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By C. A. Pickles, D. K. Xia

"In the last few decades, microwave energy has been widely employed in food processing, rubber and plastics curing, and in ceramic sintering. Recently, the application of micro waves as an energy source in extractive metallurgy has received considerable attention from a number of researchers. During the period from the mid-1960s to about 1988, the majority of the research was focussed on the behaviour of materials in microwave radiation. These research activities will continue to be important, since fundamental data on the interaction of microwaves with materials are vital for the successful application of the technology. Since1990, a number of potential applications of microwave processing have been investigated.These include: pretreatment of ores and concentrates, leaching, reduction, preheating of refractories, heating of slags and waste treatment. In this paper, the interaction of micro -waves with materials of interest in extractive metallurgy are reviewed and potential applications are discussed.IntroductionMicrowaves were first used in 1946 for the heating of materials, shortly after radar equipment was invented during the second world war. It was evident that microwaves were very effective for heating water and the technology was quickly adopted for drying and cooking. Since the introduction of the first microwave oven by Raytheon in 1952, many millions of domestic microwave ovens have been sold annually (National Research Council,1994; Atomic Energy of Canada and Voss Associates Engineering, 1990).In extractive metallurgy, microwaves are in the early stages of development (National Research Council, 1994; Atomic Energy of Canada and Voss Associates, 1990; McGill and Walkiewicz, 1987; Bradhurst and Worner, 1990;Peng et al., 1993). However, there are several reasons for the growing interest in the use of this technology in the field of metals extraction. These include the following potential advantages of microwaves: (1) rapid and selective heating of materials; (2) reactions can be catalyzed because the heating occurs on a molecular or atomic level; (3) clean and controllable energy source; (4) the gas volume is reduced and the atmosphere can be controlled as there are no gaseous combustion products; (5) the material is heated internally in comparison to external heating with conventional methods; (6)the temperature of the refractory can be minimized; and (7) the working environment is improved."

Jan 1, 1997

By Brad R. Blair

This paper will review impacts on longwall design and ground stability assessment due to advances in mine automation and sensing technology. Several new approaches to the prediction and monitoring of longwall panel and gateroad stability have recently become mature, and are ready for application in problematic ground control situations. These methods are revealing significant detail regarding deformation and failure mechanics of critical underground structures. Examples of how these technologies have worked successfully will be given, and applications for the use of these tools for cost-effective engineering design and monitoring will be suggested.

Jan 1, 1996

By Ma. X.

Passive seismic imaging is applied in underground mining to analyze the stress redistribution after the occurrence of a major seismic event. The velocity model is established to be utilized in velocity inversion. By comparing the images from velocity tomography on two different time scales, the average velocity of a mining area decreases significantly after the major event. It is highly likely that the stored energy level drops due to the occurrence of a major event. Also, total energy stored in micro-seismic events for each day is summed up and the energy change trend is plotted to illustrate the correlation of energy with a major event.

Feb 27, 2013

By Gang Chen

Conventional methods designate a factor of safety, a deterministic number, to indicate the stability of a mine excavation. However, this deterministic description of excavation stability is frequently insufficient or inaccurate and, sometimes, misleading. Employing the probabilistic analysis to determine the likelihood of mine excavation failures will lead to a better understanding of ground control problems and result in more rigorous designs of the excavations. Based on the theory of probability, two approaches are taken in this study for the probabilistic analysis of excavation stability. The first one utilizes direct integrations for the estimation of failure probabilities of mine excavations. Due to the complexity of the integration, this approach can only be applied to solve relatively simple problems. In order to overcome the limitation of the direct integration method, the second approach employs the first-order second-moment approximation of the failure probabilities for more complex ground control problems. The probabilistic analysis offers a deeper insight into the uncertainty associated with the stability of mine excavations. The study indicates that the distributions of parameter values play a significant role in the mine excavation stability, which can not be disclosed by the conventional methods of stability analysis. Greater dispersiveness of the parameter values will lead to a different probability of failure, although the factor of safety estimated by conventional methods stays the same if the mean values of the parameters are constant. By taking consideration of the probabilistic distributions of the parameters, the probability model can provide more reliable designs of mine excavations.

