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By H. Wyslouzil

"The Kelsey Centrifugal Jig is a gravity separation device which utilizes the principles of the conventional mineral jigs but with the additional feature of being able to vary the apparent gravitational field. This is accomplished by utilizing the specific induced movements of the conventional jig within a centrifuge.Pilot plant trials have been underway since July 1988 to evaluate the potential applicability of this technology to various process streams at Rio Kemptville Tin.The grade/recovery relationships for samples treated in the jig were consistently better than results obtained from tables. Recoveries of more than 90% were attained at concentrating factors ranging up to 20. When compared with electrostatic separators, the jig achieved equivalent metallurgical results in a two stage process, without the expensive requirement of filtration and drying. Recoveries exceeding 96% were achieved with final concentrate grades averaging higher than 60% tin.INTRODUCTIONMineral jigs have been used for hundreds of years. Many different types have been developed, and each one has numerous variations. In recent years, the idea of applying centrifugal forces to conventional jigs has been put to practical tests and today a number of units are in commercial production. In principle, by enhancing the apparent gravitational field, it should be possible to recover finer particles by overcoming viscosity and surface effects which tend to limit existing gravity devices. In addition, it may be possible to use gravity to separate minerals with much smaller specific gravity differences."

Jan 1, 1990

By Justin Lukens, Di Stasim Jeffrey, Frank Di Salvo

Columbia University’s Manhattanville Campus expansion includes the construction of two new business school buildings. The new buildings require development of an entire city block bound by 12th Avenue, W 131st Street, W 130th Street and Broadway in Upper Manhattan. A support of excavation (SOE) package was first released, followed by a foundation package. The SOE package consisted of approximately 100 soldier piles and 280 anchors, up to 215’ long, to support a cut anywhere from 30’- 50’ below street level. The foundation package alone included approximately 1600 drilled micropiles. Given the breadth of the work scope, Hayward Baker Inc and Moretrench joint ventured on these two projects to bring sufficient knowledge and work resources to complete the work in an efficient and timely manner. This included working with the Owner/Engineer to propose different means and methods for construction to significantly reduce the schedule while meeting the design intent, such as large diameter (36” diameter) augercast piles in place of conventionally drilled soldier piles and large hollow-bar micropiles (103/51 bars) in lieu of pressure-grouted micropiles. The anchors, ranging from 3 to 22 strands, were used for earth retention through both soldier pile and lagging walls and existing slurry walls. These anchors were complicated based not only on their size and length, but also the need to drill some of them under the historic Studebaker building. The overall magnitude of the project with considerations to resource management and material lead times will be addressed, highlighting critical strengths provided by the Contractor to ensure project success. The scope of work discussed in this paper was executed under two separate competitive bid contracts. The first contract included the support of excavation work and the second contract included the foundation package. The support of excavation comprised of drilled soldier piles (performed by Case Foundation as a subcontractor to the JV), driven soldier piles, driven sheet piles, hollow bar tiebacks, multi-strand tieback anchors and micropile soldier piles. The foundation package consisted of drilled micropiles. Due to the large scope of work and critical schedule requirements of the project, the JV had to think outside the box and present value engineered alternates to expedite installation durations.

