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Statistics is essentially a study of variability, the use of some suitable mathematical model representative of such variability, and the application of this inferred pattern of behaviour to practical problems. Probability theory is the mathematical structure devised for providing models for chance happenings. Perhaps the simplest example of a chance happening is the result obtained in tossing a coin. Although the result of a single toss can never be predicted with certainty, there is no reason why in repeated tosses the expectancy of heads and tails should not be equal. In such a case the outcomes of the experiment are said to be equally likely, so that the probability of obtaining heads (or tails) is 1 in 2, that is, 0,5. This simple probability .model refers to a 'mathematical' or 'unbiased' coin. Whether such probabilities are meaningful for actual coins tossed in any particular way is a matter for experience to determine. Probability models have also provided the basis for representing observed variability in cases where the actual under- lying probabilities are only partly known or defy analysis. A typical example of the latter case is the variability observed in the values obtained from gold or other ore samples. The interacting natural forces which gave rise to this variability are obviously very complex and are unlikely ever to be unravelled completely. In spite of this, probability theory and the more recent geostatistical theories have provided us with models which can represent this variability on a reasonable basis. Applied statistics and geostatistics must therefore never be accepted as exact mathematical sciences. Furthermore, a basic and essential concept is that in the type of applications covered in these notes, no model must ever be accepted as necessarily the final and exact answer to the problem; thus, any model must prove and continue to prove its appropriateness in practice, preferably by follow-up comparisons.

Jan 1, 1981

By John A. Wolfe, James A. Niederjohn

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, one a geologist and the other a statistician, were interested in the economic benefit which appeared to be possible in the inter-disciplinary area they call "geostatistics."

Jan 11, 1962

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 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

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 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 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 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

This chapter summarizes data on crude mineral production for the United States, its island possessions, and the Common-wealth of Puerto Rico. Included also are tables that show the principal mineral commodities exported from and imported into the United States, and that compare world and U.S. mineral production. Except for the mineral fuel commodities, the detailed data from which these tables were derived are contained in the individual commodity chapters of volume I and in the State chapters of volume II of this edition of the Minerals Yearbook. In October 1977, responsibility for the collection of data on mineral fuels-coal, petroleum, natural gas, and natural gas liquids-was transferred to the newly created Department of Energy. Although chapters covering these commodities will no longer appear in Volume I of the Minerals Yearbook, quantity and value data have been included in most of these summary tables to maintain statistical consistency in State and national value of overall crude mineral output. This shift in responsibility has also resulted in changes to the composition of the "Nonmetals" and "Mineral Fuels" groups in table 1 and table 2. The commodities-asphalt and related bitumens (natural), carbon dioxide (natural), helium, and peat-have been removed from the "Mineral Fuels" group, and are now included under the "Nonmetals" group. There has been no change in the components of the "Metals" group.

Jan 1, 1980

By Stephen D. Smith

This chapter summarizes data on crude nonfuel mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rim. Also included are tables that show the principal nonfuel mineral commodities exported from and imported into the United States and that compare world and U.S. mineral production. The detailed data from which these tables were derived are contained in the individual commodity chapters of Volume I and in the State chapters of Volume II of this edition of the Minerals Yearbook. Although crude mineral production may be measured at any of several stages of extraction and processing, the stage of measurement used in this chapter is what is normally termed "mine output." It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the output from auxiliary processing at or near the mines.

Jan 1, 1988

This chapter summarizes data on crude mineral production for the United States, its island possessions, and the Common- wealth of Puerto Rico. Included also are tables that show the principal mineral commodities exported from and imported into the United States and that compare world and U.S. mineral production. The detailed data from which these tables 'were derived are contained in the individual commodity chapters of volume I and in the State chapters of volume II of this edition of the Minerals Yearbook. Although crude mineral production may be measured at any of several stages of extraction and processing, the stage of measurement used in this chapter is what is normally termed "mine output." It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the production of auxiliary processing at or near the mines.

Jan 1, 1978

By d&apos, Kathleen J. Amico

This summary appears in Minerals Year-book volumes I and III, which cover mineral production in the United States, its island possessions, the Canal Zone, and the Commonwealth of Puerto Rico, as well as the principal minerals imported into and exported from the United States. The several commodity and area chapters contain further details on production. A summary table comparing world and U.S. mineral production also is included. Mineral production may be measured at any of several stages of extraction and processing. The stage of measurement used in the chapter is normally what is termed "mine output." It usually refers to minerals in the form in which they are first extracted from the ground, but customarily includes for some minerals the product of auxiliary processing operations at or near mines.

Jan 1, 1966

This chapter summarizes data on crude nonfuel mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rico. Also included are tables that show the principal nonfuel mineral commodities exported from and imported into the United States and that compare world and U.S. mineral production. The detailed data from which these tables were derived are contained in the individual commodity chapters of Volume I and in the State chapters of Volume II of this edition of the Minerals Yearbook. Although crude mineral production may be measured at any of several stages of extraction and processing, the stage of measurement used in this chapter is what is normally termed "mine output." It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the output from auxiliary processing at or near the mines.

Jan 1, 1988

This chapter summarizes data on crude mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rico. Included also are tables that show the principal mineral commodities exported from and imported into the United States, and that compare world and U.S. mineral production. The detailed data from which these tables were derived are contained in the individual commodity chapters of volume I and in the State chapters of volume II of this edition of the Minerals Yearbook. Although crude mineral production may be measured at 'any of several stages of extraction and processing, the stage of measurement used In this chapter is what is normally termed "mine output." It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the product of auxiliary processing at or near the mines.

