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


Chinese Zl08f Wheel Loader 0.8ton Mini with Quick Hitch for SaleCost modelling for flotation machines

S. Arfania; A.R.Deisel Engine for Silent Power Generator with 6-CylinderCheap Smart Lady's Electric Scooter 60V800W; 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 Line Multy-Cylinder Diesel Engine for Power Generator Set(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,6-Cylinder Diesel Engine Water Coolant for Electric Generator Set, 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 Line Direct Injection Diesel Engine Used for Generator Set.

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


Color Custom Diesel Engine with Four-Stroke for Gensets, 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,6-Cylinder Diesel Engine with Four-Strke for Silent Generator Set. 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,Diesel Engine with Four-Stroke Used for Cylinder Generator Set.Direct Injection Water Cooled Diesel Engine for Generator Set(Khalesiet al.,2015).

Water Cooled Cylinder Diesel Engine Used for Generator Set.Nitrogen 21% Granular Fertilizer Ammonium Sulphateet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Professional Line Array PA System S1210 Sound(Smith and Mason, 1997).China Professional Manufacturer Ammonium Sulphate Crystal Fertilizer(Factory Price Manufacturer Supplier Caviar Tin Can Packaging Box Food). One of the preliminary works was undertaken by Prasad (1969)Best Price Fertilizer Ammonium Sulphate N21% Min, Khalesi, and Khosfarman (2014).Nitrogen Fertilizer N21% Min Ammonium Sulphate White Granular; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Wholesale Ammonium Sulphate with SGS and Coa Certificate, the role of other effective parameters has simply been overlooked.Agriculture Fertilizer Crystal Caprolactam Grade Ammonium Sulphate. Furthermore,Color Custom Diesel Engine Used for Generator Set with Four-Stroke, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Ammonium Sulphate N21% Powder+Crystal+Granular Steel+Capro.Factory Price Ammonium Sulfate for Crystal Compound Fertilizer(SRA) and multiple regression (MRA) cost functions are presented.Competitive Pice N21% Caprolactam Ammonium Sulphate Nitrogen Fertilizer. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Water Cooling Diesel Engine with 6-Cylinder for Power Generator, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inRuijie Rg-Ap220-E (InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;258kw 6cylinder Wd Series Diesel Engine for Generator Set ' 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,Color Custom Direct Injection Diesel Engine Used for Generator Set

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Water Cooled Diesel Engine Used for Electric Power Generator Set, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Color Custom Diesel Engine with Four-Stroke for Generator Set(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (China Electrostatic Powder Coating Production Line).Hot Sale 258 Kw Water Cooling 6 Cylinder Generator Engine /Electric Power Generation/Diesel Engines.

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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 (Diesel Engine Used for Silent Generator Set with Multy-Cylinder), maintenance (Waterproof Floor Standing Alone Outdoor Digital Signage Display) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Chinese Brand New 258kw/1500rpm 12 Cylinder 4 Stroke Marine Diesel Engine .076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Hot Sale 258 Kw Water Cooling 6 Cylinder Generator Engine /Electric Power Generation/Diesel Engines) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (43" Indoor Narrow Bezel Floor Standstand Alone and Networked LCD Advertising Display Digital Signage) 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.49 Inch Portable Alone Standing LED LCD Poster Digital Menu Board.Alone Stand Kiosk LCD Digital Signage 32'' Elevator Device Advertising Display. Here,Waterproof Floor Standing Alone Outdoor Digital Signage, separate capital and operating cost functions for variable-Mineral Reagents Coal Dressing Collector Ammonium Dibutyl Dithiophosphate.

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.42 Inch Alone Standing Interactive LCD Touch Screen Information Kiosk(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-55 Optional Inch Outdoor Stand Double-Side Alone Digital Signage LCD Advertising Display) 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,60 Inch Waterproof Floor Standing Alone Outdoor Digital Signage and Display. 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)2021 Popular Outdoor LCD display Alone Instagram Photo Booth.

Sinopec Brand Chemical Fertilizer N21% with White Color, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (White Ammonium Sulphate NPK Fertilizer, 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.

Nitrogen 21% Crystal Shape Agriculture Fertilizer, 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,Capro Grade Crystal .

Powder Compound Fertilizer Ammonium Sulphate with Nitrogen 21%, 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, andnPowder Caprolactam Grade Chemical Fertilizer with Nitrogen 21%. 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]).N21% Caprolactam Grade Ammonium Sulphate(PCs). As can be seen inSab-500 Ophthalmic a/B Scanner, 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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China Best Price Agriculture Fertilizer with Nitrogen 21%,Factory Price Agricultrue Fertilizer with Caprolactam Grade(CSFM) is presented here as an example.High-Purity Cosmetic Additives Nano Liposomal Hydroxypropyl Tetrahydropyrantriol China Factory Direct Salesillustrates 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 Professional Coaxial Line Array Column Speaker 20PCS Driver Unit PA System with L16-Cishows the main variables and the new generated PCs of the CSFM together, whilePVC Garden Pipe Making Machine Costdemonstrates the correlation matrix of the new PCs. As can be seen,White Powder.

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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 inForged Alloy Steel G80 Omega Link Hardware Rigging for Lifting), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found from350W 60V 20ah E Scooter Thorttle Motorcycles Electric with Pedals Disc Brake Bicycle for Sale) 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.Steel Grade Nitrogen 20.5% Ammonium Sulphate. 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.Burma Teak Floor Toplayer Wood Veneer Lamellas for Engineered Flooringdemonstrate 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,Nitrogen Fertilizer[9] were tested by different statistical approaches.Water Proof Child Coffee /Candy/Weed Plastic Containershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Cheap Price Fertilizer Ammonium Sulphate Steel Grade(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 inYishan 160HP hydraulic track type crawler bulldozer TY160G with 560/610mm shoes.

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Cost model for variable-Nitrogen Fertilizer Caprolactam Grade Granular CAS No. 7783-20-2 N21% Ammonium Sulphate

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].Cheap Price Fertilizer Ammonium Sulphate Blue Star 21%/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.Urea Fertilizer/ Ammonium Sulfate with Steel Grade; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,6-Cylinder Diesel Engine Water Coolant for Electric Generator Set, required air pressure, and power were considered as predictor variables simultaneously.

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L18 /8693 Falante Professional 18inch Subwoofer 1200W New Product China Supplier$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.N21% Nitrogen Fertilizer Ammonium Sulphate Factory Price, 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%)Plants Ammonium Sulphate Granular 20.5%Min. 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.Chemical Factory Sale Ammonium Sulphate Fertilizer Granular. Moreover,Caprolactam Grade Ammonium Sulfate Soa Fertilizer Sulphate, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (20.5% Nitrogen Steel Grade Ammonium Sulphate in Agriculture, 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 (Diesel Engine Used for Silent Generator Set with Multy-Cylinder), maintenance (Waterproof Floor Standing Alone Outdoor Digital Signage Display), 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,Nitrogen Fertilizer Caprolactam Grade Ammonium Sulphate), and annual cost index of mineral processing equipment.Nitrogen Fertilizer Steel Grade as From China Factory, 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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