Jan 1, 2019

By Dana C. Reinke, David K. I Ingram

Researchers at the National Institute for Occupational Safety and Health partnered with the water well industry to develop engi­neering control technologies and training products to address noise exposure at the job site. Noise­induced hearing loss continues to be a problem in the well drilling industry. Research con­ducted by NIOSH found that air rotary drill rigs produce sound levels more than 90 dB(A) over the course of an eight­hour workday. Sounds levels above 90 dB(A), identified during hammer drilling and the hammering of casing, exposes workers to levels that can damage hearing. A typical air rotary drill rig provides no barrier, for noise and dust pro­tection, between the drill’s control panel and the drill stem. The development of a partial cab is the clearest example of NIOSH’s research partnership with the water well industry. NIOSH researchers determined that an engineering noise control to protect the oper­ator at the rig’s control panel would be effective, based on typical work site conditions. Many surface rigs do not have full cabs as a result of the original equipment manufacturer design or the high cost of aftermarket products. Developed as a partial cab, the NIOSH engineer­ing noise control design addressed stakeholders’ needs associated with cost, transport, and worker usage (Figure 1). Field tests found the partial cab effective in reducing sound levels at the rig’s control panel, a typical location for a drill rig operator. Sound levels at the control panel were reduced from 104 to 96 dB(A) (Figure 2). Coupled with continued use of personal protective equipment, such as hear­ing protection devices, the partial cab can help to reduce noise exposure. NIOSH researchers created a CD with informa­tion about noise exposure and the partial cab. Most important to well drilling companies is information on how to construct and attach the partial cab to drill rigs. The CD can be viewed on a standard computer and includes a video of the partial cab in use on a work site. Computer­aided design drawings are included on the CD and provide detail of the cab design as well as information on construction mate­rials and design details. Additionally, the CD provides background infor­mation on noise­induced hearing loss and hearing protection devices to increase knowledge about this occupational health concern. This information can be viewed by all company employees to help promote the partial cab’s importance to workers using the cab. More information on the partial cab noise control technology can be downloaded from www.cdc.gov/ niosh/mining NIOSH researchers also examined the health and safety training needs of workers in the ground water industry. It was quickly realized that most workers learn health and safety on the job and do not attend any sort of formal training. In addition, there is not a lot of time for daily “tailgate talks” or “shop talks” on health and safety issues. As a small business industry, the owner is often operating a drill rig along with his other employees. In general, new employees learn the job in an apprentice style sys­tem. As a result, workers and owners have few opportunities to access uniform health and safety information based upon the job — an outdoor work environment with daily change in work sites. With this information, NIOSH researchers devel­oped two products that deliver health and safety information to fit into the daily work of well drillers. Both are information circulars and are available through download at www.cdc.gov/niosh/mining and the NGWA Web site at www.ngwa.org/publication/ publications.cfm. These circulars are: Water Well Safety Bits. This booklet provides information in a “quick bites” style. It is pre­sented in a magazine format and can be left on

By Thomas A. Bailey

Since the advent of longwall mining, various methods and materials have been used during relocation to control the intrusion of the gob in the shield/panline area. (figure 1) Controlling this gob is critical to ensuring a safe, speedy, and productive longwall move. An uncontrolled gob can cause a number of problems, from increased worker exposure to entrapment of equipment to lost production. With an eye toward worker safety and increased productivity, several different methods have been developed to minimize gob intrusion. This presentation will take a look at the history and development of longwall ?screens? and ?mesh?, from chain-link fencing to high-modulus polyester geogrids. The benefits and advantages of these developments will be defined. Since 1994, longwall coal mines have used polymer geogrids during longwall recovery to control intrusion of gob material into the shield/pan line area. As described by Brandon and Collins (1996) in their paper presented at the 15th Ground Control Conference in Golden, CO., mines had used various forms of support, such as welded wire mesh, chain-link fencing, wooden cribbing, props, and steel cable to accomplish this. These methods worked, but were labor-intensive, slow, and provided varying degrees of gob stoppage. Although a few mines still use chain-ink fencing to control the gob, longwall coal mines have generally settled on polyester geogrids to control gob and roof and these mines have been instrumental in providing input in order to develop and improve these geogrids products. he trend during the past twelve years has been to incorporate stronger grids and to eliminate auxiliary reinforcements, such as steel cables and nylon or polyester webbing. A job that once required heavy steel cables, props, and fencing is now accomplished with strong, lightweight, high-modulus polyester grids. When we discuss high-modulus grids, we refer to the ratio between load and strain, as illustrated in figure 2. These grids are woven or knitted from yarns that have been pre-stressed. When these grids come under load, they pick up the load more quickly. This allows less deformation in, in this case, the mine roof. The same principle applies when these grids are used to control the ribs. With less elongation, the grids will hold rib material tighter, thereby keeping travel ways more open.

Jan 1, 2006

By A. Feather

The Minataur? Process (Mintek Alternative Technology for Au Refining) is a novel route for the production of high-purity gold using solvent extraction. Following the successful demonstration of the process on a pilot-plant scale, a full-scale 24 t/a production plant has been commissioned at Harmony Gold Mine in Virginia, Free State. The commercial implementation of this process represents not only a significant advance in gold-refining technology, but may be instrumental in initiating important changes in the legislation regulating the marketing of gold in South Africa. Gold of either 99.99% or 99.999% purity can be produced from intermediate process products having a wide range of gold contents. The process comprises oxidative leaching of the solid feed, followed by selective solvent extraction of the gold from the leach liquor to reject impurities, and precipitation of high-purity gold powder. This paper outlines the process, presents selected results of two pilot-plant trials in which 5 kg/d of high-purity gold was produced from silver-refining anode slime and gold-electrowinning cathode sludge, and provides some details of the cost benefits.