Jan 1, 1996

By G. van Aswegen

Large structures in mines (faults, dykes, pillars, abutments) fail when the load exceeds the strength. If the loading system stiffness (LSS, also referred to as the ‘local mine stiffness’) is lower than the stiffness of the structure the failure will be unstable. The greater the difference between these stiffnesses, the greater the energy release during unstable failure. A method has been formulated by which the LSS is established through cost-effective numerical modelling while insight into the structure stiffness (source stiffness - SS) is provided by apparent stiffness, a parameter based on the empirical relation between seismic moment and radiated seismic energy of small seismic events from the area/volume of interest. By plotting LSS vs SS a ‘stiffness diagram’ is constructed that is useful for seismic hazard ranking of different structures. A comparative back-analysis of the Dagbreek fault in Welkom, South Africa, (source of the 1990 Matjhabeng earthquake) and two other nearby faults confirm the applicability of the method. An extension of the method, where ‘hazard magnitude’ is used as a measure of the LSS, allows a ‘stiffness diagram’ to be constructed using seismic data only. Les larges structures dans les exploitations minières (failles, dikes, piliers, culées) s’écroulent lorsque la charge dépasse la résistance. Si la raideur du système de chargement (LSS, aussi appelé la « raideur de la mine locale ») est plus basse que la raideur de la structure, l’éboulement sera instable. Plus la différence est grande entre ces deux raideurs, plus l’énergie dégagée pendant l’éboulement instable est grande. Une méthode a été formulée selon laquelle le LSS est établi par modélisation numérique rentable, tandis que la raideur de la structure (SS – raideur de la source) est établie par la raideur apparente, un paramètre basé sur la relation empirique entre le moment sismique et l’énergie sismique radiée de petits moments sismiques dans l’aire/volume en question. On trace le « diagramme de raideur » en relevant les deux mesures (LSS et SS), ce qui est utile pour classer les risques sismiques de structures différentes. On vérifie l’applicabilité de la méthode en comparant la faille de Welkom, Afrique du Sud (foyer du séisme de Matjhabeng en 1990) avec deux autres failles proches. Une extension de cette méthode, dans laquelle on utilise la « magnitude du risque » comme mesure du LSS, permet de construire le « diagramme de raideur » avec des données sismiques seulement. Große Strukturen in den Gruben (Verwerfungen, Dämme, Pfeiler, Auflager) scheitern, wenn die Last die Stärke übersteigt. Wenn die Steifheit des Ladesystems (LSS, auch bezeichnet als `lokale Grubensteifheit’) niedriger ist als die Steifheit der Struktur wird der Bruch instabil. Je grösser der Unterschied zwischen diesen Steifheiten, desto grösser die Energiefreigabe während des instabilen Bruches. Es wurde eine Methode formuliert, durch die das LSS durch eine kosteneffektive numerisches Modell erstellt wird, während ein Einblick von der offensichtlichen Steifheit in die Struktursteifheit (Quellensteifheit - SS) gegeben ist, ein Parameter der auf der emipirischen Relation zwischen seismischem Moment und ausgestrahlter seismischer Energie von kleinen seismischen Ereignissen vom Interessens-/Volumenbereich basiert. Durch das Kartograpahieren der LSS in Bezug auf die SS wird ein `Steifheitsdiagramm ' konstruiert, welches für seismische Gefahrklassifizierung der unterschiedlichen Strukturen nützlich ist. Eine vergleichende Postanalyse der Dagbreek Verwerfung in Welkom, Südafrika, (Zentrum des Matjhabeng Erdbebens 1990) und in zwei anderen nahe gelegenen Verwerfungen bestätigen die Anwendbarkeit der Methode. Eine Verlängerung der Methode, in der die `Gefahrengröße' als Maß für das LSS verwendet wird, gestattet, daß ein `Steifheitsdiagramm' konstruiert wird, welches nur seismische Daten verwendet.

Jan 1, 2003

By R. C. Bratton, R. Q. Honaker

Hindered-bed separators are recognized as low-cost, high-capacity devices for both classification and density separation; however, since their inception, there have been few significant advances in the fundamental technology. Recently, Eriez has shown through modeling and pilot-scale testing that the innovative approach to feed presentation offered in the CrossFlow teeter-bed separator provides improved metallurgy when compared to traditional hindered-bed classifiers or single-stage coal spirals. This design feature prevents excess water from entering the separation chamber and disrupting the overall fluidization flow rate within the teeter zone. Most recently, a side-by-side industrial scale evaluation has verified that this technology improves overall efficiency and simultaneously reduces the separation cut-point. With regards to coal processing, data from full-scale units indicate that the CrossFlow offers good separation efficiency, high unit capacity, and metallurgical results consistent with laboratory- and pilot-scale separators.

