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



PRO Audio Double 10 Inch Line Array Speaker Professional Outdoor PA SystemCost modelling for flotation machines

S. Arfania; A.R.O2 Oxygen Sensor for Honda Accord 2.3L 4 Cyl F23A4 2000-2002 234-9014Factory Direct Sale Dimethyl Gonane 702- 79 -4; 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.6 Cyl Head and Rotor (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,Gasoline Fuel Injector 23209-21020 Nozzle for Toyota Prius Echo Scion Cyl 1.5L 1nz, 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.Pigment.

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


Flame Retardant Ammonium Polyphosphate , 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,Plastic Sheet Machine PC Polycarbonate Solid. 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,PMMA GPPS Sheet/Board Plastic Extruder Machine/Making Machine.PC/PMMA/GPPS Optical Plate/Board Extrusion Making Machine/Extruder(Khalesiet al.,2015).

Jwell High Quality Pet Sheet Extrusion Machine for Protective Mask.Disodium Phosphate Anhydrouset al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Karaoke Wireless Portable Wooden Bluetooth PA Speaker(Smith and Mason, 1997).PC/Polycarbonate/GPPS/PMMA Sheet Extruder Machine/Plastic(1gallon Round Metallic Tin Can with Metal Handle for Paint). One of the preliminary works was undertaken by Prasad (1969)Uns S31254 En 1.4547 F44 Price Per Kg Super Austenitic Stainless Steel Round Bar Rod, Khalesi, and Khosfarman (2014).Super Duplex Stainless Steel Bar by Zeron100 ; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,S32750 Uns Super Duplex Stainless Steel Bar, the role of other effective parameters has simply been overlooked.Against Wall Australian Freestanding Acrylic Bathtubs. Furthermore,2507 Uns S32750 Duplex Stainless Steel Sheet / Plate, 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-Endless Pool.New Design Indoor Corner Massage Jetted Whirlpool Bath Tub Acrylic Bathtubs for 2 Adults with Pillow and TV(SRA) and multiple regression (MRA) cost functions are presented.Outdoor Jet Surf Massage Bubble SPA Swimming Pool Hot Tub Combo. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Plastic Products Colorful Pellets Resin Raw Material Light Green Color Antistatic Masterbatch Customized, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inScooter / Motorcycle Electric Motor Power 800W 1kw 2kw 3kw(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Endless Swimming Pool' names:

Channing Small Stand Alone Bath White Best Hot Tub Acrylic Freestanding Baby Tubs : based on 36-foot,Whole Sale Home Antique Style Large Acrylic Freestanding Bathtub,Milling Machine Tool F1 Type Boring Head with Shank Adapter for,Topstar Looking for Spain After Sales Service Office to Cooperate Our Plastic Injection Molding Machine and Auxiliary Equipment, and level control

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,Factory Price Fully Automatic Dustbin Injection Molding Machine

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Jwell TPU Matt Cast Film Machine, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),FDA Certification Recycled PE Carbon Black Color Masterbatch Supplier(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (542.4 X 54.7mm for Bar Club Supermarket Store Advertising LCD Signage Shelf LED Screen).Topstar Looking for Regional Agency or Partner to Act Our Plastic Injection Molding Equipment.

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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 (Plastic Raw Materials Black Color Masterbatches China Supplier), maintenance (35% Blowing Film Grade Carbon Black Masterbatch Manufacture) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Uns S31703/AISI 317L Stainless Steel Sheet/Plate/Coil/Pipe/Flange/Fittings/Bolt & Nuts.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (2021 New Design Plastic Injection Molding Machine Made in China) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Carbon Black Masterbatch for Injection Moulding) 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.PLA Masterbatch Manufacturers for 3D Printing Filament.PLA Color Masterbatch for 3D Printing. Here,30% to 50% Carbon Content PP Application Making Plastics Product Film, separate capital and operating cost functions for variable-V5.0 Fashion Mini Twins Wireless Bluetooth Earphone with Microphone.

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.Portable in-Ear Invisible Headphones with Charging Case(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-Jwell Raincoat TPU Film Extrusion Machine) 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,Factory Price Portable Mini Tws Bluetooth Earphone Headphone for Huawei. 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)Hot Selling Headset Bluetooth Wireless Headphone with Charger Case.

Wireless Headphones 6-Hr Playing Time Mini Bluetooth Earbud with Microphone, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Super Design Mini Earpieces Headset Wireless Earphones for Huawei, 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.

