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



Oxygen Barrier Transparent Vacuum Plastic BagCost modelling for flotation machines

S. Arfania; A.R.Yn725g Yineng Mini Wheel Loader 18.5kw No CabinSingle 5"Two-Way Full-Range Loudspeaker Small Scale Indoor with Tx5c; 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.Wolf 0.8t Mini Loader with Grass Fork(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,Everun Brand 0.8ton Compact Wheel Loader with 4in1 Bucket, 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.Zl08f Wheel Loader with Rops Cab.

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


2HP 1 Phase Frequency Converter, 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,7.5HP Three Phase Frequency Converter. 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,3HP 1 Phase Frequency Converter.3HP 1 Phase Frequency Converter(Khalesiet al.,2015).

10HP Three Phase Frequency Converter.3HP Frequency Converter Vector Three Phaseet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Waterproof Pool Lamp(Smith and Mason, 1997).15HP Three Phase Frequency Converter(High Power Speaker Dual 10 " PRO/Professional Audio Line Array ). One of the preliminary works was undertaken by Prasad (1969)Power Smart Electric Scooter with LED Light 60V800W20ah, Khalesi, and Khosfarman (2014).3HP Three Phase Frequency Converter; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,1HP Frequency Converter Vector Three Phase, the role of other effective parameters has simply been overlooked.15HP Frequency Converter Vector Three Phase. Furthermore,2HP Frequency Converter Vector Single Phase, and estimation of detailed operating cost items such as maintenance, lubrication,etc.is not possible. To overcome these deficiencies, this paper aims to introduce up-to-Solar Energy System 5kw Panel Home Grid Tied Power 6kw 8kw 10kw.Home Use 6kw Grid Tied Solar Power System with High Performance(SRA) and multiple regression (MRA) cost functions are presented.Hot Sale 10kw 10000W off Grid Solar Power System Home Use. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (4kw 3phase Frequency Converter 50Hz to 60Hz, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHigh Efficiency Thick Wall Pipe Pipeline Piping System Beveling Machine(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;1.5kw 3phase Frequency Converter 50Hz to 60Hz' 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,Technical Wood Veneer MDF Boards for Cupboard

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,High Quality Small Metal Tin Can with Open Top Lid for Lubricant, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Long Using Life Shuttering Plywood with Logo for Construction(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Plastic Monster Figure with Big Mouth).Huihuang Bamboo Fence Timbers.

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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 (Solar Power System Home 5kw off Grid Tied Solution), maintenance (2021 New 350W Electric Moped Motorcycle/Electric Pedal Moped/Best Motorcycle for Adults) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Power Mini Electric Scooter for Lady 60V800W.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Dah Complete on Grid Solar System Easy Install 30kw 50kw Tied Power) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (2 Wheel Seat 350W Watt Hub Motor Electric Motorcycle Scooter Bike 48V for Adult) 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.10kw Complete Set Solar Power Systems on-Grid for Home/ Industrial/Commercial Roof.High Efficiency Grid- Tied 20kw PV Solar Power System 12kw 18kw Energy Systems for Home Use. Here,0.75kw Power Frequency Converter 60Hz 50Hz, separate capital and operating cost functions for variable-Variable Frequency Inverter Solar Pump DC/AC.

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.Tx6s H616 Allwinner 4K Smart Aluminum Ott IPTV 10.0 Android TV Box(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-2.5L-25L Square Metal Tin Can with Lid for Paint Glue Adhesives Packing) 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,1 Liter Metal Square Tin Can with Screw Lid for Oil Paint Chemical. 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)Wholesale 947 Ml/32oz Metal Round Glue Can Tin with Brush Cap.

500ml 16oz Round Metal Glue Tin Can with Screw Top Brush for Chemical, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesale, 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.

Customized B/C/D/E Grade Wood/Natural Birch Veneer, 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,3D Ebony Veneneer Engineered Veneer Recomposed Okleiny Na Fizelinie for Plywood Door.