Jan 1, 2006

By V. K. Zworykin

THROUGHOUT its development the science of electronics, like so many other branches of science and industry, has been indebted to the metallurgist. Metallurgy has provided the electronic engineer with conductors to furnish passage for electrons outside of his evacuated tubes; it. has developed tungsten and tantalum wires for emitting electrons and various refractory metals and alloys suitable for electrodes, which receive them and guide them within the tube; finally it has supplied ferromagnetic materials both for shielding electronic apparatus from magnetic fields and for forming highly concentrated fields for deflecting electron. Today I hope to show you that electronics has not been altogether ungrateful for this assistance. More specifically, I wish to indicate the role that the electron microscope, a relatively recent product of electronic engineering, is playing even now in the study of metals. Every metallographer is aware that his standard metallographic microscope will not reveal structural detail involving separations smaller than a certain fraction -at the very best a tenth-of a micron. This limitation, he knows, is a consequence of the fact that the wave length of the light employed for forming the image has this order of magnitude. It is, thus, a property of all light microscopes. To overcome it, a different imaging medium must be employed. The existence of such a medium became evident when it was demonstrated' that electrons were affected by magnetic and electric fields with axial symmetry just as light is affected by glass lenses; these fields, or "electron lenses," curve the paths of electrons reaching them from an object located on the axis of symmetry in such a manner that, at some distance from the lens, a true image of the object is formed, Furthermore, although a wave length may be ascribed to electron beams just as to light, this wave length is much shorter; for electrons accelerated through a difference of potential of 50 kilovolts, the wave length is only about one hundred-thousandth of that of visible light: Actually, the electron microscopes of today resolve detail one hundred times as fine as light microscopes; if the maximum useful magnification of the latter is taken to be a thousand, that of electron microscopes is one hundred thousand. THE ELECTRON MICROSCOPE Since electrons are readily scattered and absorbed by matter, specimens to be observed in the electron microscope must be prepared to be less than one micron in thickness; furthermore, the interior of the microscope must be carefully evacuated to prevent collisions between the electrons and the molecules of the air. Finally, as already mentioned, the lenses are formed by axially symmetric magnetic or electric fields, and not by any material medium such as glass. Apart from these basic differences, the electron microscope closely

Jan 1, 1943

By Edward L. McHugh, Stanley M. Miller, Jeffrey K. Whyatt

The point estimation method can be applied to the safety factor (SF) equation for any specified rock slope failure mode (such as plane shear, step path, or wedge) to obtain reliable estimates of the mean and standard deviation of the SF probability distribution. A gamma probability density function is recommended for modeling this probability distribution, because it allows only for positive values and is flexible enough to provide symmetrical shapes and right-skewed, exponential-type shapes for the SF distribution. The mean and standard deviation define this distribution, which then can be integrated numerically from 0 to 1 to obtain the probability of sliding, PS (portion of the SF distribution where SF < 1.0). The overall probability of failure, PF, for the potential slope failure mass is the joint probability that the rock discontinuities are long enough to allow kinematic failure (PL) and that sliding occurs along the rock discontinuities (PS); that is, PF = PSPL. This method for estimating the probability of sliding is extremely efficient computationally, and thus, expedites slope stability simulation routines used by NIOSH software to stochastically describe rock slope behavior and assist the engineer in designing catch benches for large rock slopes. Enhanced bench design translates into increased operational efficiency and safer working conditions in open pit mines and quarries.

