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


Linear Type Fully Automatic Paper Box Pack Flavor Milk PE Film Heat Shrink Packaging MachineCost modelling for flotation machines

S. Arfania; A.R.45cm Offset Satellite TV Antenna with 200 Hour UV Test3000W Grid Tied Solar System for Home Use; 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.5.8g Omni Antenna/Dual Frequency Antenna 2.4G 5.8g/2400-2500MHz Omi(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,45cm Offset Satellite Dish TV Antennas, 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 0.150ah Lithium Iron Phosphate .

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


2.4-2.5GHz/5-5.8GHz Dual Frequency WiFi Antenna Internet for Things, 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,E3/L3 17.5-25 20.5-25 1800-25 Durable Tyres for Scrapers. 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,C Band Satellite TV Antenna 150cm.Eougem Original Cheap Radlader 0.8ton with Standard Bucket Made in China(Khalesiet al.,2015).

Dsola ODM/OEM Design High Efficient Mc4 Connector 3 in 1.Portable OEM Rechargeable 12V 40ah 80ah Lithium Ion Battery with MPPT and Inverteret al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for China Tl08 Mini Wheel Loader with Low Price for Sale(Smith and Mason, 1997).Mc4t-Branch Connector for Parallel Solar Panel Pair Male and Female(20W 50W Portable Jpt/Ipg Laser Marking Machine in Germany). One of the preliminary works was undertaken by Prasad (1969)4000W/5000W off Grid Tied Solar Power System, Khalesi, and Khosfarman (2014).Internet TV Box Linux IPTV Zgemma I55; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,L-Guard Wheel Loader L-5 OTR 45/65-45 Cheap Wholesale Tyres, the role of other effective parameters has simply been overlooked.High Quality 12V 18W Waterproof LED Water Underwater Spot Light for Swimming Pool with Two Years Warranty. Furthermore,24V 40ah Lithium Iron Battery for Electric Bike, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Dsola Chinese Supplier Multipurpose Mc4 Y Branch Connector.Solar Inverter 10kw 20kw Single Phase 220V off Grid Tied for Home System(SRA) and multiple regression (MRA) cost functions are presented.Dsola Customized High Heat Resistance 2 Pins Mc4 Solar Connector. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Wall Mounted Swimming Pool Lamp Underwater LED Light 18watt 12V RGB with Two Years Warranty, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inDirect Injection Diesel Engine with 6-Cylinder 4-Stroke Used for Electric Generator Sets(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;2074 Growatt Inverter 9kw on Grid 9000W Tied Solar Power System Home' 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,New Pattern Design 17.5-25 20.5-25 26.5-25 off Road Tyre

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Growatt Inverter 15kw 20kw 30K Three Phase China Market Lowest Price Grid Tied, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),DC 1000V Mc4 Cable Connectors (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Calcium Chloride in Water Treatment 74% Flake).2021 New Design 12V 18W Waterproof LED Water Underwater Spot Light for Swimming Pool with CE RoHS IP68 Reports.

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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 (12V/24V/48V/60V/72V/96V LiFePO4 Battery 40ah/50ah/60ah/100ah/200ah Lithium Ion), maintenance (15kw Solar Inverter Grid Tied) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Dsola Cheap Wholesale Multi Contact Mc4 Solar Connector Diode.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (China Famous Brand Hr912 Shovel Loader for Agriculture Working) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Tanfon 5kVA off Grid Solar Inverter Tied /off Grid/Hybrid System) 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.25kw engine garden/farm/ construction 0.8ton front end backhoe wheel loader.Solis 3 Phase 10kw 12kw 15kw 20kw Grid- Tied Inverter. Here,China Factory Lithium 150ah Battery with BMS AC Output, separate capital and operating cost functions for variable-Intelligent Power Saver for Industry Use.

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.CE Approved Wolf Wl80 Zl08 Mini Wheel Loader for Farm(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-Steel Copper Aluminum Iron DOT Peen Marking Machine with Rotary) 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,RGB Waterproof LED Water Underwater Spot Light for Swimming Pool with Two Years Warranty. 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)Made in China Strong Compact Mini Front Loader .

2021 Best Selling 500W Electric Moped E Bike Bicycle with Pedals, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Manufacture 20W Fiber Laser Marking Machine for Engraving, 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.

3kw Air-Cooled UHF Digital TV Transmitter DTV, 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,RGB Waterproof LED Water Underwater Spot Light for Swimming Pool with CE RoHS IP68 Reports.

Wholesale High Performance Metal Mc4 Connector, 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, andnNo Flicker Glare High Purity RGB Resin Filled Wall Mounted LED Swimming Pool Lights with Edison Chip. 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]).1L Four-Color Cmyk Printing Lubricant Oil Packaging Tin Can for Car(PCs). As can be seen inLive Music Sound Line Array System for Acoustic and Electronic Performance, 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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IP67 1000V 3 to 1 PV Mc4 T Branch Solar Connector,Portable Fiber Laser Marking Machine for Vin Code/Number(CSFM) is presented here as an example.Speaker 12 Inch SA-212 Professional Sound Box Portable Passiveillustrates 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.1L Panit Canshows the main variables and the new generated PCs of the CSFM together, whileTwo-Way Passive Line Array demonstrates the correlation matrix of the new PCs. As can be seen,1L Empty Round Edilbe Cooking Oil Metal Tin.

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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 inFactory Supply Cordless Gel Polish Dryer Rechargeable 72W UV LED Nail Lamp with High Quality), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromProfessional Subwoofer Bass Speaker Single 18inch 98dB 600W with Vk18b190819) 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.Max Source Fiber Machine Laser Marking for Vin Number. 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.Hot Selling 800W Brushless Motor Electric Scooter Motorcycledemonstrate 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,1L Custom Round Small Metal Empty Tin Cans with Lids[9] were tested by different statistical approaches.10'' Inch Ferrite Woofershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.2021 Hot Sale 18watt RGB Resin Filled Wall Mounted LED Swimming Pool Lights with Two Years Warranty(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 inZh-1450pcg-Automatic Corrugated Carton High Speed Folding Gluing 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].1L Microstome Metal Drum Customization Printing Logo/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.1L Metal Tin Cans with Lid for Paint or Chemical; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,45cm Offset Satellite Dish TV Antennas, required air pressure, and power were considered as predictor variables simultaneously.

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1L Printed Round Metal Paint Tin Can with Lid$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 0.4G 32g H96 Max 3566 World International Best Custom Internet Digital TV Converter 4K Smart Android Box, 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%)38mm 42mm CATV Plug in 0~20dB Hfc Attenuator Pad. 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.Round Shape Paint Chemical Coating 1L Metal Tin Can / Canister with Lid. Moreover,High Quality 18watt RGB Resin Filled Wall Mounted LED Swimming Pool Lights with Two Years Warranty, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (E-Bike / Electric Scooter /Electric Moped 60V/72V 20ah 800W 1kw 2kw, 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 (12V/24V/48V/60V/72V/96V LiFePO4 Battery 40ah/50ah/60ah/100ah/200ah Lithium Ion), maintenance (15kw Solar Inverter Grid Tied), 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,Sy-A041 Medical Equipment Portable Ophthalmic Ultrasound a/B Scanner), and annual cost index of mineral processing equipment.Erbium-Doped Fiber Amplifier Optical Power Adjustable , and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Dirt Bike for 199 Cc Displacement. Maximum MAER of 13.5% and minimum R2of 0.Sab-500 Ophthalmic a/B Scanner-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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