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By K. Kim, T. M. Yegulalp

A new explanation of the scale dependency of rock strength is presented based on the theory of extremes. A brief review of past work on specimen size and strength relationship is followed by an introduction to the fundamentals of the underlying theory of extremes and its relationship to the scale effect. It is shown that the weakest link theory is directly related to extremal statistics and that parameters of strength distributions of rock can be derived as a function of the specimen size. Three sets of Brazilian test data are used to demonstrate the use of this approach.

Jan 1, 1994

By T. M. Yegulalp

A new explanation of the scale dependency of the strength properties of rock is presented based on the theory of extremes. A review of past work on specimen size strength relationship is followed by an introduction to the fundamentals of the underlying theory of extremes and its relationship to the scale effect on the statistical properties of the strength distribution. It is shown that the weakest link theory is directly related to extremal statistics and properties of strength distributions of rock can be derived as a function of the specimen size. Three sets of Brazilian test data are used to demonstrate the use of this approach.

Jan 1, 1992

The U.S. Bureau of Mines Information and Analysis Directorate collects worldwide data on virtually every commercially important nonfuel mineral commodity. These data form the base for tracking and assessing the health of the minerals sector of the U.S. economy. The Bureau's data collection activity was instituted by the 47th Congress in an appropriations act of August 7, 1882 (22 Stat. 329), which placed the collection of mineral statistics on an annual basis. The most recent authority for the U.S. Bureau of Mines survey activity is the National Materials and Minerals Policy, Research and Development Act of 1980 (Public Law 96-479, 96th Congress). This act strengthens protection for proprietary data provided to the U.S. Department of the Interior by persons or firms engaged in any phase of mineral or mineral-material production or consumption.

Jan 1, 1993

By C. Widham

Introduction It is generally accepted as dogma that sampling contributes most of the error in gold fire assays. Differences in assay results on pulps from the same sample interval are frequently regarded as evidence of the presence of the so called "nugget effect" of relatively coarse gold particles. It is true that coarse gold particles can contribute to substantial sampling fluctuations. But, while the process of sampling is probably the major source of error, the analytical process cannot be completely ignored as a possible contributor to erratic assay results. To maintain a stable assay process, the analytic part of the system must also be kept in control. One method of monitoring the performance of the analytic system is to systematically assay standard materials, whose sampling characteristics are carefully controlled. Gold assay standards are not prepared, nor can they be prepared, to account for both sampling and analytical errors. It is not possible to send coarse material to a lab for both preparation (i.e., comminution and splitting) and fire assaying and then come to conclusions only about the fire-assay process. Because most gold ores are very heterogeneous, sampling errors would, in most cases, completely mask the contribution of the analytical errors. Assay-standard material is prepared only to assess the accuracy and variability in the fire assay process. Because the objective of the assay standard is to provide information about the fire assaying, it is necessary to control the sampling error of the standard material, so that it is only a minor constituent of the discrepancies observed in any assay results. To do this requires that the particle size of the standard material be reduced to a point where the relative standard deviation of the sampling error (i.e... the standard deviation of the errors divided by the average gold content of the material) is 2% or less. For all but very homogeneous mineralization, this means that the material must be reduced to 100% -150 mesh before the sampling errors are adequately controlled. However, even reducing the particle size can contribute to sampling problems. The liberation of gold may cause segregation that can cause large sampling fluctuations that are not easily controlled while maintaining the desired grade. Because, in most cases, the standard material would already be in the "pulp" state when it is submitted to a lab for assay, it is not possible to entirely conceal the nature of the sample from the lab. This is a problem inherent in using assay standard material. Because of the contribution of sampling to error generation in the assay process, the use of "coarse" material does not solve the problem of submitting a totally "blind" standard to the lab. In the sections that follow, the selection, preparation, testing and use of gold fire assay standard material is discussed. While some may dismiss the production of standard material as folly, it is possible to produce and utilize standard material to stabilize and improve the fire-assay process to produce more reliable assay results. Material selection It is desirable to use material that has as nearly the same metallurgical characteristics as the samples with which the standards will be included. However, this is usually difficult. For many reasons, including the particle size at which a significant amount of the gold mineral is liberated, the sampling characteristics of even -150-mesh material may preclude the use of geologically and metallurgically similar ore as a standard. It is usually easier to get material having desirable grade characteristics with the necessary sampling properties than it is to find geologically and metallurgically similar material with the required sampling characteristics. High-grade standards are especially difficult to find and prepare. This is because, as grade increases, the size of the gold particles usually increases. Larger gold particles are liberated and tend to segregate during comminution, and the homogeneity of the material cannot be maintained. For grades much above 3 g/t (0.088 oz/ton), it is very difficult to find material that has the proper sampling properties. Old mill tailings are likely candidates for assay standards. Some of these have sufficiently homogeneous mineral contents, so that the sampling errors can be effectively controlled. Where mill tailings are either not available or are not acceptable, mineralization that has exhibited homogeneous results in reassays of the pulp material is also a good candidate for the standard. Finally, the mineralized rock being sampled may (and should) be used if adequate homogeneity in the -150mesh material exists. "Adequate" ("acceptable") homogeneity is defined below.) It is important to use standards having a wide range of grades. This alone may preclude the material being

