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By John A. Wolfe

Applications of mathematical statistics to the field of exploration are still relatively new. There are two primary reasons why little has been published in this field. First, if one discovers an effective technique for exploration, he does not like to disclose it. Second, the geologist needs to work closely with a mathematical statistician, and the communications barrier between the disciplines is formidable. The authors of this paper, one a geologist and the other a statistician, were interested in the economic benefit which appeared to be possible in the interdisciplinary area which they have called "geostatistics." An actual example has been selected to illustrate this benefit.

Jan 1, 1962

By J. M. Mutmansky, T. K. Greer

This paper takes a look at the optimal velocity to be used in coal mine entries and determines a statistical relationship for optimal velocity that can be applied under current mining conditions. This relationship provides the optimal velocity for coal mine airways under variations in power cost, mining cost differential, airway friction factor, time value of money, airway lifespan, and quantity of air carried. This enables the ventilation engineer to make an easy, rapid determination of the optimal velocity for planning purposes.

Jan 1, 1985

By Scott D. Thayer, George H. Milly

INTRODUCTION Ambient concentrations of radon and its daughter products have been measured and analyzed by a number of investigators for a variety of purposes. Principal among these purposes have been: (1) descriptive, to characterize the distribution and changes in concentrations under various conditions; (2) research in the use of radon as a tracer gas in the study of atmospheric characteristics and motions, such as eddy mass transfer, diffusivity profiles, large scale circulations, and the like; and (3) the use of radon as an atmospheric tracer in exploration for uranium deposits.* This information forms the basic data for this paper and for its placing the ambient natural, or non-anthropogenic, radon concentrations into the perspective of ambient radon health standards and lung cancer risk calculations. To enable better understanding of some aspects of the ambient radon data, review and analysis is also performed on selected measurements of radon emanation or flux from the surface of the earth into the atmosphere. These measurements have generally been made for purposes similar to those for ambient radon, i.e., (1) description of radon emanation characteristics; or (2) to support and justify the use of ambient concentration measurements in atmospheric research; or (3) in exploration for uranium. Interest is also developing in the use of such measurements for earthquake prediction. In addition, to complete the perspective, brief examination is given to anthropogenic ambient and flux radon measurements related to the mining and milling of uranium, so that comparison can he made with the values from natural sources. As a frame of reference we cite here previous summaries of studies which have presented representative values and ranges of ambient concentrations and emanation rates. H. Israel, in the Compendium of Meterorology (1951), cites eight studies of ambient radon concentrations which we have selected as representative of non-anomalous continental values. Their means generally range from [0.06 to 0.15 pCi lit-1 with the smallest reported minimum of zero and the largest maximum 0.53 pCi lit-1. The overall mean is 0.10 with a standard deviation of 0.03 pCi lit-1. Means over oceans are much smaller, and the data scarcer, with only three values ranging from 0.0004 to 0.003 pCi lit-1 and a mean of 0.0016 pCi lit-1.] Thirteen studies from Israel's list were selected as representative of mountainous terrain. These data, except for the cases of higher elevations, frequently show significantly higher values than the average cases in non-mountainous terrain described-above. The averages range from 0.10 to 0.59 pCi lit-l; the smallest minimum is zero and the largest maximum is 9.2 pCi lit-1. The overall mean is 0.30 with a standard deviation of 0.17 pCi lit-1. Israel also cites five studies of radon emanation (flux) from the earth's surface. These show a mean of 0.40 pCi-2m-2 sec-1 and a range of from 0.21 to 0.74 pCi m-2 sec-1. Data on flux are naturally scarcer in the literature than data on ambient concentrations, because of the greater interest in and utility of the ambient information. In this paper we also give special consideration to observations of the variability in time and space of radon flux rates, and to the impact of these phenomena on the use of such data for a variety of purposes. NATURAL(NON-ANTHROPOGENIC)AMBIENT RADON CONCENTRATIONS We have examined the following reports for the data selected for this category; these studies were generally intended to describe radon characteristics in the atmosphere. Jonassen and Wilkening (1970); Bradley and Pearson (1970); Wilkening (1970); Lambert, et al (1970); Pearson and Moses (1966); and DickPeddie, et al (1974). Another set of studies which was reviewed was selected because the investigators made ambient radon measurements in the course of examining the use of radon as a tracer in atmospheric research. This set consists of: Israel and Horbert (1970); Carlson and Prospero (1972); Subramanian, et al (1977); Larson (1978); Cohen, et al (1972); Hosler (1966); and Shaffer and Cohen (1972). Finally, unpublished data from uranium exploration activities (Milly and Thayer, 1976) was analyzed. [Treating the ocean cases first, the mean values are generally consistent with those quoted earlier from Israel (0.0004 to 0.003 pCi lit-1); they range from 0.001 to 0.011 pCi lit-1, with 0.003 the most frequently reported value. Continental values, from eight studies, range in means from 0.07 to 0.41 pCi lit-1 (not including mineralized areas, or "uranium country", discussed later), with maxima as high as 2.4 pCi lit -l. For comparison, the means from Israel are 0.06 to 0.15 pCi lit-1, with a maximum of 0.53 pCi lit-1. Some of these studies also present the typical decrease of-1 concentration with height to 0.01 to 0.04 pCi lit at 5 to 7 km. The vast numbers of uranium prospecting radon data of]

