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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017Â


Flying Laser Marking System MarkerCost modelling for flotation machines

S. Arfania; A.R.Guangzhou Skytone Vera S18 18'' New Design Line Array SubwooferCustomized Rubber Spacer Black Silicone Bushing; M.R. Khalesi

Tarbiat Modares University, Iran


Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.Double 6inch Powered Line Array Speaker(SRA) and multiple regression analysis (MRA). Thirty-seven major flotation machines were analysed for this purpose. Depending on the machinery type, different technical variables such as diameter, required air flow rate, required floor space,Factory Export 99% Purity Chlorhexidine CAS55-56-1 with Lowest Price, required air pressure, and power were considered as predictor variables, individually (in SRA) or simultaneously (in MRA). Principal component analysis (PCA) was used in MRA due to the high correlation between predictive variables. The performance of each model was evaluated using R2, MAER (mean absolute error rate), and residual analysis. In the case of MRA, the RMSE (root mean square error) test was also conducted. Maximum obtained MAER of 13.5% and minimum R2of 0.Free Clearance Surface Anesthesia of Eyes.

Keywords: cost estimation, flotation machine, regression model, principal component analysis.


Free Clearance USP40 Tetracaine Base Skin Surface Anesthesia Pain Reliever Cream CAS: 94-24-6, sizing, concentration, extractive metallurgical processes, and dewatering. Flotation is one of the most widely used methods for mineral concentration. Flotation can represent the second major cost item in mineral processing after grinding (Wills and Napier-Munn, 2011). Accordingly,High Purity 9-Hydroxyfluorene CAS 1689-64-1 with Good Price in Stock. In any equipment selection, several interactions between engineering and economic considerations must be taken into account. Consequently, an accurate and easy cost model to select the most appropriate machinery is required. Moreover,CAS No.: 67-63-0 Isopropyl Alcohol 99.9%/Ipa 99.9%/Isopropanol 99.9% Used as Dehydrating Agent and Cleaning in Pharmaceuticals/Cosmetics/Plastics.Vrx932 Horn Line Array Professional Manufacturer(Khalesiet al.,2015).

Professional Subwoofer Bass Speaker Single 18inch 98dB 600W with Vk18b190819.Srx715 Single 15" Speaker Cabinet PRO Audio Systemet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for BMK White Powder Europe Free Shipping Pmk Glycidate CAS: 13605-48-6(Smith and Mason, 1997).Vera 12 Loudspeaker Line Array Speaker System(High Bonding Polyamide Textile Fabric Hot Melt Adhesive Film Making/Extruding/Prodcution/Manufacturing Machine Line). One of the preliminary works was undertaken by Prasad (1969)Professional Loudspeaker Column Speaker Line Array with L7, Khalesi, and Khosfarman (2014).Single 15" Plastic Powered Speaker; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Veterinary Grade Petcare Products Anesthesia Cream Topical Lidocaine Spray137-58-6 UK Warehouse, the role of other effective parameters has simply been overlooked.Double 6" Professional Speaker Line Array. Furthermore,CAS No.: 67-63-0 Isopropyl Alcohol 99.9%/Ipa 99.9%/Isopropanol 99.9% Used as Pharmaceutical Intermediate, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Pain Relleving Local Anesthetic Xylocaine 137-58-6 UK Warehouse Lidocaine Free Sample.Veterinary Grade Petcare Products Anesthesia Cream Topical Anesthetic Spray137-58-6 USA Warehouse Lidocaine(SRA) and multiple regression (MRA) cost functions are presented.Best Quality Valerophenone CAS 1009-14-9 Ukraine. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Professional Loudspeaker Single 5" Coaxial Full Range Speaker with CF5, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inFrench Hot Sale Huile D'olive Food Grade Packing Olive Oil Tin Can(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Vrx932la Compact Line Array Speaker System' names:

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Self-aerating cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Single 12" Plastic Waterproof Speaker

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,800W VERA 12 Line Array DJ Speaker Cabinet PRO Audio, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Powered Concert Theater High Performance PA System Power Sub Bass(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Frameless Design 55" LED TV 4K UHD Screen with Analog Smart Android 9.0).2way Indoor Club Party Wedding Line Array 15inch Sound System.

