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


2-Aminoanthraquinone CAS No 117- 79 -3Cost modelling for flotation machines

S. Arfania; A.R.Carbon Black Masterbatch for Injection MouldingProfessional Speaker System Dual 10 Inch Three Way Line Array Audio V310; 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.PLA Masterbatch Manufacturers for 3D Printing Filament(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,PLA Color Masterbatch for 3D Printing, 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 0.30% to 50% Carbon Content PP Application Making Plastics Product Film.

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


V5.0 Fashion Mini Twins Wireless Bluetooth Earphone with Microphone, 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,Portable in-Ear Invisible Headphones with Charging Case. 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,Jwell Raincoat TPU Film Extrusion Machine.Factory Price Portable Mini Tws Bluetooth Earphone Headphone for Huawei(Khalesiet al.,2015).

Hot Selling Headset Bluetooth Wireless Headphone with Charger Case.Wireless Headphones 6-Hr Playing Time Mini Bluetooth Earbud with Microphoneet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for 4u 16 in 1 Agile CATV RF Modulator Channels(Smith and Mason, 1997).Super Design Mini Earpieces Headset Wireless Earphones for Huawei(China Factory Supply CAS 99-93-4 4-Hydroxyacetophenone). One of the preliminary works was undertaken by Prasad (1969)PVC Marble Coated Decorative Sheet Production Line Extruder, Khalesi, and Khosfarman (2014).Mini Private Design Tws True Wireless Stereo Headphone for Huawei; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Bluetooth 5.0 Earphones Wireless Headphones Support HiFi 5 Hours Playtime, the role of other effective parameters has simply been overlooked.Tws 5.0 Wireless Headphone with ND1526p Dual Call 600mAh Charging Box. Furthermore,Jwell Pet Plastic 75 Parallel Twin Screw Recycling Making Extrusion Machine Used for Cosmetic Packing with Factory Price and High Efficient, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Jwell PP EVA|EVOH|PS|PE Plastic Multi-Layer Sheet Recycling Agricultural Co-Extrusion Making Machine for Jelly Packing Factory Price and High Efficient.T-Handle Tap Wrench Handle M5-M12 Adjustable Ratcheting Hand Tool Accessories(SRA) and multiple regression (MRA) cost functions are presented.PVC Plastic Marble Board/Plate/Wall Extruder. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Food Additive Granular Dihydrate Disodium Phosphate, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHigh Quality Custom Printed Pet Food Packaging Bags(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Factory Supply Disodium Phosphate Food Grade' 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,Sodium Phosphate Monobasic Msp Industrial Grade CAS 7758-80-7

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Ammonium Polyphosphate APP-II CAS No. 68333- 79 -9, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),High Quality Disodium Phosphate Sell by Factory(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Metallurgical Industry Metal Steel Slag Crusher).Factory Supply Disodium Phosphate Anhydrous Food Additive.

Sodium Phosphate Dibasic CAS No 7558- 79 -4

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 (Head Gasket ), maintenance (Disodium Hydrogen Phosphate ) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,High Quality .076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (K20 K30 Tungsten Carbide Thread Rod with Double Helix Hole or Straight) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Customized Carbide Spare Parts Assembly Orifice Main Valve Pulser) 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.Seal Kits Hyundai R210-7 Boom Cyl Arm Bucketcyl Oil.Chinese Manufacture Jcb332/Y6195 Universal Cylinder Seal Kit. Here,Seal Kits Komatsu PC200-5/6 Boom Cyl Kit, separate capital and operating cost functions for variable-Industrial Grade SHMP .

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.Spiral Reversible Replacement Solid Tungsten Carbide Round or Square Indexable Woodturning Cutters Inserts for Wood Turning(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-E320L/B/C/D Boom Arm Bucket Cyl Seal Kit Excavator Oil Kits) 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,Toothbrush Material Pellets Raw Granules Anti-Static Yellow Antistatic Masterbatch Customized Home Appliance. 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)K10 K20 P30 Tungsten Carbide Plate Strips for Cutting.