Jan 1, 1981

By Ali Dehghani Ahmadabadi

Gravity separation technique is widely used in mineral beneficiation practices for its low cost, ease of operation, and eco-friendly nature. The most commonly used gravity methods for beneficiation of iron ores are shaking table, jig and spiral methods which aren't very effective for iron mineral fines. Multi-Gravity Separator (MGS) is suitable for the treatment of fines with a maximum particle size of approximately 500 µm. This study was performed on a low-grade haematite iron ore from Chadormalutailing dams. Detailed mineralogical, physical and chemical characteristics of a goethiticlateritic iron ore showed that the sample contained porous and friable oxides and hydroxides of iron. The ore sample had a feed grade of 35% Fe, 1.1% FeO, 15.5% SiO2 and 8.5% Al2O3. Haematite and goethite are the main iron-bearing minerals while quartzite and kaolinite are the major gangue mineral constituents. In this paper, the statistical evaluation and optimization of grade and recovery using a factorial design of experiment (DOE) method has been carried out for Chadormalulow grade ultra-fine haematite tailings with MGS. The input process parameters considered are drum speed, tilt angle, wash water flow rate and pulp density. The results show considerable improvements in both the quality characteristics such as grade and recovery with statistical evaluation and optimization, compared to the initial value of grade and recovery. Keywords: multi-gravity separator, mgs, statistical evaluation, optimization, haematite

Sep 1, 2012

By G Anders

The effectiveness of two types of powder used in long-wall slashing was compared. The evaluation of the results can serve as a good example of how the application of statistical methods to underground test data can help to minimize the number of tests to be carried out. The conclusions are stated concisely, including a definite assessment of the reliability of the tests. Introduction AN assignment at the Algom Nordic mine called for a performance comparison between 70 per cent Cilgel B and 75 per cent Dygel in longwall stope slashing, particularly taking into account, in both cases, the build-up of bootlegs as dependent on hole deviation. Stopes were usually 8 to 10 ft. high and inclined at about 17 degrees. Starting from a raise, they were widened by consecutive longwall slashes to 60 ft., and, al-lowing for drift pillars, were approximately 300 ft. in length along the incline.

Jan 1, 1964

By S. Al-Thyabat

Conditioning of flotation feed is an important prerequisite for efficient flotation. This process depends on parameters such as conditioning time, slurry concentration and slurry pH. The objective of this paper is to optimize the conditioning process for the flotation feed. This was achieved by first conducting preliminary experiments at constant slurry pH to determine the significant ranges of slurry concentration and conditioning time. Then, factorial experimental design (32 experiments) was used to investigate the significance of the above parameters and their interactions on flotation recovery and grade. Statistical analyses using ANOVA approach showed that flotation recovery (R) and concentrate grade (g) were affected by feed conditioning. It was found that concentrate grade was linearly proportional to the slurry concentration and conditioning time, while flotation recovery was exponentially proportional to the conditioning parameters. A contour plot of the flotation response (recovery and grade) against conditioning parameters showed that the optimum operating parameters for flotation feed conditioning was a conditioning time of 1.5 to 2 minutes and a slurry conentration of 55% to 60%.