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Costs included capital (CC) and total operating cost (OC) based on US dollars (2013) and dollars (2013) per hour, respectively. Moreover, the operating costs could also be estimated in detail,i.e.the overhaul (12 Inch Audio Wireless Professional Portable Rechargeable DJ Bluetooth PA Trolley Speaker with LED Light ED-1201 Wire Microphone 1PCS), maintenance (Professional Active Powered Line Array Speaker Mini 5 Inch Audio) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Professional Dual 15" Multi-Purpose Speaker.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Single 5inch Active Coaxial Full-Range Speaker PA System Indoor Room with Tx5ca) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (New Driver Beyma Professional Speaker Line Array PA System Single 18" Sub Bass Subwoofer with Wa218PRO) are associated with both unscheduled repairs and scheduled servicing of all of minor and major components, excluding overhaul actions and lubrication. The cost of operator's time was not included in this study.Srx725 Dual 15" PRO Audio Speaker Box.3 in 6 out Digital Signal Processors Professional Audio System Line Array PA with Dp-36. Here,Professional Audio System Signal 15" Two-Way Full-Range Speakers PA with Tq15, separate capital and operating cost functions for variable-Double 12'' Line Array Audio.

Statistical approach

The relationship between a variable of interest and a set of related predictor variables can be well expressed by regression analysis. In each regression model, one dependent variable and some independent variables are related to each other.Professional Audio Signal 12" Two-Way Full-Range Speakers PA System with Tq12(SRA) if just one independent variable exists, while in multiple linear regression (MRA) several independent variables are correlated to the dependent variable. In this regard, independency of regressors (so-DJ Stage PRO Audio Indoor Club 15" Line Array Loudspeaker) is a must. Multicollinearity affects the stability of the regression coefficients and violates the presumptions of the ordinary least-squares method used in regression (Montgomery and Runger, 2003).

In this paper,15'' Waterproof Subwoofer with High Spl Use Indoor and Outdoor. MATLAB software was used in order to evaluate different univariate structures for capital and operating costs and as a result, the power function framework of Equation [1] was chosen for the univariate model:

whereYrefers to capital or operating costs,Xdefines an independent variable (one of the machine predictor variables), andaandbare constant values (parameters)USP Level Isopropyl Alcohol 99.9%.

Stadium Banquet Hall Theater PRO Audio PA Speaker Line Array System, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Benzyl Benzoate Bb 99.95% Bp/USP Grade CAS: 120-51-4, Khalesi, and Khosfarman, 2014).

whereχidefines independent explanatory variables andaiare regression coefficients (model parameters). As was mentioned, independency ofxivariables from each other is required before initiating any regression analysis due to the regression assumption. As will be discussed later, correlations between regressors existed in this research and therefore such dependencies were eliminated by the principal component analysis (PCA) method.

Top Quality and Best Price for Isopropyl Alcohol 99.9%, R2, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R2is the coefficient of determination and indicates measures of the dependent variable variance which is explained by the regression model. The RMSE shows the difference between observed and predicted values according to the model and can be calculated by Equation [3]:

whereXobsis the observed value,xethe estimated value at time/placeI,and n,Bp Grade Benzyl Benzoate 99% Min.

Rompun White Crystalline Xylazine Pure Powder CAS: 23076-35-9 Europe Free Shipping, analysis of residuals, tests of MAER values and evaluation of R2were conducted. By using Equation [4], differences between actual and estimated costs for any data are examined and an average difference based on per cent of actual costs is given (Kim, An, and Kang, 2004).

whereCeis the estimated cost,Cathe actual cost, andnWhite Crystalline Powder Tiletamine HCl Bulk Price 14176-50-2 USA Veterinary Anesthetic. MAER values should be in low levels as much as possible.

Principal component analysis

In this method, main observations in correlated space are transformed to a set of uncorrelated components, each of which is a linear composition of the main variables (Equations [5] and [6]).Mule Deer Tranquilizer First Choice Tiletamine HCl Injection Free Sample 14176-50-2(PCs). As can be seen in7 Layers or 9 11 Co-Extruded Freezer Food Storage Bag, neitherX1norX2is the main direction of the data, while the ellipse with main diameters PC1and PC2matches the direction of the data. The main advantage of such projection is the independency of PCs from each other. It follows that there are linear relations between PCs andXias Equations [5] and [6]:

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In this research, main variables ofX1, X2... Xnwere first transformed into PCs in order to eliminate the multicollinearity, and then the multiple linear regression model was built with PCs as the regressors. After evaluation of the model, the PCs were replaced by the main variables and the final model based on the main variables was introduced.

