distance (SD) associated with properties of the rock body (orientation, frequency and angle of geological discontinuities; depth of bedrock and thickness of the soil overburden) in the variation of the peak particle velocity (PPV). This approach yielded variables with larger influences (loads) on the variation of ground vibration, as well as behavior and space tendency of this variation. The results showed a better relationship between PPV and D, with D being the most important factor in the attenuation of the ground vibrations. The geological joints and the depth to bedrock have a larger influence than the explosive charges in the variation of the vibration levels, but frequencies appear to be more influenced by the amount of soil overburden.

Jan 1, 2002

Six simulations by the Mpnte Carlo method employing both classical and geostatistical techniques are presented for the determination of the probability distribution of the in situ value of a coal seam. To avoid the problem of qualitative estimation of parameter variability in the calculation of an arbitrary seam value, only data values from borehole information were used to quantify the variation in four coai seam parameters.The method which is suggested as being the most appropriate is a particular geostatistical approach that employs the best linear unbiased estimate and the error of estimation for a number of two dimensional blocks. The results indicate that the variance of the coal seam unit value may be much higher than that indicated by the classical approach because of the spatial variability that is properly incorporated in the geostatistical approach.The model used in the Monte Carlo simulation to determine the economic value of a coal seam can be extended to incorporate all those parameters which are necessary for a true estimation of the probability distribution of the coal seam value. A time value concept for discounting can also be incorporated to optimize the economic return of a coal mining project.

Jan 1, 1983

By F. P. Agterberg

"IntroductionTHE KNOWLEDGE about the mineral resources in a region ranges from relatively precise ore-reserve estimates for known deposits to probabilistic estimates concerning the speculative resources which may be discovered in future at greater depths and in the less-explored parts of the region. Previously developed probabilistic methods for regional resource evaluation (1) are based on the following two assumptions.(1) The probability that a specific block of rock, or part of a region close to the topographic surface, contains undiscovered deposits can be estimate d by weighting selected geological, geophysical or geochemical parameters for that block. The weights are computed by considering similar environments which are known to contain deposits.(2) Some of the characteristics of the undiscovered deposits, such as ore tonnages and average grades of metals contained in the ore, can be evaluated by considering probability distributions f or known deposit data. These methods were initially applied to Precambrian deposits in the Abitibi Volcanic Belt of the Canadian Shield (1).Since 1972, statistical methods for quantitative resource evaluation have been applied to the occurrences of the mainly Paleozoic base metal deposits in t he Canadian Appalachian Region. The objectives of this project (Project Appalachia) have been discussed by Leech (2) in a paper that introduces 8 papers with results of the exploratory data analysis. Project Appalachia represents an effort to develop and apply methods of combining information and concepts from regional geology, metallogeny and geomathematics for computer- aided regional mineral resource evaluation."

Jan 1, 1977

Statistical frequency distributions may be used to characterize the overall variation of grade in orebodies. Special types of distribution (e.g. lognormal, log-type A) are necessary to describe skewness inthe case of rare metals. Also needed (but for the most part hitherto neglected) is the serial correlation function which describes the tendency for grades near together in an orebody to be closer together than grades at points relatively far apart.The sampling problem for orebodies is interpreted in statistical terms. Different methods are reviewed, and the effect of serial correlation discussed.A discussion is given, based on experiments and observations made by the author, of biases arising in the minei:l material by such methods as chip sampling and grab sampling due to such causes as nonrepresentative selection by the sampler.INTRODUCTIONMiners have always recognized the large element of chance in their operations. Chance is the raw material of statistical theory and, provided there is some recognizable pattern or underlying regularity in a set of data arising from the operation of chance events, statisticians are able to formulate mathematical models to study them. Mining engineers, geologists, and statisticians have gone a long way between them towards finding general statistical rules which describe the distribution of minerals and metals in orebodies, and even the distribution of orebodies over the earth's surface.These rules do not have the force of physical laws, though they obviously derive from them and have been used to throw light on them. From statistical theory it is possible to find methods of estimating from sampling some of the characteristics of orebodies which are of importance to...

Jan 1, 1962

By V. M. Lsoitko

Statistical methods of technological mineralogy are used to model processing flowsheets in order to improve ore dressing efficiencies. The procedure involves determining geological and mineralogical characteristics of ores, classifying ore types and metallurgical procedures, and developing computer programs to interpret essential mineralogical parameters from on-stream analysis data. The on-stream analysis data include magnetism, radioactivity, luminescence and assays. The data are interpreted by computer and appropriate adjustments are made automatically in the plant.