Jan 1, 1997

By Randall M. Wheeler, Kenneth K. Eltschlager

Blasting Seismographs use microphones to measure air overpressure from blasting. The microphone height above the ground has been the object of some controversy. The current ISEE “Field Practice Guidelines for Blasting Seismographs” specify microphone placement within 1.2 inches of the ground or over 3 feet above the ground. In this study, air overpressure measurements were taken at different height intervals and compared. Blasting seismographs constructed to the ISEE “Performance Standards for Blasting Seismographs” were used to monitor construction, quarry, and coal mine blasting. Near and far field measurements were taken to obtain representative spectral and amplitude ranges. The comparative analysis shows that microphone height has negligible impact on air overpressure measurements.1

Jan 1, 2005

The Bureau of Mines Minerals Information organization collects worldwide data on virtually every commercially important non fuel mineral commodity. These data form the base for tracking and assessing the health of the minerals sector of the U.S. economy. This data collection activity was instituted by the 47th Congress in an appropriations act of August 7, 1882 (22 Stat. 829), to place the collection of mineral statistics on an annual basis. The most recent authority for the Bureau of Mines Minerals Information activity is the National Materials and Minerals Policy, Research and Development Act of 1980 (Public Law 96-479, 96th Congress), which 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, 1984

Argentina follows Venezuela and Mexico as the largest producers of crude petroleum and natural gas in Latin America. Argentina 1S practically self-sufficient in fuels, but relies substantially on imports for its supply of copper, iron ore, ferroalloys, sulfur, and fertilizers. Mining activity is limited and is in an incipient stage of growth, considering the country's potential for mining. Most nonfuel mineral output in 1979 consisted primarily of minerals used for construction, while only 9% are other nonmetallic, and 2% are metallic minerals. Argentina is Latin America's major producer of boron minerals and uranium (yellow cake). Mineral exports consist primarily of borates, uranium concentrates, and of late, some tin. These exports have in the past been shipped mostly to Great Britain. London banks have been involved in arranging financing for St. Joe Minerals Corp. IS planned development of the El Pachon copper deposit (see map), and were being counted upon to also back the development of large copper and manganese projects. The following is a review of Argentine mineral production in 1979: (For 1981, the production of boron minerals is put at 167,000 metric tons and uranium at 300,000 metric tons.)

Jan 1, 1982

By J. Ekengård, H. Srinath, M. Andersson, P. Jönsson, D. S. Sarma

The present paper deals with mixing between the metal and slag phase during the ladle refining process, including vacuum degassing. Dispersion of metal drops in ladle slags has been studied. The results show a larger quantity of metal droplets in ladle slag during the alloying and stirring phase than during the subsequent vacuum degassing phase. The thermodynamic and kinetic aspects of the interaction between metal drops and the slag matrix have been considered and probable reasons for the observed distribution discussed.

Jan 1, 2004

By M. Görnerup, M. Hayashi, S. Seetharaman, C. -Å Däcker

The mould flux plays a crucial role in the continuous casting operation of steel due to its multi-functional assignment as lubricator and heat flux controller. In reality, the commercial fluxes can fall short of the expectations of the operator. In such cases, the performance of the mould flux reduces production throughput in the casting machine. This paper presents the results of a study of two different commercial mould fluxes in continuous casting of steels. The results of online sampling during casting, as well as off-line measurements in the laboratory, are presented. Mould flux powder and slag samples from the caster have been characterized with respect to melting behaviour, interfacial tension and thermal diffusivity, using various measuring techniques. An experimental technique has been developed in order to simulate the melting behaviour of a flux in the mould, which has been found to be useful for qualitative studies. A cross-sectional view of different powders reveals that up to four different material layers may exist in the bed: a loosely packed powder layer, sintered layer, semi-solid layer and liquid slag layer. It is found that the melting rate of the mould flux is dependent on the liquid slag layer thickness. Thus, in a continuous casting operation the melting rate is likely to be non-uniform with position in mould due to the difference in liquid slag layer thickness. Mould slag composition is found to be influenced by the starting powder for as long as 30 min, representing a large part of the first heat casting time. Observations of gas formation indicate that interfacial reactions between the steel and slag take place. Keywords: continuous sacting, mould flux, mould slag, properties

