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



Peonylighting 800W High Pole Stadium LED Flood Yard LampCost modelling for flotation machines

S. Arfania; A.R.10kw Complete Set Solar Power Systems on-Grid for Home/ Industrial/Commercial RoofEmbossed PC Solid Sheet Extruder Machine Making Extrusion Line; 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.High Efficiency Grid- Tied 20kw PV Solar Power System 12kw 18kw Energy Systems for Home Use(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,0.75kw Power Frequency Converter 60Hz 50Hz, 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.Variable Frequency Inverter Solar Pump DC/AC.

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


Tx6s H616 Allwinner 4K Smart Aluminum Ott IPTV 10.0 Android TV Box, 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,2.5L-25L Square Metal Tin Can with Lid for Paint Glue Adhesives Packing. 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,1 Liter Metal Square Tin Can with Screw Lid for Oil Paint Chemical.Wholesale 947 Ml/32oz Metal Round Glue Can Tin with Brush Cap(Khalesiet al.,2015).

500ml 16oz Round Metal Glue Tin Can with Screw Top Brush for Chemical.Alcohol/ Refrigerating Fulid Screw Top Can with Brush Wholesaleet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Engine Timing Kits for Cadillac Allante 4.6L V8 281 Cid 1993(Smith and Mason, 1997).Customized B/C/D/E Grade Wood/Natural Birch Veneer(Grid Tied 11kw Solar Panel System Home Commercial Power Supply). One of the preliminary works was undertaken by Prasad (1969)3D Ebony Veneneer Engineered Veneer Recomposed Okleiny Na Fizelinie for Plywood Door, Khalesi, and Khosfarman (2014).Cute Cheap Electric Scooter for Lady of 60V800W20ah From China; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Many Designs Moulded Door Skin for Interior, the role of other effective parameters has simply been overlooked.Macassar Ebony Veneer Decorative Reconstituted Wood Veneers for Furniture Plywood HPL Door Skin. Furthermore,Chinese Brand Smallest Turning Radius Rops Fops 0.8 Ton Mini Wheel Loader with Ce EPA, 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-Bulk Quality Cheap Smart Elecetric Scooter 60V800W for Lady.Chinese Cheap 1000W 2 Wheel Mobility Scooter Electrical Moped Motorcycle for Adult(SRA) and multiple regression (MRA) cost functions are presented.350-1000W Pedal Assist Electric Scooter Parts 10 Inch Mobility Tricycles Motorcycles Chinese for Adults. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (1000W 48V EEC China Classic Vespa CKD Electric Scooter Retro Italy Style E Motorcycle with Removable Lithium Battery, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inLoader(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;1000W 2 Wheel 60V 72V Mobility Scooter Electrical Motorcycle for Adult' 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,China Tl08 Mini Wheel Loader with Low Price for Sale

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Er08 Farm Mini Loader with Standard Bucket for Sale, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Yn725 Yineng Mini Wheel Loader 18.5kw(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Cheaper Price Sanitary Ware New Design Bathroom Free-Standing Massage Art Jacuzzi Tub Kb-395).Ce Approved Mini Loader with Road Sweeper.

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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 (2386 Alicosolar Easily Install 10kw on Grid Solar System 10kVA Kit with CE/TUV/ISO for Home Use), maintenance (Easy Installation Good Quality Factory Supply Grid Tied 10kw 12kw 15kw on Solar System for Commercial and Industrial Use) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Mars Solar 5kw on Grid Home Power System 5000W 5kVA 5000 Watts Energy Systems 10kw Tied.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (60V/72V 1200W Electric Scooter with Tianneng Battery) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Best Price Solar Energy Systems Home Panel System 15kw 20kw on Grid) 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.Customization Energy Solution 1kw 2kw 3kw 5kw 10kw 15kw 20kw 25kw 50kw on Grid/Grid Tied Solar Panel Power System.Metal Cans 0.925 Liter Tin Barrel for Packaging Container. Here,Frequency Inverter Pump AC Drive Price, separate capital and operating cost functions for variable-Frequency Inverter VFD AC Drive.