Jan 1, 1989

By K. R. Long

Until it was defunded in 1995, the U.S. Bureau of Mines maintained a Cost Estimating System (CES) for prefeasibility-type economic evaluations of mineral deposits and estimating costs at producing and non-producing mines. This system had a significant role in mineral resource assessments to estimate costs of developing and operating known mineral deposits and predicted undiscovered deposits. For legal reasons, the U.S. Geological Survey cannot update and maintain CES. Instead, statistical tools are under development to estimate mining costs from basic properties of mineral deposits such as tonnage, grade, mineralogy, depth, strip ratio, distance from infrastructure, rock strength, and work index. The first step was to re-estimate ?Taylor?s Rule? which relates operating rate to available ore tonnage. The second step was to estimate statistical models of capital and operating costs for open pit porphyry copper mines with flotation concentrators. For a sample of 27 proposed porphyry copper projects, capital costs can be estimated from three variables: mineral processing rate, strip ratio, and distance from nearest railroad before mine construction began. Of all the variables tested, operating costs were found to be significantly correlated only with strip ratio.

Jan 1, 2011

By M. J. Daly

Historically, engineers and scientists, particularly those involved in the coal-mining industry, have been slow to adopt statistical methods. However, the need to obtain the maximum information .from expensive exploration and development programmes, and the current focus on total quality management, have led to a change in perceptions if classical statistical and geostatistical methods and their application as planning tools. Some if the underlying issues associated with the generally poor communications between statisticians and engineers/physical scientists, which contribute to some if the misconceptions relating to statistical methods, are discussed The potentially profitable application if a number if statistical techniques in the fields if geological evaluation and mine planning! development is also reviewed, with specific reference to the coal industry.

Jan 1, 1995

By Wignall. T. K., J. De Geoffroy

Statistical models are fitted to the observed distributions of eighteen characteristics of the population of commercial porphyry deposits of North and South America. The statistical base required for the formulation of the statistical models includes 58 commercial porphyry-copper-molybdenum deposits of the Cordilleran Belt from which geological, geometric and economic data were collected. Predictive and composite models are derived from the statistical study to assist explorat10n. planning, engineering studies and fmanc1al analyses as required for the development of new porphyry deposits in the Cordilleran Belt.

Jan 1, 1973

By J. Z. Cui

In this paper a statistical multi-scale method for the mechanics parameter prediction of the rock mass with random distribution of multi-scale cracks/joints is presented. First the micro-structure of the rock mass with random distribution of multi-scale cracks/joints is represented. Then the statistical second-order two-scale method for the mechanics performance predictions of the rock mass structure with random cracks/joints distribution is presented, including the statistical second-order two-scale expression on the vector-valued displacement, strain tensor and stress tensor, and the algorithm procedure of statistical multi-sale computation for the mechanics parameters. Finally some numerical results for mechanical parameters for the rock mass with random distributions of multi-scale joints/cracks by statistical multi-scale method are shown.

May 1, 2009

By L. Yacher

Most metallurgical plants already have sophisticated control systems as well as a process-historian that manage thousands of real-time and historical variables. There exists a huge potential for operational improvement through the inference of patterns, correlations and cause-effect relationships within these records. The ability to run online and offline advanced multivariate statistical analyses represents a great potential for the mining industry, in various areas such as cathode quality improvement in an SX/EX plant, the analysis of the correlation between the ore characteristics and the mill throughput, the determination of early failure alerts for major equipment, etc. The background theory is described, as well as some practical experiences of operations in Chile and Peru. Cu2007

Jan 1, 2007

By F. Romero, L. Yacher, M. Orchard

Specific software tools for Statistical Multivariate Analysis combined with real time process data were applied to Concentrator Plant at Compañía Minera Doña Inés de Collahuasi SCM in Chile, basically to two Mill Lines, each one with one SAG mill (32’x15’8MW)and one Ball mill (22’x36’9.7MW). The main objective was to empower the operator actions using process patterns references instead of process variable set-points. Pattern clustering and the analysis of pattern deviations regarding normal or desired pattern, allows for improvements in process control and the further implementation of soft sensors for those variables not included in the initial model.

Jan 1, 2003

By G. Reed Marchant

The control systems engineer is often faced with the problem of designing tests or experiments where the cost of obtaining information is expensive. This is true in aerospace as well as in process industries. In these situations the details of test design should be carefully evaluated before any test is executed so that the maximum amount of information is obtained for the effort expended. In recent years there has been a steady trend towards increased automation, In the process industries this has resulted in extensive review of process variables and, instrumentation techniques, development of more accurate system mathematical models, and extensive investments in complex control system as well as completely automated plants. When planning and developing these systems, where each measure of a process variable is usually expensive, it behooves the design engineer to give considerable thought to the details of test design before instrumentation is procured and installed so that the maximum amount of information can be obtained for the expense incurred.