Applicaton of Agricultural Residues from Pyrolysis in Flotation of Black Coal

Sep 13, 2010

By B. J. Clauzier

"The Falconbridge Limited approach to employing communication equipment is first, to determine what is required in a given situation, second, to evaluate the possible alternatives, third, to select the most suitable hardware and, fourth, to determine what modifications, if any, are required to ensure not only successful implementation but continued low-cost reliability. Two examples are examined.The first situation required remote video monitoring of an acid loadout station. Several alternatives for linking to theremote site were investigated, including hard-wired, slow-scan and microwave. A comparison of these alternatives is shown and an appraisal of the performance of the selected microwave link is presented.The second situation required direct voice contact between the two members of an underground tram crew. Alternative solutions are described and an evaluation of the selected system- SHF portable radios - is presented.ObjectivesIn general, projects must have four main objectives: (1) to improve the safety of its operations; (2) to reduce its operating and capital costs; (3) to increase the efficiency of its work force; and (4) to increase its productivity. ScopeCommunication, when used wisely, can be a good tool to achieve these objectives. Projects can be kept simple using existing technology and adapting it to a particular task. To ensure the success of the project, it was necessary: to determine the project objectives; to evaluate the possible alternatives; to select the most suitable hardware; to adapt the hardware to the application, if required; and not to provide more than is necessary.Application at FalconbridgeTo illustrate this approach, two examples of actual installations at the Sudbury Operations are presented, sulphuric acid loadout, and the Falconbridge Mine haulage system."

Jan 1, 1987

There is a difference in design aspects between steel linings and rubber linings for grinding mills. The basic design rules for rub- ber are described as well as the liner designs for different applications.

Jan 1, 1978

By Rodrigo Craig Cerello

The Brazilian economy has always presented a strong correlation with the mineral activity. Since colonization days, due to the territorial expansion caused by the explorers search for gold, mining in Brazil became a basic sector of national economy. Currently, the Brazilian mineral sector¹ estimates a 550% production increment (Figure 1A) in the last 10 years, reaching the US$ 50 billion value, reflecting the increased global demand for raw materials from mineral origin. According to the Brazilian Constitution², mineral resources belong to the Federal State and, consequently, their exploitation must be authorized, under penalty of engendering federal crime. Furthermore, activities of this nature are prone to cause environmental degradation such as, but not limited to, deforestation, pollution, soil deterioration and water contamination. The GPEMA represents the forensics group of the Brazilian Federal Police responsible for the technical analysis of traces related to crimes against the environment and consequently, illegal mining cases.

Aug 1, 2013

By S. Thorley

In engineering design of operator?s compartments, in underground mining equipment, ergonomics principles are often neglected or not given the full recognition they deserve. This paper defines ergonomics, applies it to machinery in an underground mining environment and describes the ergonomics analysis undertaken during the design phase of an EJC extra-low-profile mining loader. Encompassing the design of the operator?s compartment of this new loader, this paper illustrates the importance of ergonomics principles within the collective design process, ensuring that it is fully integrated into the design approach. An ultimate aim of this study is to ensure that all future designs follow this route to guarantee not only the outcome of a highly efficient, cost-effective and productive machine but that it is also takes the human factor into account, not only in maintenance but also in operation. Maximizing comfort will have the ultimate outcome of actually increasing productivity.

Jan 1, 2006

By Roger G. Rowe

The Crandon deposit, located in northern Wisconsin, is a 65.8 million ton Precambrian volcanogenic massive sulfide deposit which averages 1.4% copper and 5.8% zinc. The deposit is classic in origin, mineralogy and shape. Comprehensive understanding of the geology of both the deposit and the project site has been fundamental to the credibility and success of Project feasibility studies and regulatory permit preparation. Mine development in the current investment and regulatory climate requires thorough and timely application of geologic tools. From 1977-1980 geologic activities were focused on the typical objectives of orebody delineation, reserve estimation, depositional geology, and general site investigation. Results from these programs formed the basis for the Project&apos;s preliminary feasibility studies. Since 1981 further geologic investigations have provided criteria for project design, site management, and operational permitting. Activities have included mine entry position definition drilling, developing geostatistical reserve modeling, large diameter (150 mm) core drilling for mill pilot samples, rock mecha¬nics testing, and evaluation of the glacial overburden/deposit geohydrology for computer simulation.

Jan 1, 1983

By Holger Witthaus

Beside the traditional geomechanical evaluation methods the geotechnical parameters are recognized as important facts of the planning work for multiple seam mining. Standards for applied monitoring and investigation methods for geotechnical determination of drill cores, laboratory rock-tests and observation of roadheadings are the basics for rock mechanics classification and support design. The geomechanical classification is in this context an essential element. The planning procedure, as it is becoming more and more detailed, beginning with the panel layout up to the technical instructions of roadway development and design of roadheading machinery, nowadays uses a lot of geotechnical information that also are expanding to include quantitative determination of more parameters. The current monitoring system includes the description of separation planes using drill cores and roadheading observation as well as laboratory tests of rock-strength and geophysical borehole examinations. This information is analyzed within the geomechanical standard-classification. The re-engineering process of comparison the predicted support success to the actual monitoring results provides the opportunity for continuous optimization of the planning work und support design. This way of empirical analysis is used for basic planning work in Germany for decades. But using the technical standard of information technology and a centralized database now it is possible to reach quick-win effects in implementing research results on the one hand and actual experiences on the other hand.

