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By W. H. Tuttle, H. R. Ahlquist, A. J. Carlson

Variations of the EVOP technique are accepted as the foun- dation in the development of Erie Mining Company's mining, concentrating and pelletizing complex at Hoyt Lakes, Minnesota. The basic one-variable- at-a-time technique served its purpose through the laboratory pilot plant as well as the full-scale production sized pilot plant. However, recognition by Erie Mining Company management of the potential of computer application and statistical experimentation in plant operation and testing led to acquisition of an IBM 1620 computer in 1961. Adaptation of established techniques in statistically designed experimentation and analysis of results is presented in actual case form including the following: 1. Determination and use of variance, standard deviation, standard errors; application of t-test in determining true differences between daily aver ages of product assays; formulation of quality control limits; determining sample size; and application of normality tests will be discussed. 2. Use of mathematical modeling and regression analysis for establishing mill storage conditions based on bin level indicator lights. 3. Polyvariable random balance design of a balling circuit test and resultant identification of primary control variables.

Jan 1, 1969

By Mehrotra G. M, Frohberg M. G

Based on the concepts of statistical thermodynamics of athermal mixtures, an approach is developed which is capable of quantitatively explaining the thermodynamic properties of binary silicate systems. Expressions for the ionic fractions of various anionic linear and nonlinear chain polymers are derived. The developed expressions for free energy of mixing are tested by applying these to the system PbO-SiO2. The ionic fractions of various chain polymers in this system are calculated. The two cases, namely, of linear and nonlinear chain polymers are compared with each other.Limitations of earlier models are pointed out.

Jan 1, 1975

By Regina Krachler, Herbert Ipser

"The principles of the derivation of statistical-thermodynamic models to interpret the compositional variation of thermodynamic properties in non-stoichiometric intermetallic compounds are discussed. Two types of models are distinguished: the Bragg-Williams type, where the total energy of the crystal is taken as the sum of the interaction energies of all nearest-neighbor pairs of atoms, and the Wagner-Schottky type, where the internal energy, the volume, and the vibrational entropy of the crystal are assumed to be linear functions of the numbers of atoms or vacancies on the different sublattices.A Wagner-Schottky type model is used for the description of two examples with different crystal structures:For B'-FeAl (with B2-structure) defect concentrations and their variation with composition are derived from the results of measurements of the aluminum vapor pressure; the resulting values are compared with results of other independent experimental methods.For Rh3~ (with an NiAs-derivative structure) the defect mechanism responsible for nonstoichiometry is worked out by application of a theoretical model to the results of tellurium vapor pressure measurements. In addition it is shown that the shape of the activity curve indicates a certain sequence of superstructures.In principle, there are no limitations to the application of statistical thermodynamics to experimental thermodynamic data as long as these are available with sufficient accuracy, and as long as it is ensured that the distribution of the point defects is truly random, i.e. that there are no aggregates of defects."

Jan 1, 1996

By Michael C. Stanley

The set of discoveries for a mining district or camp is a reflection of the exploration history. In the western Abitibi greenstone belt of Ontario, future exploration can be guided by a study of statistical trends of known gold deposits. In this area simple trends indicate a strong decrease in the contained quantity of gold discovered through time. Much of this decrease is attributed not to falling mining grades but to smaller tonnages of ore. A plot of the largest discovery in each ten year time period suggests that deposit discoverability is following a size-biased sampling model. Cumulative ounces of discovered gold indicate that an asymptotic value has been reached where exploration is not expected to add significantly to known reserves. This is substantiated by a downward trend in the exploration success ratio of the number of new deposits discovered versus the number of new mineral prospects. The set of discovered deposits reflects a non-random sampling process where size- biased modeling suggests that the largest deposits will be discovered early in the exploration effort. It is the exceptionally large deposit contributing to the observed size-biased distribution. Although this pattern is observed for the western Abitibi the model is complicated by recent, large reserve additions that are attributed to the original discovery. There is present in this area a subtle learning process in exploration leading up to the largest discovery. For comparison a learning model was estimated using cumulative size of discovery per unit of time. This model yielded results consistent with the statistical trends and is thought to be a superior forecast of future discoveries in this region.

Jan 1, 1992

By H. S. Sichel

Statistical valuation of diamondiferous deposits By H. S. SICHEL, D.Sc The valuation of diamondiferous 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 number 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), (il) and (iii) leads to a meaningful appraisal of diamondiferous ground expressed in monetary value per production unit of mining. Finally, confidence limits are calculated which allow for inferences from sampling to recovery.