Jan 1, 1968

By S Taylor, B Lumsden, G Long

Statistical metallurgical plant trials are becoming more widespread, as a valuable tool for increasing plant profitability. Generally, a single parameter like metal recovery varies under the trial condition while all other variables such as average metal feed grade or average metal concentrate grade are equal for the two test conditions during the period of the test. Metal recovery is usually the measured variable because concentrate grade is fixed by smelter terms, and plants operate to maximise recovery at the required concentrate grade. However, in all flotation plants there is a relationship between concentrate grade and metal recovery, and under the same conditions increasing one results in a decrease in the other. At MMGÆs Rosebery Mine the zinc concentrate produced is generally above smelter specifications, so zinc concentrate grade can vary during a test. During trialling of magnetic conditioning in the Rosebery zinc circuit, the difference in both zinc recovery and zinc concentrate grade were analysed. The analysis of changes in zinc grade and recovery during the trial raised some interesting questions about the relationship between concentrate grade and recovery. A paired statistical method was developed and tested to combine in each pair the change in concentrate grade and recovery in a single result that could be analysed by a paired t test. This method was found to be very sensitive to combined, varying changes in concentrate grade and/or metal recovery. It was also evaluated on plant test results from another flotation plant to verify its applicability in other plants. CITATION:Long, G, Taylor, S and Lumsden, B, 2012. Statistical plant trials - Efficiently combining concentrate grade and metal recovery results, in Proceedings 11th AusIMM Mill OperatorsÆ Conference, pp 355-362 (The Australasian Institute of Mining and Metallurgy: Melbourne).

Oct 29, 2012

By E. Barsky

Physical principles of two-phase flows with a polyfractional solid phase have not received a sufficient theoretical interpretation as yet. Two-phase flows in the separation mode with a counter-flow of particles are even more complicated. Only statistical methods give an insight into general regularities of such processes. These processes can be interpreted best by analogy with the statistical model of an ideal gas developed by L. Boltzmann, although here a number of difficulties arise. The notion of a statistical system for such flows is substantiated. A mathematical estimation of a statistical system is presented. New notions are introduced, namely, potential extraction of a system and lifting factor. A relationship having the physical meaning of entropy is derived for a two-phase flow in the separation modes. The connection of this new entropy with flow parameters, such as the number of particles, separation factor and chaotizing factor, is established. Properties of this entropy are analyzed, as well as the analogy and difference between this entropy and Boltzmann?s entropy. The notion is formulated and the definition of the chaotizing factor of a process is suggested. In the framework of a statistical approach to two-phase flows in the separation mode, the notion of flow mobility has been formulated. Principal regularities of mass transfer in zone/apparatus sys-tem are analyzed. Principal ideas of a cellular model of the process are formulated, and main relationships for its description are derived. Proceeding from the cellular model, a dependence describing the degree of fractional separation of a narrow size grade is found. The analysis of this dependence makes it possible to reveal the crucial role of the Froude criterion for gravitational separation processes. It is found empirically that this parameter is a basis for the affinization of separation curves (Barsky E, Barsky M, 2006; Barsky, 1980).

Jan 1, 2014

By E. L. Schrader

Statistical Process Control (SPC) is a cooperative arrangement between a component or raw materials supplier and a manufacturing customer. The supplier must analyze his own manufacturing process and determine, predict, and control those variable elements in the circuit which affect finished product characteristics according to the customer's specifications. The results include: control of fluctuations in product characteristics to a narrow range, close communication between supplier and customer, and an increased responsibility for quality control placed on the supplier. In the mining and. processing of airfloated kaolin some unique problems arise with the SPC concept: 1) The SPC system was designed for manufacturing facilities that did not have to deal with natural variations in their raw material; 2) The airfloat process is relatively simple and offers limited opportunity to change processing steps or "fine tune" a circuit for special product needs; 3) Determining adequate sampling frequency for a plant which processes hundreds to thousands of tons per day is statistically difficult; and, 4) Due to the variety of customer industries served, different SPC programs must be set up to deal with widely varying specifications. For airfloated kaolin, SPC is "in line" process control, not after the fact "quality" control. The emphasis must be on statistically valid sampling of the kaolin ore and complete monitoring of its path through the beneficiation circuit.