Jan 1, 1977

By Rose L. Ballard

This chapter summarizes data on crude nonfuel mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rico. Included also are the tables that show the principal nonfuel mineral commodities exported from and imported into the United States and that compare world and U.S. mineral production. The detailed data from which these tables were derived are contained in the individual commodity chapters of volume I and in the State chapters of volume II of this edition of the Minerals Yearbook. Although crude mineral production may be measured at any of several stages of extraction and processing, the stage of measurement used in this chapter is what is ordinarily termed "mine output." It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the output from auxiliary processing at or near the mines.

Jan 1, 1983

By Stephen D. Smith

The following tables summarize data on crude nonfuel mineral production for the United States, its island possessions, and the Commonwealth of Puerto Rico. Although crude mineral production may be measured at any of several stages of extraction and processing, the stage of measurement used in these tables is what is termed "mine output." It usually refers to minerals or ores in the form in which they are first extracted from the ground, but customarily includes the output from auxiliary processing at or near the mines. Because of inadequacies in the statistics available, some series deviate from the foregoing definition. For copper, gold, lead, silver, tin, and zinc, the quantities are recorded on a mine basis (as the recoverable content of ore sold or treated). However, the values assigned to these quantities are based on the average selling price of refined metal, not the mine value. Mercury is measured as recovered metal and valued at the average New York price for the metal. The values shown are in current dollars, with no adjustments made to compensate for changes in the purchasing power of the dollar.

Jan 1, 1995

By H. S. Sichel

"The valuation of diamond ferous deposits depends on (i) the density distribution, (ii) the size distribution of stones and (iii) the selling price structure prevailing at a particular time.In the density distribution the stochastic variable is defined as the Dumber of individual stones found per sample unit irrespective of the stone size. The density distribution is discrete and allows for barren sample units.As diamonds often occur in clusters, a Poisson mixture distribution is derived which is entirely new, as existing discrete distributions cannot represent the stone number frequencies found in nature.For the sizes of diamonds, which are measured by weight, a new compound logarithmic normal distribution is developed.Combination of (i), (H) and (iii) leads to a meaningful appraisal of diamond ferous ground expressed in monetary value per production unit of mining.Finally, confidence limits are calculated which allow for inference from sampling to recovery."

Jan 1, 2014

What is a nugget effect? In the early development of geostatistics, the term ?nugget effect? was coined for the apparent discontinuity at the beginning of many semivariogram graphs. This name was chosen to reflect the large differences found between neighbouring samples in ?nuggety? mineralizations such as Wits gold reefs. Geostatistical theory assumes that the difference between a sampled value and a potential repeat sample at the same location is actually zero. Included in this ?nugget effect? would be true variation between contiguous samples due to the nature of the mineralization, micro-fracturing, nugget or crystal size, and so on. Also included in the nugget effect would be any ?random? sampling variation which might occur due to the method in which the sample was taken, the adequacy of the sample size, the assaying process, etc. Arguments were put forward that ?sampling errors? actually exist at zero distance. Some geostatistical schools actually maintain that the ?nugget effect? is all sampling error. This would imply that ?perfect? sampling would eliminate the nugget effect entirely. There is now a dichotomy both in the geostatistical world and in the software packages provided for geostatistical analyses. It may seem academic to argue over whether the semivariogram model should take a value of zero, a value equal to the nugget effect, or a partial value at distance zero. However, the decision can have a profound effect on both the estimated resource and in our confidence on that resource. Whereas most geostatistical texts define the semivariogram model as taking the value of zero at zero distance, others imply that the full nugget effect should be used at zero distance. For example: ?The nugget effect refers to the nonzero intercept of the variogram and is an overall estimate of error caused by measurement inaccuracy and environmental variability occurring at fine enough scales to be unresolved by the sampling interval3 ?Christensen4 has shown that the ?nugget effect?, or non-zero variance at the origin of the sernivariogram, can be reproduced by a measurement error model ?The nugget effect is considered random noise and may represent short-scale variability, measurement error, sample rate, etc.5. In many training texts and Web courses, the definition of the semivariogram is ambiguous as the formulae for semivariogram models is not actually specified at zero distance6,7,8.

Jan 1, 2010

By Mike Muchard

STATNAMIC load testing augmented with embedded instrumentation has been successfully used to obtain structural and geotechnical design information on large diameter spun cast concrete cylinder piles on many large marine construction projects. The paper focuses on one particularly interesting large marine project involving a new bridge to St. George Island, Florida where instrumentation and STATNAMIC load testing was used in conjunction with static load testing on high capacity piles. The information presented includes embedded instrumentation measurements taken during pile fabrication (post-tensioning), during pile driving, during static load testing, and STATNAMIC load testing. As much of this data is the first of its kind on concrete cylinder piles, it is exciting to present the foundation industry with this additional insight as to the behavior of this pile type and the accuracy of the methods used to test them.

Jan 1, 2005

By Mike Muchard

Augered cast-in-place piles are one of the most cost effective deep foundation options available to designers but have been largely underutilized due to skepticism associated with quality assurance and hence capacity. When installed correctly, unit friction values can rival any other competing foundation system. To this end, many means have been implemented to increase confidence in the competence of the foundation. One such method is load testing via the Statnamic test method. This paper presents an overview of the Statnamic test method, advantages and disadvantages of its use, and several case studies where Statnamic testing of augered cast-in-place piles confirmed quality construction, brought about design changes, or proof tested problematic installations.

Jan 1, 2000