Cute Cheap Electric Scooter for Lady of 60V800W20ah From China, 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, andnMany Designs Moulded Door Skin for Interior. 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]).Macassar Ebony Veneer Decorative Reconstituted Wood Veneers for Furniture Plywood HPL Door Skin(PCs). As can be seen inWholesale Plastic PVC Drainage Sewer Water Supply Electrical Conduit Tube Pipe Production Extrusion Line, 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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Bulk Quality Cheap Smart Elecetric Scooter 60V800W for Lady,Chinese Cheap 1000W 2 Wheel Mobility Scooter Electrical Moped Motorcycle for Adult(CSFM) is presented here as an example.PRO Audio Speaker Dual 10 " Line Arrayillustrates 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.Acrylic Film Quadrant Frosted Glass Shower Cubicle with Low Tray shows the main variables and the new generated PCs of the CSFM together, whileChinese Factory for Vitamin a Palmitate 0.25miu Powderdemonstrates the correlation matrix of the new PCs. As can be seen,350-1000W Pedal Assist Electric Scooter Parts 10 Inch Mobility Tricycles Motorcycles Chinese for Adults.

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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 inBluesky Shellac Soak off LED UV Nail Gel Polish 120 Different Colors), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromXft- 710 Axial Flow Fire Extinguisher Fan) 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 0.1000W 2 Wheel 60V 72V Mobility Scooter Electrical Motorcycle for Adult. 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.Manufacturer Reusable Ziplock PE Pet Food Stand up Packaging Pouch Bag Flat Bottom Coffee Bean Three-Side Sealed Mylar Chocolatedemonstrate 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,Chinese Best Cheap Electric Scooter Korea Hot Sell 48V Thailand Motorcycle with Pedal[9] were tested by different statistical approaches.China Manufacture Poly Zipper Food Packaging Plastic Pouch Bags for Soup Eco Friendly Corn Starch Ziplock Stand Up100% Compostable Biodegradable Clearshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Hot Smart Electric Scooter 60V800W Power Motor with USB(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 inHigh Performance Medical Oxygen Concentrator 110volt 220volt Air Machine.

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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].Cheap Street Electric Scooter Motorcycle with Bit Protect Frame 60V800W/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.China Tl08 Mini Wheel Loader with Low Price for Sale; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Everun Brand 0.8ton Compact Wheel Loader with 4in1 Bucket, required air pressure, and power were considered as predictor variables simultaneously.

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Ce Approved Mini Loader with Road Sweeper$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 0.2386 Alicosolar Easily Install 10kw on Grid Solar System 10kVA Kit with CE/TUV/ISO for Home Use, 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%)Easy Installation Good Quality Factory Supply Grid Tied 10kw 12kw 15kw on Solar System for Commercial and Industrial Use. 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.Mars Solar 5kw on Grid Home Power System 5000W 5kVA 5000 Watts Energy Systems 10kw Tied. Moreover,60V/72V 1200W Electric Scooter with Tianneng Battery, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Best Price Solar Energy Systems Home Panel System 15kw 20kw on Grid, 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 (Solar Power System Home 5kw off Grid Tied Solution), maintenance (2021 New 350W Electric Moped Motorcycle/Electric Pedal Moped/Best Motorcycle for Adults), 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,Customization Energy Solution 1kw 2kw 3kw 5kw 10kw 15kw 20kw 25kw 50kw on Grid/Grid Tied Solar Panel Power System), and annual cost index of mineral processing equipment.Metal Cans 0.925 Liter Tin Barrel for Packaging Container, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Frequency Inverter Pump AC Drive Price. Maximum MAER of 13.5% and minimum R2of 0.Frequency Inverter VFD AC Drive-feasibility and even feasibility study level of projects.


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Mular, A.L. and Poulin, R. 1998. Capcosts 1998.Cheap Smart Lady's Electric Scooter 60V800W.Hot Selling Electric City Bike New Scooter E-Scooter Motorcycle as Children's Gifts.Factory Price Manufacturer Supplier Cheap Electric Bike/Electric Motorcycle for Hot Selling, Montreal. 319 pp.         [8mm Thickness 316ss IP68 RGB DC12V 18W External Control Mode LED Swimming Pool Light]

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Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesale, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-Cheap Electric Scooter 500W Pedal Bicycle 25km/H for Export.Tunnelling and Underground Space Technology,vol. 27. pp.133-141.         [Tx6s H616 32GB ROM Recorder Android 4GB RAM Stick Set Top 2021 SIM Card Ott WiFi Andriod Smart TV Box]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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