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

By J. D. Cooper, D. W. Thompson, J. Basiuk, W. Cass, R. Ilves

The Department of Thoracic Surgery and Pathology at the Toronto General Hospital have had a long standing interest in the early detection and treatment of carcinoma of the lung. Our initial experience was with a population at risk due to a prolonged period of cigarette smoking. More recently our efforts have turned to industrial exposure, specifically in the nickel and uranium industries. [Initial Screening Project] (1) For a three year period 1963 to 1966 a cytology screening program was carried out through the Out-Patient Department. The study was limited to cigarette smokers over 40 in age. A total of 1586 patients were examined. Of the sputa collected, the classification is seen in Table 1. There were 11 malignant sputa present. Added to this number were 25 patients with symptoms, normal chest X-rays, but malignant cells on cytology, and a further 5 patients in whom an abnormality (eventually proven non-malignant) showed on X-ray, and sputum showed malignancy which was radio logically occult. (Table II). This gave a total of 41 patients with malignant sputum who were evaluated between 1960 and 1966. The clinical course of these patients is seen in Table III. Only 19 of 41 patients had localization and treatment of their tumour during that study period and this low rate of localization attests to the technical difficulties endoscopy in that day presented. The method of localization was as follows: a) 6 patients showed an area of segmental pneumonitis somewhere in this time period b) Using the rigid bronchoscope localized the tumour in 9. This was proven by direct biopsy, and frequently required more than one bronchoscopy over a prolonged time period. c) bronchograms and tomograms showed abnormalities in 5 patients. Of these 19 patients, 5 were treated by radiotherapy because of general condition or refusal of surgery. Three of the irradiated patients died of recurrent cancer within three years. The other two died within one year of unrelated disease. Fourteen patients underwent resection, with one operative mortality. At pathology, the tumours were "in situ" in 6 and invasive in 13. There was no evidence of nodal spread. When last followed up in 1979, there were no cases of recurrent tumour and no cases of second lung primary tumours. Similar experiences have been reported from the Mayo Clinic (2), Johns Hopkins (3) and Memorial Hospitals (4). Early detection of radiologically occult tumours which are in situ or minimally invasive has given uniformly good results. There have been no deaths from recurrent or metastatic cancer in surgically resected patients, and only one second primary tumour has been detected. Interestingly, the Hopkins group reports that 5 patients with Stage I squamous cell tumours refused operation. One refused any treatment and died of disease at 12 months. Three were radiated, and were alive from 14-38 months post-treatment, all with evidence of recurrent disease. [Sudbury Sintering Plant Study](5) From 1948 to 1963 an open travelling-grate sintering process was employed to convert nickel sulfide to nickel oxide at an International Nickel Company operation. The environment in this plant was particularly dusty and filled with fumes. It became apparent by 1969 that the incidence of bronchogenic carcinoma was markedly increased in workers from this plant. A concerted effort was made to track down all workmen with this exposure. During 1973 and 1974, 268 men were studied. Chest radiographs were done and showed no mass lesions. Sputum was collected on three consecutive days and analyzed. There were 12 men with malignant sputum, all of the squamous cell variety. Two refused any investigation, one presenting 31/2 years later with extensive hronchogenic carcinoma, and the other 5 years later with extensive carcinoma of the maxillary sinus. In the remaining ten patients careful rhinolaryngeal examination as well as a detailed bronchoscopy, involving examination, brushings and biopsy of all pulmonary segments was carried out. One patient was found to have laryngeal carcinoma and was treated by radiation. In nine patients, the malignancy was localized to the lung, leading to six lobectomies, two pneumonectomies and one sleeve lobectomy at operation. However, the follow-up in these cases suggests a different biological behaviour with these industrially related tumours. While no tumour has recurred locally, one patient has died of metastatic cancer and two patients have developed second and one patient a third pulmonary primary cancer. However, survival has still been much better than wits radiographically manifest lung cancer. [Technique of Localization] (6) Following a careful rhinolaryngeal examina examined and then the lower respiratory tract is examined. This is all performed under general anaesthesia. The trachea is examined with the rigid Jackson bronchoscope, collect-

Jan 1, 1981

By J. H. Schuenemeyer

Uncertainty estimates on coal resources were computed as part of the U.S. Geological Survey’s National Coal Resource Assessment study of more than 60 coal beds and zones in the Appalachian Basin, the Colorado Plateau, the Gulf Coast, the Illinois Basin, and the Northern Rocky Mountains and Great Plains. The estimates were made to provide zone specific measures of uncertainty on the historical categories of geological assurance, namely measured, indicated, inferred and hypothetical. Previous estimates were based solely upon distance from a drill hole. These new estimates incorporate site-specific variability and spatial correlation and indicate that there is considerable difference in variability within and between regions. Uncertainty estimates for the measured category are discussed in this paper.

Jan 1, 2001

INTRODUCTION TO STATISTICS It is necessary now to digress from the direct study of appraisal techniques to consider an important tool for the mineral appraiser. Whenever a great deal of data have been accumulated, such as might be gained through the sampling process discussed in the preceding chapter, the application of statistical methods should be considered. Statistical methods are used for descriptive purposes and for the organization and summarization of quantitative or numerical data. Descriptive statistics covers the tabulation of data, its presentation in graphical or pictorial form, and the calculation of its several descriptive measures. It is not the intent of the brief summary of statistics that will be outlined hereafter to cover the total breadth and scope of mathematical statistics. It is the intent of this and the following chapters to review a few of the statistical concepts that have the most direct bearing upon the problems involved in mineral evaluation. Should the reader desire to go more fully into statistical theory and mathematics, numerous texts and publications are available.

