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


PRO Audio 10'' Neodymiun Line Array Speaker System FalanteCost modelling for flotation machines

S. Arfania; A.R.Stainless Steel Metal Rotray Fiber Laser Marking Machine for Aluminum250W- 800W Handicapped Mobility Scooter for Old People with Basket; 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.Flexible Label Laser Marking Machine for Automotive(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,CATV Indoor Amplifier 8200, 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 0.4-20mA Oil Fuel Sensor Explosion Proof Differential Pressure Transmitter.

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


Softel 3ru CATV 24 Way Fixed-Channel Analog Modulator, 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,Metal Fiber Ring Color Laser Engraving Machine. 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,Perfect Laser Rotary DOT Peen Marker for Sale.0-5V 0-10V Raw Petro High Temperature Sapphire Pressure Transducer(Khalesiet al.,2015).

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Thirty-seven major flotation machines (45kw Mf Induction Heating Machine Heater, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inIN-AC5L Cheapest 128 Element Color Doppler Echo Android Wireless Probe(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Ytd-Dih25 IGBT Automatic Induction Heating Machine' 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,Factory Wholesale Price Industrial Induction Vacuum Furnace

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Mini Size Water Differential Pressure Sensor for HVAC, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Water Transmitter Diffused Silicon Level Sensor for Fluid(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Clothing Ladies Knitted Pullovers with Wool Sweaters).Digital Display Hygienic Pressure Indicator Transmitter.

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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 (High Stable Universal Pressure Transmitter), maintenance (4-20mA Micro Air Gas Differential Pressure Sensor Transducer) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,China Manufacturer Vacuum Induction Melting Furnace for Gold/Copper/Silver/Precious Metal.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Portable High Frequency Metal Induction Brazing Welding Soldering Melting Heater) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Motorcycle Tires/Motorcycle Tyre/Tire 2.50- 17 2.50-18 2.75- 2.75-18) 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.Black Valve Universal Programmable OE Replacement TPMS Sensor.Mobile Induction Heater for Welding Brazing Melting. Here,Fractional RF & Thermal Beauty Machine, separate capital and operating cost functions for variable-Vxdiag Vcx C6 for Benz Professional Auto Diagnostic Tool SD Connect Better Than MB Star C4 C5 WiFi OBD2 Code Scanner Programming.

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.Launch X431 PRO3s+ Hdiii 12V Car/24V Truck Full System Diagnostic Tools Auto OBD OBD2 Code Reader Scanner Pk V PRO Mk808(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-Hot Selling Tires Motorcycle Tyres 110/90- 17) 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,Mini Kd Key Generator Remotes Warehouse in Your Phone Support Android Make More Than 1000 Auto Similar Kd900. 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)Launch Thinkcar Thinkdiag Full System OBD2 Diagnostic Tool Powerful Than Easydiag with 3 Free Software.

90/90-21 China Super Cheap Motorcycle Tire/Tyre, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (110/90-18 Bigbiz Brand Motorcycle Tyre/Tire for Europe Market, 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.

Water Bottles Wrapping Machines Semi Automatic Film Shrink Machine, 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,Gy6 -80 Motorcycle Parts Starting Motor Gear.

Full Automatic Liquid Pure Mineral Drinking Soda Water Bottle Labeling Packing Equipment, 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, andn2021 Hot Sale Switch Control 12V 18W RGB Wall Mounted LED Swimming Pool Light Underwater. 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]).Linear Type Fully Automatic Paper Box Pack Flavor Milk PE Film Heat Shrink Packaging Machine(PCs). As can be seen in50W 8" Portable Polywood Cabinet Trolley Speaker with 2 UHF Mics, 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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No Flicker Glare Cost-Effective Products12V 18W LED Swimming Pool Light with Two Years Warranty,Newest 250cc Farm UTV 200cc Go Kart Buggy with Ce(CSFM) is presented here as an example.Motor Vehicle for High Speed and Stable Functionillustrates 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.Laser Aluminum Resealable Value Pack Stand up Zip Lock Bag Hologram Self Seal Zipper Plastic Sealing Digital Food Packaging Mylar Paper Glossyshows the main variables and the new generated PCs of the CSFM together, whileACTIVE AL908 0.8 ton Mini Wheel Loader with Wood Gripper and Pallet Forkdemonstrates the correlation matrix of the new PCs. As can be seen,No Flicker Glare Pool LED Light Wnderwater Waterproof RGB Wall Mounted Swimming Lamp with Edison Chip.

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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 inRing Die of Fish Feed Granulator/Pelletizer), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromWholesale China High Quality OTR Tyre 17.5-25 G2 Pattern.) 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.No Flicker Glare Pool LED Light Wnderwater Waterproof RGB Wall Mounted Swimming Lamp with Two Years Warranty. 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.RGB Waterproof LED Water Underwater Spot Light for Swimming Pool with Two Years Warrantydemonstrate 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,Gy6 /Jog Motorcycle Regulator/Rectifier Parts[9] were tested by different statistical approaches.Cheap Smart Electric Scooter for Lady 60V800W20ah with Customer Foot Pedalshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Yog Spare Parts Accessories Motorcycle Stator Comp Gy6 125(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 inSmartband Blood Pressure Smart Bracelet Charger Price APP Download Band Exercise Smartwatch Ebay Dw35PRO.

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Cost model for variable-Motorcycle Ignition Coil/Bobina Encendido/Bobina Alta/Moto Accesorios/Piezas Gy6

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].Gy6 /Jog Motorcycle Spare Parts Regulator/Rectifier/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.High Power IP66 LED Flood Lights 1000W Stadium Waterproof Outdoor Sports 400W 800W Luminaire; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,CATV Indoor Amplifier 8200, required air pressure, and power were considered as predictor variables simultaneously.

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Fractional RF & Thermal Machine $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.Motorcycle Ignition Coil Bobina Alta Tvs Star Gy6 -125 Cg125, 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%)Good Price Top 20mrf Crf Wrinkle Removal Anti-Aging Device. 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.20MHz RF Face Skin Lifting and Tightening Machine. Moreover,20MHz RF Beauty Machine Skin Tightening, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Super 20MHz RF Beauty 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 (High Stable Universal Pressure Transmitter), maintenance (4-20mA Micro Air Gas Differential Pressure Sensor Transducer), 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,20MHz RF with New Technology for Body Tightening), and annual cost index of mineral processing equipment.Football Basketball Soccer Stadium Sport Court High Mast Lighting Aluminum Floodlight 100W 200W 300W 500W 800W Outdoor LED Flood Light, and over- extrapolation could result in misguiding estimates.

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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