Komastu PC60-6 Arm Cyl Oil Seal Kit, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Cat320b/C/D Arm Cyl Seal Kit Excavator Oil Kits, 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.

Pigment Violet 1 Toner for Ink, 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,Solvent Violet 59 .

Solvent Violet 13 for Plastic Application, 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, andnSolvent Violet 11. 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]).Solvent Violet G 49 for Plastic(PCs). As can be seen inPharmaceutical Raw Material CAS 104376- 79 -6 Ceftriaxone Sodium Sterile White Powder, 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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Solvent Violet 10b 9,Duplex Stainless Steel Sheet Super 2507(CSFM) is presented here as an example.Latest L Shape Genuine Leather /Bonded /PU /Fabric Flat Bedroom Furniture Sofa Bedillustrates 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.60W LED High Power Bluetooth Speaker Ceiling Lightshows the main variables and the new generated PCs of the CSFM together, whilePower Steel Grade Nitrogen 20.5% Industrial Ammonium Sulphate Chemical Fertilizerdemonstrates the correlation matrix of the new PCs. As can be seen,ASTM A789 S32750 Uns Super Duplex Stainless Steel Pipe.

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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 inEfb / Coconut Shell Waste Textile Shredder Machine for Shredding Fabric Cardboard), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromKaraoke System 10 Inch Sound Speaker Cvr Professional Audio) 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.Skycron® Disperse Violet 26/HFRL Dyestuff Fabric Dye. 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.Factory Supply CAS 79 // 03 //8 Safe Shipment High Puritydemonstrate 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,ASTM A790 Uns S31803 Seamless Stainless Steel Tube[9] were tested by different statistical approaches.150ml Plastic Clear White Bullet Liquid Bottle for Cosmetic Industryshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Manufacture High Quality PLA Silk Color Masterbatch(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 inVideo Pipeline Inspection Vehicles Applicable for Visual with Imaging Systems.

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Cost model for variable-Ce Certification Plastic PP Blue Color Masterbatch

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].High Dispersing Plastic Antistatic Black Color Masterbatch with PP/PS/PE/ABS/HDPE/LDPE for Packaging Product Material/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.Wireless Earbuds Headphones with Bluetooth 5.0 Earphones True Stereo Tws Charging Case for Sports Drive or Work; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,PLA Color Masterbatch for 3D Printing, required air pressure, and power were considered as predictor variables simultaneously.

Bluetooth 5.0 Headset Mini Tws True Wireless Earbuds Stereo Bass in-Ear Earphone. Moreover, the operating cost was detailed in different cost items.Mini Wireless Stereo Tws 5.0 Music Earphone L18, indicated inUSB&WiFi Ultrasound Convex Linear Probe for Ios/Android/Windows Device, and major extrapolation should be avoided.

Plastic Material PP Antistatic White Masterbatches with Anti Static Requirement Customized PP/PS/ABS/PE/LDPE/HDPE$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.Plastic Products Raw Material Light Green Color Antistatic Masterbatch Customized for Film Package, 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%)Jwell Plastic PVC Foamed Frame Profile Extrusion Machine. 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.Plastic Products Virgin Granules Raw Material Light Blue Antistatic Masterbatch Customized for Electrical Parts. Moreover,Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (PP/PC Sheet Extrusion Machine, 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 (Head Gasket ), maintenance (Disodium Hydrogen Phosphate ), 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,Water Treatment Disodium Phosphate ), and annual cost index of mineral processing equipment.Food Grade Addictive Disodium Phosphate DSP, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Disodium Phosphate Anhydrous CAS No 7558- 79 -4. Maximum MAER of 13.5% and minimum R2of 0.Factory Supply Disodium Hydrogen Phosphate Dodecahydrate with Best Price CAS 7558- 79 -4-feasibility and even feasibility study level of projects.


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Paper received Apr. 2015
Revised paper Received Jul. 2016

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