Jan 1, 2004

By P. J. Lloyd

There are few data on the composition of discard coal in South Africa, and no overall view of the discards for the entire industry. As a result of work on coal qualities in South Africa, a database was established which enabled a good estimate to be made of the composition of the discard from every mine. The data are presented in the form of histograms of ash, volatile matter and fixed carbon content of the 43 million tons of material which were discarded in 1990. The results are discussed in terms of the closeness of the composition of much of the discard material to presently used power station coal. It is concluded that it is mainly developments in equipment, particularly fluidized bed boilers, which inhibit the wider use of discard coal. However, other factors must be noted, including the relatively high sulphur content of the discards, and the fact that even with the most careful storage the material ages and may become unusable after about 15 years.

Jan 1, 2000

By J. -Y. Jia, G. -B. Qiu, C. -G. Bai, D. -F. Chen

Due to the great importance of the smelting process, it is essential to establish a calculation model on the viscosity of the slag system containing titania. In this paper, the calculation models of mass action concentrations and viscosity for the CaO-SiO2-TiO2slag system have been established according to the coexistence theory of the slag structure, as well as the referenced viscosities ofCaO-SiO2-TiO2at different temperatures and TiO2compositions. With the two models, corresponding calculated programs are made by means of programming language Matlab5.3, and the curves of viscosity of the TiO2concentration (?TiO2/%) at 1400°C, (R=0.9~1.0) are plotted. The results show that mass action concentrations of TiO2increases with increasing percentage ofTiO2, while the viscosity of CaO-SiO2-TiO2system is decreased. The results show that the models are in good agreement with the experimental and referenced data. They also shows that the models are reasonable for the CaO-SiO2-TiO2slag system. Keywords: coexistence theory; CaO-SiO2-TiO2slag system; viscosity ; calculation models.

Jan 1, 2004

By Johnna Muinonen

"The Thompson Mill processes ores from the Thompson and Birchtree Mines. While the Thompson ore has very little magnesium containing gangue, the Birchtree orebody consists of veins of massive sulphide in a rock matrix that contains a high proportion of magnesium silicate minerals. A significant fraction of the magnesium is floatable, which lead to MgO levels varying from 3-11 wt% in the Birchtree concentrate. The magnesium in the concentrate causes a higher operating temperature in the smelter, reducing furnace life.Birchtree ore represented 20-30% of the mill ore receipts prior to October 2003. Since then the fraction of Birchtree ore has increased to 50%. A reduction of the MgO in concentrate to less than 3% in the total mill concentrate was required to allow safe and economic smelter operation.In October of 2002 a miniplant was set up to simulate the Birchtree plant circuit. Several flow sheet modifications were tested that led to a proposal for a circuit having increased cleaning capacity for the scavenger concentrate and a recleaner on this concentrate. Addition of CMC in rougher cleaner feed was also found to be required. The solution was confirmed through pilot plant testing in the mill in December of 2002. A full-scale installation was designed, engineered, and installed between February and September of 2003 with commissioning in September and October of 2003. Target metallurgy was achieved one week after start-up on slurry to coincide with the Birchtree Mine tonnage increase. This paper highlights the development, design and commissioning stages of the project.The new MgO rejection circuit has successfully allowed the processing of Birchtree ores producing concentrate consistently below 3% MgO. In addition, the new circuit increased overall nickel recovery in the mill.INTRODUCTIONThe Thompson Nickel Belt located approximately 700km north of Winnipeg was discovered in the early 1950’s. Inco first produced nickel from the area in 1960. Over the years the mill has processed several ores from different ore bodies in the area. Currently the Thompson Mill processes two significantly different ores from two mines, Thompson and Birchtree. The Thompson ore is a massive sulphide orebody hosted in schist, containing feldspars, quartz and biotite. Thompson Ore is characterized by high nickel recoveries and clean, low MgO containing concentrates (<2.5% MgO). The Birchtree ore is ultramafic and contains a high percentage of Mg-silicates such as serpentine, chlorite, biotite, amphiboles and talc. Some of these Mg-silicates report to the nickel concentrate and prior to commissioning of the MgO rejection circuit the Birchtree nickel concentrate typically contained 5-8% MgO"