Jan 1, 2006

By Clara María Lamus Molina

The following minerals found in the residual black sands from gold mining in El Bagre Antioquia (Colombia) were identified as having major economic interest: Ilmenite (FeTiO3), with an average of 49% of TiO2, frequently altered presenting crowns; lamellaes of rutile and alteration textures; titanomagnetite with up to 25% of TiO2; magnetite (Fe3O4) in individual grains or associated with others minerals as hematite and ferromagnesian silicates rutile (TiO2) with considerable quantities of Nb2O5(0.1-3.7%Wt); zircon (ZrSiO4) with 66%Wt of ZrO2 and monazite with an average of 63.43%Wt of REE, this frequently associated to xenotime and thorite forming textures as little drops. Analysis in EPMA and SEM/EDS showed percentages of minor elements and traces, thereby clearly establishing the applications of these minerals in diverse industries. Furthermore, a detailed granumetric study of the different minerals and textural relationships among them also allowed for establishing the basis for possible processing and exploitation.

Jan 1, 2006

By Panagiota Tsolis-Katagas, Basilios Tsikouras, Tassos A. Grammatikopoulos, C. Katagas

"Mineralogical techniques including microscopic methods, reflected and transmitted light microscopy, Cathodoluminescence (CL) and Scanning Electron Microscopy equipped with an Energy Dispersive Spectrometer (SEM-EDS), are useful in determining the quality of industrial minerals. They are essential for studying ores and metallurgical products including the evaluation of physical characteristics of the mineral, paragenetic relationships, associations with possible deleterious contaminants (e.g., sulphides), spatial distribution within the ore zones and liberation characteristics. The methods are inexpensive, and provide quick identification and distinction among the industrial minerals and the gangue minerals in a section. Additionally, SEM is necessary to reveal complex textural sequences and 3-D measurements of minerals and quick semi-quantitative analysis.Common analytical methods include Electron Microprobe Analyses (EMPA) and Whole Rock Analysis (WRA) (commonly with XRF and ICP) for major and trace elements. The EMPA analyses of industrial minerals provide information on the purity of the analyzed grains as opposed to the bulk chemical analyses that may be misleading due to contamination by other associated common “gangue” minerals. These techniques have been implemented for the case studies of wollastonite, V-magnetite and muscovite. Therefore, these methods can provide extremely useful information and lead to the implementation of a successful pilot-testing programme.MINERALOGICAL EVALUATION OF DEPOSITSDespite their considerable and increasing economic importance, industrial mineral deposits have traditionally been neglected by economic geologists, and are only rarely the subject of the detailed analysis widely lavished on metallic mineralization. Moreover, in that they generally represent concentrations of “normal” rock-forming minerals, albeit commonly with particular textural and/or geochemical features, they have tended to fall between the mainstream of petrogenetic studies and mineral deposit research (Grammatikopoulos 1999). For many industrial minerals, little attention has been paid to the factors responsible for their local concentration as large and high-grade bodies. This comparative neglect has particularly been the case for minerals such as talc and wollastonite, widespread in metamorphic rocks, in which they are reasonably interpreted as components of assemblages derived, respectively, from pelitic sediments, ultramafic igneous rocks and siliceous limestones."

