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By G. Pouskouleli, T. A. Wheat

"The role and benefits of using statistical methodology in the development and optimization of materials and processes is examined. It is shown that considerable benefits accrue from the use of an appropriate design in which a number of factors (process parameters) are varied simultaneously while the system response such as percent recovery, degree of separation, purity, etc. is monitored and ultimately optimized.Compared with the commonly encountered one-factor-at-a time approach, this schema exploits reduced experimentation (thereby requiring reduced resources [staff, time, dollars, etc.]) yet yields quantitative information on the significance of each factor and their combinations on the measured response."

Jan 1, 1992

By Daniel Hodouin, Antoine Berton

Mineral processing plants are monitored and controlled using measurements that are usually processed by on-line material balance calculation techniques. However, gross errors, due to sensor biases or failures, may corrupt all the process variable estimates. On-line gross error detection methods are required to ensure efficient mass balance evaluation. In the proposed approach, material imbalances and raw measurement corrections are tested by statistical techniques designed to detect and isolate sensor problems.

Jan 1, 2000

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 M. Bhattacharya, A. Dutta, P. Barat

"Pinning of dislocations at nanosized obstacles like precipitates, voids and bubbles, is a crucial mechanism in the context of phenomena like hardening and creep. The interaction between such an obstacle and a dislocation is often explored at fundamental level by means of analytical tools, atomistic simulations and finite element methods. Nevertheless, such studies fail to predict the effect on the overall plasticity on account of insufficient information about the underlying statistics of this process comprising a large number of dislocations and obstacles in a system. Here we propose a new statistical approach, where the statistics of pinning at idealized spherical obstacles is explored by taking into account the generalized size distribution of the obstacle along with the dislocation density within a three-dimensional framework. The application of this approach has been demonstrated for dislocation pinning at nanovoids in neutron irradiated type 316-stainless steel.IntroductionPresence of nanoscale obstacles like precipitates, voids and bubbles play a crucial role in determining the deformation behavior of a crystalline solid on account of the interactions between the line defects and such localized obstacles. In the context of the glide motion of dislocations, the obstacles can offer resistance to a moving dislocation, thereby causing a hardening effect [l-3]. In some other cases, inclusions like voids and bubbles can affect the rate of dislocation climb through diffusive [4] and non-diffusive [5] mechanisms. Over the last few decades, numerous studies have been performed to gain an insight of the dislocation-obstacle interactions at a fundamental level. These include the interactions responsible for the hardening effect, in addition to those pertaining to the non-conservative motion of dislocations.Although the elementary mechanisms of the various dislocation-obstacle interactions have been vastly explored and understood by means of analytical theory and numerical simulations, it remains difficult to quantitatively understand their effects on the macroscopic deformation behavior. This is due to the fact that their influence on the gross plastic deformation of a bulk sample would be the collective outcome of a large ensemble of such interactions. As a result, it becomes infeasible to predict the bulk deformation behavior of a material until the statistics of pinning of the dislocations at the localized obstacles is available. In the context of precipitate hardening, some well known attempts to extract the pinning-statistics were made by Friedel-Fleischer [6] and Mott [7] by analytical means, which were later tested through simplified 2-dimensional in-silica modeling [8]."

Jan 1, 2014

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

By S Pfaff, R Rajic

In the case when the number of independent variables is greater, a careful design for carrying out tests has to be made in order to obtain, with the smallest possible number of tests, as much as possible neutral information about the influence of independent variables on the dependent ones. Only on the basis of such design and its statistical analysis it is possible to come to right conclusions about the function of the whole system. The influence of pressure, temperature, humidity and granulation of the coal upon the resistance to pressure and the water absorption of the briquettes has been tested, with the aim to examine how each of the two dependent variables changes depending on the values assumed by any of the four independent variables and which of the mentioned independent variables significantly influences the dependent ones. The full factorial design with 16 experiments and the central composite design with 27 experiments have been applied. The influence of the independent variables upon the dependent ones has been examined by applying the analysis of variance. The influence values of individual factors and their interaction upon the dependent variables have been stated as well as coefficients of curvilinear equation.

Jan 1, 2003

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 G. B. Gould

EVERY mathematical statement of a measure of anything (as distin-guished from a count) is followed by a qualification always implied if not explicity stated--that the statement is only an estimate, which may vary from absolute accuracy within certain limits, according to the accu-racy of the measuring instrument. This basic fact, so obvious to engineers, is not so well understood by many that make use of laboratory coal tests. The tolerances that must be allowed in measurements of coal quality are very important in both their commercial and engineering applica-tions-and the significance of these tolerances depends upon the use made of the laboratory coal test. Only in recent years has there been any intensive study of this ques-tion of tolerances as applied to measurements of coal quality. There is very little in our published literature on the subject, and what has been published is not, readily comprehended by those who sell coal, or buy coal and use it, unless they happen to have made a study of the subject them-selves. There is great need for more widespread understanding of what has been discovered and how it applies to the use of laboratory coal tests. What follows is an attempt to condense into a few pages the results of the major investigations so far reported, and to explain their meaning in simple nontechnical language, with the addition of some recent illustrative experiments.

Jan 1, 1937

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

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