Jan 1, 1997

By S. Davis

It has been accepted almost as dogma that sampling contributes most of the error to fluctuations in gold fire assays. Differences in assay results on pulp material from the same sample interval are frequently regarded as evidence of the presence of the so called "nugget effect" or relatively coarse gold particles. It is true that if coarse gold particles are present they contribute to substantial sampling fluctuations, but while the process of sampling is probably the major source, the analytical process cannot -be completely ignored as a possible contributor to erratic assay results. In order to maintain a stable assay process, the analytic part of the system must be kept in control as well as the sampling and preparation part. One way of monitoring the performance of the analytic system is to systematically assay standard material whose sampling characteristics are carefully controlled. Gold assay standards are not prepared nor can they be prepared to account for both sampling and analytical errors. It is not possible to send coarse material to a lab for preparation (which includes both the processes of comminution and splitting) followed by fire assay, to make inferences only about the fire assay process. Because most gold ores are very heterogeneous, sampling errors would in most cases completely mask the contribution of the analytical errors. Assay standard material is prepared only to assess the accuracy and variability in the fire assay process.

Jan 1, 1995

By Robert F. Shurtz

This paper discusses and compares methods of statistical analysis of the information relating to the evaluation of an asbestos deposit. From a study of 10-ft. lengths of drill core, the separate effects of visual evaluation errors were determined, as well as the deviations between evaluators and the deviations produced by a slight displacement in the center lines of the check drill holes. The importance of careful statistical analysis of such information is stressed.

Jan 1, 1966

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 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 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

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 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 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 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 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

By Richard M. Crowell

"As thorough sampling is usually expensive, the cost of a complete job is often unwarranted, and a cheaper approximation must be substituted. The engineer should, however, weigh the situation thoroughly before subscribing to an alternative other than an accurate assay basis on which to build his conclusion." Examination and Valuation of Mineral Property. R. Parks, 1949

Jan 1, 1994

By K. Cothern, S. Novack, D. A. Johnson, R. Borden, S. Pavlou

A procedure is presented for ranking hazardous waste sites for remedial decisions, and an example with application to mining waste sites is discussed. Typical contaminant concentrations are calculated from field data. Exposure indices that compare these measured concentrations with allowable limits are then computed. The limits are selected to protect both the health of humans (for both carcinogen and noncarcinogen effects) and the health of key organisms in the ecological food web. The additive exposure index for a site, defined as the sum of all contaminant-specific exposure indices, is then used in ranking the sites and assigning each a priority for remedial action. One key source of uncertainty in the process is the estimation of a typical site concentration from data that include values reported as "below certified reporting limit" (BCRL). This uncertainty is compounded in the additive exposure index and therefore may have a substantial effect on the assignment of remediation priority. A general approach is presented for incorporating consideration of BCRL data into uncertainty evaluation when assigning remediation priority designators to hazardous waste sites.

Jan 1, 1992