Jan 1, 2008

In making any attempts to determine the depositional environments in which coal seams accumulated it would be useful to establish whether there is a pattern, or patterns, of development which the majority of the seams have followed. To this end, the distribution of types of coal seam sequences found in the standard petrographic profiles of about a hundred Australian coal seams of Permian and Triassic age has been examined statistically, using the "chi square test" with the limiting probability set at O·Gl.Results indicate that non-random conditions have probably prevailed during the deposition of most of the seams. More samples are needed for conclusive results.The plants, or some other internal feature of the swamp environment, have been the important controlling factor in the development of the seam sequences.Comparison has been made with some British Carboniferous coals.

Jan 1, 1972

INTRODUCTION TO STATISTICAL INFERENCE The intent of the mineral appraiser in collecting samples from a mineral deposit is to arrive at accurate conclusions concerning the size and value of the deposit. In other words, he wants to derive reliable inferences about the total mineral population from the collected sample data, which (he hopes) is representative of the whole. The discussion of sampling theory in Chapter 2 was oriented toward assuring that our sampling techniques and sampling units would indeed be representative of the total mineral population. Chapter 3 described the most common statistical parameters for defining distribution in various populations. Chapter 4 gave some insight into theoretical distributions of random variables and the probabilities associated with them. The intent of this chapter is to derive inferences from the preceding information about the population mean and the population variance. Knowing something about the normal distribution, and assuming our samples represent a roughly normal population, we can make inferences or logical deductions about the estimated interval or the limits of values which can be assigned to a mineral population. ESTIMATION OF POPULATION PARAMETERS In the application of statistics to mineral deposits it is never possible to know the actual values of the parameters or the theoretical distribution of values within the deposit for which our data are samples. Even after the deposit has been mined out it is questionable if the true value of the parameters can be retrieved accurately, due to dilution, mining, and processing losses. Therefore, our problem is to determine what function of our sample values we should use to estimate the unknown parameters of greatest interest to us-namely, the population mean and the population variance of the deposit. Since we cannot know

Jan 1, 1980

By H. Stocker, C. E. Makepeace

"This paper presents the statistical analyses of several sets of data acquired in several programs of sampling of radon daughters in uranium mines. The measurements were taken over periods of days or weeks for given locations or location occupations within these mines. Because the sampling applies to specific intervals of time and specific locations, a method is suggested f or the eventual application of a monitoring program which would be suitable on an annual basis for these locations. The present data and analyses thereof are not justifiably applicable to a monitoring regimen on an annualbasis, without a number of additional assumptions.The aim of the present analyses of concentration measurements is the determination of the minimum number of measurements required to achieve an annual radon daughter exposure estimate, for individual workers, having an error no greater than 50% at the 95% confidence level. The criterion of accuracy is taken from a statement in the American National Standard, Radiation Protection in Uranium Mines (ANSI NI3.8-I973), and is currently used, in somewhat modified form, as a guide to uranium mining licensees in Canada. Uncertainties associated with occupancy time are ignored in the present analysis. IntroductionOne of the principal aims of any scheme of radiation protection is that of improving the accuracy of exposure estimation for workers. The example presented here is from the area of radon daughter exposure estimation for uranium miners. The conventional means of estimating workers' exposures is grab sampling of radon daughter concentrations combined with occupancy time weighting in the various work and travel locations. Uncertainties exist in each of these components, and in an environment of highly variable radon daughter concentrations (such as an active uranium mine) one is always uncertain as to the representativeness of the grab sample (compared to the average concentration) unless a sophisticated monitoring scheme has been implemented based on previous experience in such an environment.Improvements in the accuracy and precision of employee radon daughter exposure records depend, primarily, on three factors;"

Jan 1, 1980

By Arthur W. Rose

Statistical techniques are being widely used in geochemical exploration to answer questions involving sample spacing, analytical and sampling errors, thresholds, data smoothing, and optimum combination of several elements into one measure of favorability. The applications of sampling theory, mean and standard deviation, trend surfaces, moving averages, factor analysis, cluster analysis, discriminant analysis, and regression analysis to these questions are discussed with examples. Although the techniques are very useful as means of handling large amounts of data, they require as much geological and geochemical judgment as any other approach to data interpretation.

Jan 1, 1973

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

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 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 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 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