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



10 " Inch Speaker System PRO Audio Entertainment Speakers Cost modelling for flotation machines

S. Arfania; A.R.China Radlader Zl08 Auto 800kg Small Garden New Mine Carregadeira Lown Mower Tractor Front Handle Mini Wheel Loader with CabinProfessional PRO Audio DJ Mixer DSP Powered Full Range Line Array Speaker; 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.Chinese Eougem Zl08 Wheel Loader with Torque Converter(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,Articulated Mini Wheel Loader Er08 Telescopic Boom, 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.Cable TV Pendoo X99 Max Rk3399 4G 32g Android 7.1 Internet Smart Box with HD Satellite Receiver.

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


Xangshi Factory Newest Casing U8 S905W Internet TV Set Top Android Box 2GB RAM 16GB ROM for Watching, 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,New Design Go Kart 150cc . 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,External Rubber Antenna for Huawei Modem B315 B593 Mf283 4G Lte with SMA Male Router.48V/60V 800W Electric Scooter with Lead-Acid Battery(Khalesiet al.,2015).

800W 60V Lead-Acid Battery Electric Bicycle with Back Rest.Electric Motorcycle 800W for Adult Motoret al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Professional Subwoofer Bass Speaker Single 18inch 98dB 600W with Vk18b190819(Smith and Mason, 1997).Hot Sale Lady Style 60V 800W 20ah Electric Scooter with USB(Mexico Warehouse Free Sample Intermediate 103-63-9/96-48-O/1009-14-9/49851-31-2/79099-07-3/125541-22-2). One of the preliminary works was undertaken by Prasad (1969)800W -1000W 60V/72V Electric Scooter with Lead-Acid Battery, Khalesi, and Khosfarman (2014).Rosen 5kw on Grid Solar System with Tied Inverter; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Solar Energy System 5kw Panel Home Grid Tied Power, the role of other effective parameters has simply been overlooked.200kw Grid Tied Solar System for Factory Use. Furthermore,Grid Tied Inverter 10kw 15kw 20kw Home Set Solar System, 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-1kw Solar Power System Grid Tied 1000W on Panel Price.Commercial Solar System 100kw Grid Tied /on 100kVA 60kw(SRA) and multiple regression (MRA) cost functions are presented.Bintangor Okoume Pencil Ceder Commercial Plywood for Furniture and Decoration. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Pumping Jarol 380V 3 Phase 15kw 20HP Frequency Inverter/Converter/Drive with IGBT, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inMylar Laminated Ziplock Plastic Stand-up Food Packaging Bag for Nut/Gel/Food/Vitamin(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Hot selling compact 800kgs wheel loader for garden' names:

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Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Carb E0 Glue Cabinets Grade 18mm White Birch Plywood From China, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Variable Speed Drive Phree Phase Frequency Converter 1000Hz(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Self Supported Wire Drawing Polycrystalline Dies).Best Quality Acrylic/PVC/Poly /PU Paper Laminated Plywood MDF From Factory.

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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 (3 Phase VFD AC Drives 1.5kw 2.2kw 4kw Variable Frequency Drive), maintenance (Carb P2 Okoume Plywood for Furniture) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,15mm AAA Grade Film Faced Plywood with WBP Glue.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (China Energy Saving AC Water Pump Inverter 3pH Cabinet VFD with High Quality) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Hot Sale 250ml Small Can of DOT3 Brake Oil Tinplate Packaging) 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.150CC Go Kart .Full Size 150cc Go Kart . Here,Go Kart , separate capital and operating cost functions for variable-Emtpy 250L Round Clutch Brake Fluid Small Can with Plastic Lid.

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.Wolf Wl80 Mini Dumper Euro 5 Loader for Sale(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-0.8 Ton Chinese Low Cost High Quality Hydraulic Wheel Loader) 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,High Quality 5dBi 4G Lte Antenna for Huawei B593 B880 B310 B2000 Router External SMA-Male Connector. 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)WLAN WiFi Yagi Antenna.

External 2.4GHz/ 5GHz Dual-Band Small Antenna/Flexible Antenna, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (150cc Go Kart with EEC , 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.

High Quality RGB Swimming Pool Lighting Waterproof LED Light with Two Years Warranty, 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,Grid Tied 5kw Solar Energy System Home Power 5000W for Roof Tile.

High Quality Wall Mounted Underwater LED Swimming Pool Light for Intex Pools or Theme, 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, andn800W Power Electtric Motorcycle Scooter / Electrical Motorcycles Bicycle . 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]).2021 Hot Sale Wall Mounted Underwater LED Swimming Pool Light with Two Years Warranty(PCs). As can be seen inPeptide Cosmetics CAS 155149- 79 -4 Capixyl, 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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Hot Selling A5X Max Rk3328 4GB 32GB Android TV Box 4K Full HD Quad Core Smart for Internet Set Top,Topleo I96 King 1GB/2GB RAM Smart Android 7.1 Quad Core Internet 4K Ultra HD Support TV Box(CSFM) is presented here as an example.Color Custom in-Line Diesel Engine for Generator Setsillustrates 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.Modern Style Leather Sofa Top Grain F226shows the main variables and the new generated PCs of the CSFM together, while14" to 22' Inch Replica Aluminum Alloy Wheel for KIA Rimsdemonstrates the correlation matrix of the new PCs. As can be seen,15kw Grid Tied Solar Power System for Home Use.

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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 in4* Feet Plywood Production Line/4*8 Veneer Peeling Line), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromChina Wholesales Wheel Loader HR912 with Pallet Forks) 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.Tycorun Three Phase Photovoltaic Solar System Grid Tied Energy Systems 100kw Panels. 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.5GHz 18dBi Dual Polarized Panel Antenna demonstrate 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,Factory Direct Sale Grid Tied Solar Power System on 1000wp 5000wp 10000wp for Wholesale[9] were tested by different statistical approaches.Manufacturer of Enigine Oil Canshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Vimode Electric Scooter Adult Motorcycle for Adults 800W 650W(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 inCAS 10124-56-8 Sodium Hexametaphosphate with a High Exposure Rate and Favorable Price.

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Cost model for variable-Adv. 1 Alloy Wheel

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].150cc 4-Stroke/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.Outdoor 5GHz 30dBi Long Range Parabolic Grid Antenna; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Articulated Mini Wheel Loader Er08 Telescopic Boom, required air pressure, and power were considered as predictor variables simultaneously.

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New Design 800W 1000W Electric Scooter Motorcycle for Riding$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 0.5.8GHz 30dBi Single-Pol Die Cast Grid Antenna, 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%)Mimo Antenna 5150MHz~5850MHz WiFi Panel. 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.5GHz 20dBi Panel WiFi Antenna. Moreover,Fast Ship 800W 1000W 1200W 60V 72V 20ah Battery Electric Motorcycle From China, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Hot Sale 2.4/ 5GHz 9dBi Rubber WiFi Antenna, 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 (3 Phase VFD AC Drives 1.5kw 2.2kw 4kw Variable Frequency Drive), maintenance (Carb P2 Okoume Plywood for Furniture), 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,5GHz 12dBi Dual Polarity MIMO Omni Antenna), and annual cost index of mineral processing equipment.Electric Motorcycle Fashion Design 800W with Removable Battery, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,5GHz 18dBi Dual Polarization Panel WLAN Antenna. Maximum MAER of 13.5% and minimum R2of 0.Guangzhou Manufacturer Empty Anti Bacterial Diesel Additive Can for Fuel Cleaner-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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