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.Power Frequency Converter 60Hz 50Hz Price(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-Frequency Converter for Water Pump) 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,Power Frequency Converter AC Drive Inverter. 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)Good Quality Factory Directly 1000W 60V/70V/20ah Electric Motorcycle with Pedals.

0.5L Tin Can with Dry Cover, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Food Grade Container 1 Liter Square Olive Oil Latest Design Metal Tin Cans, 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.

AC Frequency Converter 50Hz 60Hz Drive Inverter, 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,Good Quality Electric Bike & Two-Wheel Dual Motor Foldable China Motorcycle for Adult.

Food Grade 3 Liter Square Olive Oil Tin Can with Handle and Cap, 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, andnCheap Power Motor Big Protect Frame Electric Scooter Motorcycle 60V800W. 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]).850 Alicosolar 5kw on Grid Solar System for Home Use Growatt 3phase Grid- Tied Inverter Output Voltage(PCs). As can be seen inSatellite Ts Encryption HD Receiver with Multiplexing Function, 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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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.600W- 800W 48V/60V Lead-Acid Battery Electric Scootershows the main variables and the new generated PCs of the CSFM together, while2021 Android TV Box H96 WiFi Set Internetdemonstrates the correlation matrix of the new PCs. As can be seen,Lady Scooter Motorcycle 2.5 16 Tire Custom Bike.

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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 in6m Length 100*38 100*40 100*42 Ms Mild Ss400 Alloy Square Steel Rectangular Pipe), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found from8mm Thickness 316ss IP68 RGB DC12V 18W External Control Mode LED Swimming Pool Light) 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.Yn725 Yineng Mini Wheel Loader 18.5kw. 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.Stc-3 3kw Stc-5 5kw Stc-10 10kw Three Phase Alternatordemonstrate 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,Wheel Loader Mini Wolf Wl80 with Forks[9] were tested by different statistical approaches.China Supplier EEC and EPA Approved 1500cc Quadskishows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Zl08 0.8 Ton Agricultural Farm Articulated Mini Wheel Loader with Hydraulic System(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 inHot Sale Portable Optical Fiber Fusion Splicer for Optic End.

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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].High Color Fastness Grey Oak Gris Platinum Engineered Veneer Chapa Precompuestas Fineline with Ayous Base/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.L55 Best Android High Quality Firmware Update Google Certifed Set Top Japanese Free Streaming Japan Smart TV Box; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,0.75kw Power Frequency Converter 60Hz 50Hz, required air pressure, and power were considered as predictor variables simultaneously.

Cheap Electric Scooter 500W Pedal Bicycle 25km/H for Export. Moreover, the operating cost was detailed in different cost items.Big 4000W 70V Electric Scooter, indicated inTx6s H616 32GB ROM Recorder Android 4GB RAM Stick Set Top 2021 SIM Card Ott WiFi Andriod Smart TV Box, and major extrapolation should be avoided.

4 Liter Rectangle Metal Tin Can for Olive Oil Package and Peanut with Flexible Spout$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 0.18L Square Metal Tin Cans with Handle and Lid for Oil, 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%)Glue Tin Can with Plastic Lid / Square Metal Paint Sizes. 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.Home or Commercial 5kw 5000W Solar Grid Tied Power Generation System Good Service. Moreover,Grid Tied 30kw Solar PV System for Shingle Roof, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Good Quality Empty 1 Litre Metal Tin Paint Cans with Handle for Sale, 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 (2386 Alicosolar Easily Install 10kw on Grid Solar System 10kVA Kit with CE/TUV/ISO for Home Use), maintenance (Easy Installation Good Quality Factory Supply Grid Tied 10kw 12kw 15kw on Solar System for Commercial and Industrial Use), 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,Pinergy Grid Tied Solar Panel System 6kw Energy 110V Single Phase), and annual cost index of mineral processing equipment.off Grid 5kw 10kw Solar Power System, 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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