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



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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.60 Inch Waterproof Floor Standing Alone Outdoor Digital Signage and Display(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,2021 Popular Outdoor LCD display Alone Instagram Photo Booth, 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.Sinopec Brand Chemical Fertilizer N21% with White Color.

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


White Ammonium Sulphate NPK Fertilizer, 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,Nitrogen 21% Crystal Shape Agriculture Fertilizer. 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,Capro Grade Crystal .Powder Compound Fertilizer Ammonium Sulphate with Nitrogen 21%(Khalesiet al.,2015).

Powder Caprolactam Grade Chemical Fertilizer with Nitrogen 21%.N21% Caprolactam Grade Ammonium Sulphateet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Eougem 0.8ton Articulated Payloader Zl08 with Changchai Engine(Smith and Mason, 1997).White Color Crystal Nitrogen N21% Ammonium Sulfate(Supply Alcohol Soluble Polyamide Resin for Ink). One of the preliminary works was undertaken by Prasad (1969)China Best Price Agriculture Fertilizer with Nitrogen 21%, Khalesi, and Khosfarman (2014).Factory Price Agricultrue Fertilizer with Caprolactam Grade; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,White Powder, the role of other effective parameters has simply been overlooked.Crystal Nitrogen 21% Agricultural Fertilizer. Furthermore,Steel Grade Nitrogen 20.5% Ammonium Sulphate, 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-Nitrogen Fertilizer.Cheap Price Fertilizer Ammonium Sulphate Steel Grade(SRA) and multiple regression (MRA) cost functions are presented.Nitrogen Fertilizer Caprolactam Grade Granular CAS No. 7783-20-2 N21% Ammonium Sulphate. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Cheap Price Fertilizer Ammonium Sulphate Blue Star 21%, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHot Sell Isopropyl Alcohol 99.9%(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Urea Fertilizer/ Ammonium Sulfate with Steel Grade' 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,Plants Ammonium Sulphate Granular 20.5%Min

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Chemical Factory Sale Ammonium Sulphate Fertilizer Granular, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Caprolactam Grade Ammonium Sulfate Soa Fertilizer Sulphate(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Double Row Biscuit Packing Machine Flowpack Type).20.5% Nitrogen Steel Grade Ammonium Sulphate in Agriculture.

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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 (Nitrogen Fertilizer Caprolactam Grade Ammonium Sulphate), maintenance (Nitrogen Fertilizer Steel Grade as From China Factory) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Nitrogen Chemical Fertilizer Ammonium Sulfate 21%Min.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (White Crystal Steel Grade Ammonium Sulphate with N20.5%) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Floating Agent Ammonium Dibutyl Dithiophosphate Supplier) 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.Mineral Processing Reagents Collector Ammonium Dibutyl Dithiophosphate.Nitrogen Fertilizer Ammonium Sulphate for Agriculture. Here,China Suppllier Ammonium Sulphate 21% Nitrogen Fertilizer, separate capital and operating cost functions for variable-Granular Ammonium Sulphate.

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.Fertilizer N21%(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-China Supplier Ammonium Sulphate Compound Fertilizer) 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,Crystal Fertilizer Ammonium Sulphate for Coumpound. 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)Raw Material of Making Compound Fertilizer Ammonium Sulfate N1%.

Vegetable and Fruit Fertilizer Crystal Caprolactam Grade Ammonium Sulphate, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Crystal Caprolactam Grade Ammonium Sulphate Vegetables and Fruits 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.

Hipower Top 10 Speakers Professional Audio PA Loudspeaker 8ohm, 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,Professional Audio PA Subwoofer Component Speakers.

650W-18 Inch Subwoofer Speaker Manufacture China Factory Directly, 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, andnNh4 2so4 Chemical Formula for Ammonium Sulfate Fertilizer. 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]).280mm Magnet(PCs). As can be seen inPublic Address System IP Network 20W Poe Active Hanging From Ceiling Pendant Sphere Speaker with Digital Amplifier Loudspeaker, 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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Professional Audio PA Subwoofer Component Speakers Bocinas,L18 /86130 100%Good Feedback! Professional 18 Inch PA Speaker 1000W RMS Subwoofer(CSFM) is presented here as an example.Factory Direct High Quality Glue Round Tin Cans with Brushillustrates 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.Cheapest Set Top Box Mxq PRO Rk3229 Android 7.1 Quad Core 1GB 8GB TVshows the main variables and the new generated PCs of the CSFM together, whileTCP/IP Network 15W Poe Active Horn Speaker Waterproof Outdoor Usedemonstrates the correlation matrix of the new PCs. As can be seen,Additive PE Green Color Masterbatches Manufacturer.

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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 inLED PAR36 Warm White Lamp with Lenses High Concentration Super Bright Bulb), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromChina Manufacturer Supply High Purity Food Grade Lactic Acid CAS 50-21-5) 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.L18 /86138-Good Feedback! Professional 18 Inch PA Speaker 1500W RMS Neodymium Subwoofer. 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.Tp01 Piezo Electric Dome Tweeterdemonstrate 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,L18 / 6620- 18 Polegadas PRO Audio Subwoofer Alto Falante 650W[9] were tested by different statistical approaches.Draught Fan Digital LED Micro Air Wind Pressure Sensorshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.OEM Custom Square Rectangle Round Rubber Cover(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 inMarsh Buggy with Premium Engine.

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Cost model for variable-N21% White Granular 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].Vegetable and Fruit Fertilizer Ammonium Sulfate Nitrogen 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.Agriculture Fertilizer N 21% Ammonium Sulfate; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,2021 Popular Outdoor LCD display Alone Instagram Photo Booth, required air pressure, and power were considered as predictor variables simultaneously.

21% Fertilizer Ammonium Sulphate Caprolactam Grade Crystalline. Moreover, the operating cost was detailed in different cost items.Agriculture Fertilizer Nitrogen 21% Ammonium Sulfate China Factory, indicated inEconomic Mulifunctional Line Array System Speaker Dual 10 Inch, and major extrapolation should be avoided.

Power Steel Grade Nitrogen 20.5% Industrial Ammonium Sulphate Chemical Fertilizer$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.White Extrusion Granular Ammonium Sulphate China Factory, 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%)Granular Grade Ammonium Sulphate N20.5% Nitrogen Fertilizer. 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.Nitrogen Fertilizer Color Granular Ammonium Sulphate 20.5+24s. Moreover,China Suppliers Alone Type Wraped Beam Disc Machenism Padlock, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Dust Proof Steel Shackle Padlocks with Master Key, 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 (Nitrogen Fertilizer Caprolactam Grade Ammonium Sulphate), maintenance (Nitrogen Fertilizer Steel Grade as From China Factory), 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,Padlock-G38PDP), and annual cost index of mineral processing equipment.Breaker Lock, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Padlock. Maximum MAER of 13.5% and minimum R2of 0.Alone Type Wraped Beam Leaves Iron Padlock -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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