Jan 1, 1987

By Henry Eyring, Jay W. Fredrickson

MANY theories have been advanced to explain the phenomena of elastic and plastic deformation. The object of this report is to present a mechanism for deformation, not radically differing from existing theories, but embodying certain principles and concepts of these theories. This proposed theory cannot be the complete answer to the age-old problem of deformation but it is believed that it will be a step further in the proper direction. The plastic properties of solids have recently been reviewed by Seitz and Read.1 Zener2 has reviewed and correlated the existing work on the anelasticity of metals. With these and othersa3,4,5 present theories of deformation are well-known. Of the many theories now extant, those receiving most attention have been proffered by Griffith,6 Becker,7 Smekal,8 Polanyi,9 Orowan10 and Taylor.11Although differing quite widely in details, these theories are based more or less on a common principle of flaws or dislocations that exist in the crystal lattice. The effect of stress concentrations surrounding a flaw or crack has been treated most recently by Fisher and Hollomon.12 The various authors differ as to the exact nature of the flaws or dislocations, the causes of their appearance, or the manner in which they initiate slip. All of the theories agree that the number of dislocations increases with progressing deformation. It is universally agreed that the shearing process is not a simple gliding of ideally perfect atomic lattice planes. It is also agreed that the "macroscopic process of gliding, or slip, is brought about by the spreading of a large number of locally initiated "glide steps" through the whole crystal. The occurrence of these "glide steps" is closely related to the presence of some kind of deviations from the "ideal" lattice structure, even in the undeformed crystal. These deviations are overcome "one at a time," in a manner of speaking, due to some stress-concentrating effect." PROPOSED THEORY Many solids show a continuously increasing deformation if subjected to a constant load of suitable magnitude in an extended range of temperature for a sufficient time. This deformation, or flow, may be said to be due, in general, to the tendency of the atoms or molecules in an elastically stressed body to readjust themselves in such a way that if the deformation were kept constant, a release of stress would take place. If rupture does not occur, this process of relaxation causes the rate of flow to obtain a final constant value, as shown in the curve (Fig I) obtained by Taylor and Quinney.14 In. this state the release of stress by relaxation exactly counterbalances the increase due to the elastic strain on the test pieces. .

Jan 1, 1948

By D. N. Cleaver

Like other influence function methods, the SWIFT subsidence prediction program, developed within the Mineral Resources Engineering Department at the University of Nottingham, requires calibration to regional data in order to produce accurate predictions of ground movements. Previously, this software had been solely calibrated to give results consistent with the Subsidence Engineer's Handbook (NCB, 1975). This approach was satisfactory for the majority of cases based in the United Kingdom, upon which the calibration was based. However, in certain circumstances within the UK and, almost always, in overseas case studies, the predictions did not correspond to observed patterns of ground movement. Therefore, in order that SWIFT, and other subsidence prediction packages, can be considered more universal, an improved and adaptable method of regional calibration must be incorporated. This paper describes the analysis of a large database of case histories from the UK industry and international publications. Observed maximum subsidence, mining geometry and Geological Index for several hundred cases have been statistically analysed in terms of developing prediction models. The models developed can more accurately predict maximum subsidence than previously used systems but also, are capable of indicating the likely range of prediction error to a certain degree of probability. Finally, the paper illustrates how this statistical approach can be incorporated as a calibration system for the influence function program, SWIFT.

Jan 1, 1995

By H. McLeod

Introduction In the period from 1939 to the present, Canada has experienced a remarkable industrial expansion, rising to probably seventh in rank amongst world countries. In the early part of this period, the desperate need for military supplies unloosed tremendous amounts of capital for building new factories and for expanding and converting existing facilities. Mines, factories, and other divisions of the industrial economy bent every energy toward greater and greater output. The result was an 80 per cent increase in the volume of the nation's production within a period of four years, a truly remarkable accomplishment and one in which the mining industry had a very vital part. After the critical year, 1944, the tempo of industry eased off a bit, dropping approximately 20 per cent by 1946. At this time the prospects or post-war industry were clouded by monetary and political chaos in overseas countries, by trade restrictions, and by market uncertainties. There was, of course, a pent-up demand, both at home and abroad, for civilian goods that had been curtailed during the war and for capital equipment that had been destroyed. In the midst of this world-wide uncertainty, if anyone had ventured to predict that by the end of 1950 Canada's industrial output would be back to the 1944 level and humming along at nearly twice the best pre-war pace, he would have been considered rash indeed. Yet this has been the case.

Jan 1, 1951