Jan 1, 2006

By Paul Singh

Blasting is an integral part of mining activity and is an inherently destructive process. The quality of the rock mass in which an excavation is being driven has a strong influence on the level of dynamic forces to which the rock can be subjected and sustain damage. Though each specific rock mass occurrence is unique, yet there are common rock mass features which influence the outcome of controlled blasting in a similar way. A field study was conducted which involved assessment of blast damage at several operating mines and blasting of small scale models. The effects of block size and strength, joint parameters, ground water, weathering of rocks and rock mass rating on the results of controlled blasting have been investigated and discussed in this study. The influence of number and thickness of weak layers on overbreak control has been discussed in the light of practical data. Critical particle velocity ranges for damage to rock masses with different qualities have been outlined. An approach for the judicious design of perimeter hole pattern and charge concentration has been proposed.

Jan 1, 2007

By S. Strömberg, A. Jokilaakso

Two complex copper concentrates and one arsenical nickel concentrate were oxidized in simulated flash smelting conditions using a laminar-flow furnace. The concentrates contained tetrahedrite as Sb-bearing mineral and arsenopyrite and gersdorfite as As-bearing minerals. At high temperatures and low oxygen potentials, Sb tended to vaporize, but with high oxygen potentials it was captured in mixed oxide phases with copper and iron. Arsenic was found to follow antimony in copper concentrates, although with less sharp contrast between low and high oxygen potentials. In the nickel concentrate studied, arsenic was found to vaporize from the gersdorffite particles and, subsequently, condense on the other particles.

Jan 1, 1998

In surface mining operations, ultra-heavy trucks operate on haul road networks which are typically from 10?40 km in length. These road networks are often not optimally designed and maintained and as a result, identifying and remediating road functional defects is problematic. Most surface mine operators agree good roads are desirable, but find it difficult to translate this into an effective road maintenance system. This paper presents a haul road maintenance management system which utilizes an assessment of rolling resistance based on a functional performance evaluation of a haul road, together with mine haul truck operating cost models to derive the optimal frequency of road maintenance. A typical application is presented which illustrates the potential of the technique to manage maintenance as and where needed with resultant reduction in total road user costs and an improvement in service provided for the road user. Keywords: Haul road, surface mining, road maintenance, transportation, pavement design

Jan 1, 2003

By Michelle Mouton, Johanna van Deventer, Jussi Vaarno

Mintek has been involved in numerous projects to remove Fe and Mn from dilute Co sulphate solutions by means of oxidative precipitation using air/SO2. Test work was done using a gas induction system, designed and supplied by Outotec. Various aspects, such as SO2 concentration, SO2 flowrate, impeller rotation speed and pH were investigated on a 2 m3 scale. Batch tests were performed using a residence time of 5 hours. Mintek has been involved in numerous projects to remove Fe and Mn from dilute Co sulphate solutions by means of oxidative precipitation using air/SO2. Test work was done using a gas induction system, designed and supplied by Outotec. Various aspects, such as SO2 concentration, SO2 flowrate, impeller rotation speed and pH were investigated on a 2 m3 scale. Batch tests were performed using a residence time of 5 hours. Impeller rotation speeds of 0-220 rpm were tested, and it seemed that speeds of between 80 and 220 rpm gave similar Fe and Mn removal rates. Co and Cu losses were generally below 1% and 5% respectively at pH 3.

Jan 1, 2007

By R M. Briggs

Kapowai Caldera Complex (KCC), located 10 km west of Tairua (eastern Coromandel Peninsula), is a late Miocene composite collapse caldera, formed during eruption of several small and large volume andesitic rhyolitic ignimbrites. Numerous epithermal Au-Ag mineral deposits and associated alteration zones at the KCC are related to caldera (rhyolite lava domes, intracaldera faults) or regional structures (faults). The main epithermal deposit exposed in the central KCC is associated with an E-W striking structural boundary fault that cuts the Welcome Jack rhyolite dome. Propylitic (calcite - chlorite) and sericitic (quartz - sericite) alteration haloes surround this deposit. Sporadic zones of sericitic alteration are also exposed within and on the margins of the Bulls Run rhyolite dome complex. Epithermal systems post-dated emplacement of these rhyolite domes, but were controlled by them. Propylitic alteration of ignimbrite in the floor of the Kapowai and Kauaeranga valleys is related to the major NE-trending Kapowai Fault which extends SW to south of Thames. Alteration along this fault pre-dates alteration associated with the rhyolite lava domes. Numerous sericitic and propylitic altered welded ignimbrite, rhyolite and andesite lava lithic fragments have been sampled from intracaldera ignimbrites, and although no direct source is known, they infer the presence of buried epithermal systems. Repeated epithermal activity at the KCC is inferred by the exposed epithermal deposits/alteration zones and the older buried geothermal systems. Silicic caldera volcanoes are considered to be critical volcanic environments for epithermal Au-Ag mineralisation in Coromandel, but are highly variable and need detailed stratigraphic, structural, petrologic, and geophysical studies to characterise them.