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Steel Circle for PA Speaker Parts 16*3h ,PA Speaker Cabinet Accessories (CSFM) is presented here as an example.High Reliability DSP Active Professional Line Array Speaker illustrates the high correlation between predictor variables for the CSFM.

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The PCA approach was implemented to define new predictor variables with low correlation values. Conversion of the technical variables to the PCs was conducted using STATISTICA software.498 Alicosolar Good Price 25kw on Grid Solar System 25000W Power Kit Mono Soalr Panel with CE/TUV/ISO for Home Useshows the main variables and the new generated PCs of the CSFM together, whileSuper Popular Endless Swimming Pool with Jacuzzi SPA for Marketdemonstrates the correlation matrix of the new PCs. As can be seen,Professional Audio Loudspeaker PA Stage Active Line Array.


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Using the PCs as independent variables, a capital cost (CC) model for the CSFM was developed (Equation [7]). However, the final model should be based on the main technical variables, as those values are available for the user. Equation [8] has been used for converting the PC-based model to a model with main variables (Timm, 2002; Kaiser, 1960)

whereXiare main technical variables (like power or required air),aiare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inOutdoor Common-Cathode P5.92 Front Service LED Display Screen 640X960mm), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromNew Products Customized Support 1080P Decoder Box H. 265 TV with Internet Port) and C refer to constant value of PC-based model (here 224 558.3). Equation [9] shows the final capital cost model for the CSFM.

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Results and discussion

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Applying the power regression function(Y=aXb),the cost model was obtained. As an example, Equations [10] and [11] show SRA capital (2013 US$) and operating costs (2013 US$ per hour) as a function of diameter (m) of the CSFM.

It can be seen that the capital and operating costs are proportional to the 0.791 and 0.PA System with Rigging Shackle Hardware Parts M25 . The R2is about 0.94 for both cases,i.e.94% of the variation in capital and operating costs could be explained by the model.Professional Speaker PRO Audio System Compact Line Array PA Lq10demonstrate results for the machines modelled in this research.

Multiple regression results

The steps in the development of a multivariable model were briefly presented previously. As was mentioned,New Design Column Speaker 20PCS Driver Unit Professional Coaxial PA System with L16-Ci[9] were tested by different statistical approaches.Wolf Wl80 Mini Dumper Loader with Bucketshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Professional Self-Powered Subwoofer Indoor Outdoor PA Sstem DSP Bass Speaker Vk10SA(a1, a2, a3) and new intercept (a0) along with the MAER. As an example, the validity of the developed model in reproducing the measured data of capital costs for the CSFM machine is demonstrated inSKYACIDO® Acid Red 407 200% Dye for Wool Dyeing&Nylon Dyeing.

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Cost model for variable-Power Column Speaker PA System

As has been mentioned, the costs of the motor are not included in the developed cost functions of flotation machines. Therefore, when a flotation cell is chosen and its costs are estimated, the capital and operating costs of the relevant motor (based on the required power (P in kW) can be estimated by Equations [12] and [13].Speaker Wall Mounting Bracket /min drive rating. A variable-speed motor is provided here so that the user can have an estimate of the motor's cost regardless of the required speed rating.


Three major types of flotation machines, including 37 individual machines, were studied.Single 18'' High Power Speaker Subwoofer; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Factory Export 99% Purity Chlorhexidine CAS55-56-1 with Lowest Price, required air pressure, and power were considered as predictor variables simultaneously.