Jan 1, 1980

By K Hooper

Over the past 20 to 30 years statistics as a science has grown in significance. Not a day passes without reference to the latest statistics by the print, audio and audio-visual media. The Northern Territory Government has been part of this growth and like other public and private sector organisations collects a broad range of statistics. The Northern Territory Department of Mines and Energy participates in the government's statistics collection process. Statistics collected and published by the Department of Mines and Energy include geoscientific; mining and exploration tenure; environmental (e.g. mine site waste water management); production of minerals, oil and gas; mining sector employment; and occupational health and safety. The importance of statistics collection to the Northern Territory Government is discussed in the paper.

Jan 1, 1994

By E. Z. Lajtai

The probability distribution of fracture data from a rock mechanics test contains information about the effectiveness of the testing procedure and/or about the nature of the operating failure mechanism. The tensile strength of Lac du Bonnet granite forms a bimodal probability distribution when determined through line loading as in the Brazilian test. The same data obtained from three point bends tests are unimodal. The bimodality can in part be removed by distributing the line load over a finite area. Moisture has the anticipated effect in lowering both the average compressive and the average tensile strength of Lac du Bonnet granite. The reduction in strength however is not uniform within the probability distribution; the change is the largest at low and the smallest at high strength. Conversely, long-term loading is more damaging to the high strength members of the distribution. The large scatter of failure times in static fatigue experiments can in part be removed or even utilized when the probability distribution of instantaneous strength is taken into account.

Jan 1, 1982

Multiple regression analysis applied to ventilation records of stopes on the Witwatersrand showed that it was possible to estimate the temperature increase per 100 ft for a new stope with a standard deviation of 0' 5°F. The analysis also threw light on the relative effect on this estimate of five different factors.Application of the analysis of variance technique to a factorialexperiment on the production of dust during rock drilling showed that the effects of air and water pressure were quite small but also showed that the between-machine variation was unexpectedly large.Analysis of variance also proved a valuable means for assessing the bias and random error variation of aneroid barometers used in pressure surveys.INTRODUCTIONThree examples are discussed to illustrate the use of the techniques of "analysis of variance" and "multiple regression" in research on the ventilation of gold mines. Although the techniques are basically similar their application to each example has a slightly different emphasis and the examples were chosen for this reason. The variation ofemphasis is as follows.1. Temperature increases in stapes. This work was undertaken as a preliminary to possible extensive controlled experimentation (Lambrechts, 1959). Data collected in routine work by the mine ventilation personnel were used for analysis and no specific experiments were carried out. The main object was to see whether such data could provide any strong pointers to factors which might be worthy ofmore careful study and to factors which could initially be ignored. Of course, there was hope that the study might provide an empirical formula for rough forecasts.

Jan 1, 1962

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 semi-variogram 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 ?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 semi-variogram 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 semi-variogram 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 semi-variogram is ambiguous as the formulae for semi-variogram models is not actually specified at zero distance6,7,8.

Jan 1, 2009

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 H. P. Greenwald

IN the year just passed the Coal Division's Committee on Rock-Dusting reviewed the status of this safety measure in American coal mines and prepared a paper thereon which will be presented at the February meeting of the Institute. This paper supplements one appearing in Vol. 139 of the "Transactions," page 87 (1940). Because that paper will be issued soon, only a summary is given herein.

Jan 1, 1944

By Vijia K. Karra

Making sure workers within the aggregates industry go home safely each day is the goal of aggregate companies throughout the United States. At the National Institute for Occupational Safety and Health (NIOSH) researchers are contributing to NIOSH’s vision of safety and health through a fact-finding approach to reducing injuries/illnesses in various mineral sectors. Surveillance data from the Mine Safety and Health Administration (MSHA) has been the primary source for such analyses. It helps to focus research efforts on key machinery, workers, and their tasks. The crushed stone category referred to in this article is represented as crushed and broken stone in the MSHA database.

By Vijia K. Karra

The goal of aggregates producing companies across the United States is to ensure their workers go home safely each day. At the National Institute for Occupational Safety and Health (NIOSH), researchers are pursuing this vision of safety and health through a fact-finding approach for reducing injury illness in various mineral sectors. Surveillance data from Mine Safety and Health Administration (MSHA) has been the source for such analyses. It helps to focus research efforts on key machinery, workers, and their tasks. The second installment of this two-part series follows last month's focus on crushed stone.

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

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, 2013

By Matthew Janes

Statnamic load testing is becoming widely accepted as a method to quickly and economically determine the load-deflection behaviour and ultimate static resistance of high capacity deep foundations. Strain instrumented large diameter bored shafts were tested at four locations for the federal and state Departments of Transportation in the United States. Tests were conducted vertically (to 30 MN) and laterally on the shafts and, in some cases, testing was completed over water. Instrumented shaft test results provided shaft load distribution with depth and shaft shear transfer stress throughout the soil stratum. Shaft end bearing and ultimate end bearing stress values were provided. On two projects, Osterberg load cells provided comparative static data for skin friction and end bearing. Correlations between Statnamic derived static load-displacement results and Osterberg load-deflection results are very good. Statnamic lateral load test results were correlated with static lateral results in addition to providing useful dynamic response and damping data.

Jan 1, 1996