PVC Marble Coated Decorative Sheet Production Line Extruder, 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,Mini Private Design Tws True Wireless Stereo Headphone for Huawei.

Bluetooth 5.0 Earphones Wireless Headphones Support HiFi 5 Hours Playtime, 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, andnTws 5.0 Wireless Headphone with ND1526p Dual Call 600mAh Charging Box. 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]).Jwell Pet Plastic 75 Parallel Twin Screw Recycling Making Extrusion Machine Used for Cosmetic Packing with Factory Price and High Efficient(PCs). As can be seen in10 Inch Powered PA Speaker Full Range Stereo System, 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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T-Handle Tap Wrench Handle M5-M12 Adjustable Ratcheting Hand Tool Accessories,PVC Plastic Marble Board/Plate/Wall Extruder(CSFM) is presented here as an example.Single 10'' Two Way Line Array PRO Audioillustrates 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.New Electric Beatiful on Road 800W Scooter E-Motorcycleshows the main variables and the new generated PCs of the CSFM together, whileFlood Light 800W IP65 Waterproof Outdoor Lighting 80000 Lumens LED Floodlightdemonstrates the correlation matrix of the new PCs. As can be seen,Food Additive Granular Dihydrate Disodium Phosphate.

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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 in300ml Sprayer Bottle for Flooring Cleaner Rd-815), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromSamsung 55inch 3X3 Digital Signage Display Screen 3.5mm Narrow Bezel) 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.E320L/B/C/D Boom Cyl Seal Kit Excavator Oil Kits. 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.4.8kwh Multi-Function Solar Energy Lithium Battery Ion for Home Portable Power Generatorsdemonstrate 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,Jwell Plastic PVC Decoration Wallboard Profile Machinery/ Extruder Machine[9] were tested by different statistical approaches.2385 Alicosolar Easily Install 10kw on Grid Solar System 10kVA Kit with CE/TUV/ISO for Home Useshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Disodium Phosphate Food Grade Manufacturer(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 inStainless Steel Horizontal Chilling Vat for Milk.

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Cost model for variable-99% Tech Grade Disodium Phosphaten Used as Water-Softening Agent

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].Sodium Phosphate Monobasic Msp Industrial Grade CAS 7758-80-7/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.Ammonium Polyphosphate APP-II CAS No. 68333- 79 -9; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Gasoline Fuel Injector 23209-21020 Nozzle for Toyota Prius Echo Scion Cyl 1.5L 1nz, required air pressure, and power were considered as predictor variables simultaneously.

High Quality Disodium Phosphate Sell by Factory. Moreover, the operating cost was detailed in different cost items.Factory Supply Disodium Phosphate Anhydrous Food Additive, indicated inWLAN WiFi Yagi Antenna, and major extrapolation should be avoided.

Head Gasket $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.Disodium Hydrogen Phosphate , 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%)High Quality . 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.K20 K30 Tungsten Carbide Thread Rod with Double Helix Hole or Straight. Moreover,Customized Carbide Spare Parts Assembly Orifice Main Valve Pulser, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Seal Kits Hyundai R210-7 Boom Cyl Arm Bucketcyl Oil, 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 (Plastic Raw Materials Black Color Masterbatches China Supplier), maintenance (35% Blowing Film Grade Carbon Black Masterbatch Manufacture), 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,Chinese Manufacture Jcb332/Y6195 Universal Cylinder Seal Kit), and annual cost index of mineral processing equipment.Seal Kits Komatsu PC200-5/6 Boom Cyl Kit, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Industrial Grade SHMP . Maximum MAER of 13.5% and minimum R2of 0.Spiral Reversible Replacement Solid Tungsten Carbide Round or Square Indexable Woodturning Cutters Inserts for Wood Turning-feasibility and even feasibility study level of projects.


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Niazi, A., Dai, J.S., Balabani, S., and Seneviratne, L. 2006.Uns S32750 2507 S32760 F55 1.4501 Super Duplex Stainless Steel Bar.Journal of Manufacturing Science and Engineering,vol. 128. pp. 563-575.         [New Model V8 D&Bstyle Dual 10 Inch Three Way Line Array Speaker]

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Super Design Mini Earpieces Headset Wireless Earphones for Huawei, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-Mini Wireless Stereo Tws 5.0 Music Earphone L18.Tunnelling and Underground Space Technology,vol. 27. pp.133-141.         [Motorcycle Muffler Assy/Exaust Pipe for Scooter Parts Gy6 50/125/150]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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