Jan 1, 1999

By Suzanne Young

The effect of LiF additions on liqt.1id1.:1s temperature and electrical conductivity over a wide range of cryolite bath ratios (1.0 to 1.5 weight ratio) was investigated. Results did not agree with multi-regression equations reported by Dewing and Choudhary over the entire region. New regression equations were developed. Reasons? are given for the differences. The models are used to discuss the economic implications of LiF additions to Hali cell electrolytes.

Jan 1, 1985

By M. Yavuz

Underground mining method selection (UMMS) is one of the most important issues in mining engineering. Underground mining method should be primarily selected to make use of underground resources optimally. It is nearly impossible to change the mining method once selected by the reasons of rising costs and mining losses. Because of these reasons, UMMS process is extremely important in mine designs and economics. The strategy of underground mining method selection has been studied by different researchers in the literature. Boshkov and Wright (1973) proposed a classification system; Morrison (1976) suggested a selection chart; Laubscher (1981) proposed a selection methodology; Nicholas (1981) presented a classification system; Hartman (1987) developed a selection chart and Miller-Tait et al. (1995) modified the Nicholas? system and developed the UBC mining method selection process. In reality, UMMS is one of the important Multiple Attribute Decision Making (MADM) problems and mining engineers have always some difficulties in making the right decision in the multiple criteria environment. To make a right decision on UMMS, all known criteria related to the mining method selection should be analyzed and the problem solved according to suitable decision making techniques. A review of the literature reveals that decision making techniques have been used for UMMS applications. Kesimal and Bascetin (2002), Bitarafan and Ataei (2004), Bascetin et al. (2006), Alpay and Yavuz (2007), Karadogan et al. (2008) and Samimi Namin et al. (2008) used decision making techniques in UMMS applications. In this paper, two different MADM methods: Analytic Hierarchy Process (AHP) and Fuzzy Multiple Attribute Decision Making (FMADM) are applied to select the optimal underground mining method for a chromite mine and final solutions are then compared. THE AHP METHODOLOGY The AHP method developed by Saaty gives an opportunity to represent the interaction of multiple factors in complex unstructured situations (Triantaphyllou, 2000). The method is based on the pair-wise comparison of components with respect to attributes and alternatives. A pair-wise comparison matrix n×n is constructed, where n is the number of elements to be compared. The method is applied for the hierarchy problem structuring. The problem is divided in to three levels: problem statement, object identification to solve the problem and selection of evaluation criteria for each object. After the hierarchy structuring, the pair-wise comparison matrix is constructed for each level where a nominal discrete scale from 1 to 9 is used for the evaluation as shown in Table 1 (Saaty, 1980; Saaty, 2000). The next step is to find the relative priorities of criteria or alternatives implied by this comparison. The relative priorities are worked out using the theory of eigenvector. For example, if the pair comparison matrix is A, then, [Amax=××- [1] ] To calculate the eigenvalue ??max? and eigenvector w=(w1, w2,..., wn), weights can be estimated as relative priorities of criteria or alternatives. [ ] Since the comparison is based on the subjective evaluation, a consistency ratio is required to ensure the selection accuracy. The Consistency Index (CI) of the comparison matrix is computed as follows: [CImax--= [2] ] where ?max is maximal or principal eigenvalue, and n is the matrix size. The consistency Ratio (CR) is calculated as: [CR= [3 ] where ?RI? Random Consistency Index. Random consistency indices are given in Table 2. [ ] Table 2. The consistency indices of randomly generated reciprocal matrices As a general rule, a consistency ratio of ?0.10? or less is considered acceptable. In practice, however, consistency ratios exceeding ?0.10? occur frequently. THE FMADM METHODOLOGY The FMADM methods have been developed due to the lack of precision in assessing the relative importance of attributes and the

Jan 1, 2009