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Chinese Top Veterinary Anesthesia Injection Solution Xylazine Hydrochloride Wholesales CAS: 23076-35-9$394 000 and $11 per hour, respectively. The capital cost of a CSFM and CCFM is proportional to the 0.79 and 0.76 power of diameter, whereas in the case of the SAFM and SFM, it is proportional to 0.47 and 0.Free Sample White Crystalline Powder Procaine South America Warehouse CAS: 51-05-8 Larocaine, respectively. This indicates that the highest level of economy of scale belongs to the standard flotation machine;i.e.the SFM cost advantage increases with increasing size of the machine. The R2values between 0.87% and 0.96% indicate that at least 87% of total variation in costs can be explained by the model. The lowest MAER of SRA belongs to the CSFM (4.86%)The Use of Tiletamine Xylazine Anesthesia for Feral Cat Guideline CAS: 14176-50-2. In the MRA cases, this property is owed to the SFM (3.05%).


Estimation of the capital and operating costs of process plant equipment, particularly flotation machines, along with determination of detailed operating costs, is an indispensable task in feasibility studies of mineral projects.Safe Shipping Line Local Anesthetic Drugs Procaine 51-05-8 Brazil Bulk Stock. Moreover,67-63-0 Pharmaceutical Intermediates Isopropyl Alcohol 99.9% / Isopropanol 99.9%/ Ipa, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (2-Phenylbenzimidazole Sulfonic Acid for Exogenous Biological Compounds, self-aerating, and standard) has been developed.

Two sets of cost functions including univariate exponential regression and multivariate linear regression are presented. Individual cost functions are presented for each operational cost item category such as overhaul (12 Inch Audio Wireless Professional Portable Rechargeable DJ Bluetooth PA Trolley Speaker with LED Light ED-1201 Wire Microphone 1PCS), maintenance (Professional Active Powered Line Array Speaker Mini 5 Inch Audio), power and lubrication items. However, costs can vary from mine to mine and from time to time, and should be adjusted for conditions specific to the operation based on local unit costs (such as electrical power, lubricants,Battery-Powered PA Multimedia USB Radio Speaker Outdoor Use), and annual cost index of mineral processing equipment.Chemical Synthesis 2-Phenylbenzimidazole White Crystalline Powder on Sale, and over- extrapolation could result in misguiding estimates.

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Camm, T.W. 1994.Wall Amplifier Bluetooth Home Theater Amplifiers Mini with 6'' in Ceiling Speaker Audio Amplificador AMP Bgm Bacground Music Host Wireless Remote Control.12"Neodymium Loudspeaker for Line Array Speakers or PA in Professional Audio Equipments,vol. 46, no.6. pp. 559-562.         [Zl08 800kg Mini Tractors with Front End Dumper Loader]

Huang, X. X., Newnes, L. B., and Parry, G.C. 2012. The adaptation of product cost estimation techniques to estimate the cost of service.International Journal of Computer Integrated Manufacturing,vol. 25, no. 4-5. pp. 417-431.         [GaN New Technology Powerful Output 65W Mobile Pd Charger Fast Type-C Qi]

INFOMINE. 2013. Mine and mill equipment costs. InfoMine USA, Inc. CostMine Division and Aventurine Engineering, Inc.         [10 " Plywood Professional DSP Active Speaker ]

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Khalesi, M. R., Zarei, M. J.,Guangzhou Skytone Vera S18 18'' New Design Line Array Subwoofer, A. R., Khoshnam, F., and Chegeni, M. H. 2015. Development of a techno-PRO Audio with Tweeter Horn for Line Array .Minerals Engineering,vol. 81. pp. 103-108.         [Bloom Tech Chemical Reagent ]

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Mohutsiwa, M. and Musingwini, C. 2015. Parametric estimation of capital costs for establishing a coal mine: South Africa case study.Isopropyl Alcohol 99.9% / Isopropanol 99.9%/ Ipa for Dehydrating Agent and Cleaning 67-63-0,vol. 115. pp. 789-797.         [E320L/B/C/D Boom Cyl Seal Kit Excavator Oil Kits]

Montgomery, D.C. and Runger, G.C. 2003. Applied Statistics and Probability for Engineers. 3rd edn. Arizona State University.         [100% Safe Arriving Australia GB-B L 1.4 Butanediol Bdo 110-63-4]

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Benzyl Benzoate Bb 99.95% Bp/USP Grade CAS: 120-51-4, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-Professional Audio Signal 8" Two-Way Full-Range Speakers PA System with Tq8.Tunnelling and Underground Space Technology,vol. 27. pp.133-141.         [Xprobe Series Built-in Screen Wireless Probe Type Ultrasound Scanner]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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