Jan 1, 2003

By A M. Hagni

Certain copper ores from the Nchanga Copper Mine in the northern Zambia Copperbelt are refractory with respect to conventional beneficiation techniques. This paper reviews recent study of those ores to determine their mineralogy, textures and nature of copper occurrence. Two suites of refractory ores were selected for study: 1.&nbsp; samples of stockpiled ores from an open pit, and 2.&nbsp; drill core samples from copper ores. Both sample suites are from the upper orebody at Nchanga and contain about 0.3 - 1.4 per cent copper as determined by atomic absorption, but they represent separate stratigraphic, mineralogical and beneficiation problems. Ore microscopic examination showed that fine-grained copper sulfides are totally lacking from both suites of refractory ores. Petrographic study found malachite in the refractory ores from the open pit, but that malachite probably is post-mine. The opaque mineralogy of the open pit refractory ores is dominated by goethite that occurs mostly as pseudomorphic grains after pyritohedral pyrite crystals that average 200 - 250 ¦m across. Haematite occurs as bands within or as outer shells of the goethite grains. Additional goethite occurs locally as finer-grained areas of exotic goethite. The opaque minerals in the drill core refractory ores are dominated by euhedral ilmenite crystals about 50 - 175 ¦m long. Anatase is the dominant opaque mineral in some drill core samples where it is largely pseudomorphic after ilmenite crystals. Goethite accompanies malachite in unusual drill core refractory ores that have experienced intense hydrothermal alteration. Thus, ore microscopy and petrography showed that fine-grained chalcopyrite and bornite and pre-mine malachite were not the causes of the refractory nature of the ores studied. Electron microprobe revealed that most of the copper occurred in solid solution within micas. Application of automated SEM techniques has provided a detailed understanding of the distribution of copper in these refractory ores.

Jan 1, 2008

By F Gervilla, J Laukkanen

The Kevitsa Ni-Cu-PGE deposit in northern Finland contains disseminated Ni-Cu-Fe sulfides, and platinum-group minerals (PGM). The 2.05 Ga-old ultramafic-mafic, funnel-shaped intrusion is intruded into a volcanosedimentary sequence. The major ore minerals are pentlandite, hexagonal pyrrhotite and troilite, chalcopyrite, cubanite and magnetite. Pyrrhotite and pentlandite are replaced by pyrite, millerite and heazelwoodite near the surface. Nickeline, maucherite and gersdorffite are locally abundant. A pilot feed sample of 575 t of the main orebody at Kevitsa had average grades 0.45 per cent Cu, 0.36 per cent Ni, 1.85 per cent S, 0.33 g/t Pt, 0.34 g/t Pd and 0.19 g/t Au, with 0.06 per cent Ni contained in silicates. Higher PGE contents (2 - 27 ppm) occur in a vertical N-S bearing fault zone. The PGM (n = 6022) mapped in specimens of four drill holes, consist of sperrylite 34.7 vol per cent, braggite and cooperite 18.5 vol per cent, geversite 17.2 vol per cent, moncheite 14.7 vol per cent, merenskyite 6.7 vol per cent, stibiopalladinite 4.3 vol per cent, sobolevskite 1.9 vol per cent, kotulskite 0.7 vol per cent, michenerite 0.6 vol per cent, keithconnite 0.3 vol per cent, rustenburgite 0.1 vol per cent, melonite, froodite, laurite together 0.1 vol per cent and only a few grains of sudburyite, irarsite, vysotskite, erlichmanite, hongishiite, Pt-Cu-alloys, three undefined Pd and Pt bismuthinides and antimonides and a Pd-Cu-bearing Pt-Ni-Fe sulfide. Most of the PGM, 62 per cent, are enclosed in silicates, 29 per cent are intergrown with sulfides, nine per cent are within sulfides. A portion of the PGE occurs in solid solution in sulfides and arsenides. Ni flotation yielded smelter-grade concentrates averaging 12.2 per cent nickel. The average sulfide Ni recovery is 78.8 per cent and total Ni recovery is 65.3 per cent. The average Pt is 10 g/t at 55 per cent recovery, Pd 7.7 g/t at 38 per cent recovery and Au 1.6 g/t at ten per cent recovery. Cu concentrates averaged 28.6 per cent Cu with an average recovery of 78 per cent and further 11 per cent in the nickel concentrate. The copper concentrate contains 4 g/t Au at 24 per cent recovery. The average Fe to MgO ratio 17.9 is well above the targeted minimum of 4.5. The pilot results show that the previously used TETA (triethylene tetramine) can be avoided and good quality, smelter-grade concentrates can be produced from the Kevitsa ore at economical levels of recovery by conventional flotation methods.

Jan 1, 2008

By J. W. Merks

Applied statistics provides scores of powerful tests and techniques that are widely used and abused in science and engineering. The variance is the basic measure for variability, precision and risk. The formulas for the variances of the arithmetic mean and the weighted average are derived from the variance of a general function, as defined in probability theory. The requirement of functional or mathematical independence in probability theory translates into the concept of degrees of freedom in applied statistics. Geostatistics is the only variant of statistics in which functional dependence and degrees of freedom are irrelevant. This paper examines whether such basic elements of probability and statistics can be ignored with impunity.

Jan 1, 1997