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vol.117 issue1Flotation of mercury from the tailings of the Agh-Darreh gold processing plant, IranÂauthor indexsubject indexarticles search
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On-line version ISSN2411-9717
Print version ISSN2225-6253

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


2021 Selling The Best Quality Cost-Effective Products LED Swimming Pool Light with Two Years WarrantyCost modelling for flotation machines

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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.Veterinary Use Bulk Pirce of Oxytetracycline CAS: 79 -57-2(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,100% Copper Wire St-7.5kw Single Phase Alternator Factory Price, 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 0.100% Copper Wire St-5kw Single Phase Brush Generator.

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


Home Theater Speaker, 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,Dual 6" Coaxial Full Range Speaker for Entertainment Room. 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,12inch Stage Monitor Speaker.KTV Single 8" Full Range Audio&Sets(Khalesiet al.,2015).

St-2kw 230V/50Hz Single Phase Brush Alternator for Sale.Stc-12kw/15kVA Three Phase AC Electric Generator on Saleet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Skin Tightening(Smith and Mason, 1997).St 5kw Single Phase AC Electric Alternator Generator(43''46''55''65''75'' Commercial LCD Screen Display Full Color Waterproof Sunglight Readable Android Touch Monitor Kiosk). One of the preliminary works was undertaken by Prasad (1969)Wilson Parts Eim Module Engine Interface 258 -9753 2589755 Control, Khalesi, and Khosfarman (2014).258 -9754 Electric Engine Interface Moudle 12V Eim Basic; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,12inch Loudspeakers Professional Stage Outdoor Speaker Full Range Audio, the role of other effective parameters has simply been overlooked.Android Digital Signage Intelligent Hand Sanitizer Display. Furthermore,55 Inch Outdoor Double-Side LCD Display Self Service Airport Kiosk Touch Screen Multimedia Information, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-New Brand Diesel Engine with Four Stroke Multy-Cylinder Used for Generator Set.LCD Digital Signage 21.5 Inch Automatic Induction Hand Sanitizer Billboards(SRA) and multiple regression (MRA) cost functions are presented.43" Dual Screen LCD Ad Player Full HD Double Display All in One No Touch Android Advertise System. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Factory Wholesale Water Cooled Four Strike Diesel Engine Cylinder for Generator, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inProfessional Powered Line Array Selfpowered Speakers Active System(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;10 " Woofer Speaker' 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,Super Quality and Best Price Nitrogen Fertilizer Ammonium Sulfate N21%

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 Color Custom for 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),Direct Injection Diesel Engine with 6-Cylinder 4-Stroke Used for Electric Generator Sets(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (-40'c~ 20'c Insulating Customized Cold Room with PU Panels).Nitrogen Fertilizers Agriculture N20.5% Granular Ammonium Sulphate.

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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 (China Weichai Steyr 258 -450kw Marine Diesel Engine Wp6 Boat with High Quality), maintenance (White Crystalline Ammonium Sulphate for Compound Fertilizer) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Deisel Engine for Silent Power Generator with 6-Cylinder.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (in Line Multy-Cylinder Diesel Engine for Power Generator Set) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (6-Cylinder Diesel Engine Water Coolant for Electric Generator Set) 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 Line Direct Injection Diesel Engine Used for Generator Set.Color Custom Diesel Engine with Four-Stroke for Gensets. Here,6-Cylinder Diesel Engine with Four-Strke for Silent Generator Set, separate capital and operating cost functions for variable-Diesel Engine with Four-Stroke Used for Cylinder Generator Set.

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.Direct Injection Water Cooled Diesel Engine for Generator Set(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-Water Cooled Cylinder Diesel Engine Used for Generator Set) 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,Nitrogen 21% Granular Fertilizer Ammonium Sulphate. 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)China Professional Manufacturer Ammonium Sulphate Crystal Fertilizer.

Best Price Fertilizer Ammonium Sulphate N21% Min, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Nitrogen Fertilizer N21% Min Ammonium Sulphate White Granular, 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.

Wholesale Ammonium Sulphate with SGS and Coa Certificate, 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,Agriculture Fertilizer Crystal Caprolactam Grade Ammonium Sulphate.

Color Custom Diesel Engine Used for Generator Set with Four-Stroke, 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, andnAmmonium Sulphate N21% Powder+Crystal+Granular Steel+Capro. 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]).Factory Price Ammonium Sulfate for Crystal Compound Fertilizer(PCs). As can be seen inSeal Kits Hyundai R210-7 Boom Cyl Arm Bucketcyl Oil, 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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Water Cooling Diesel Engine with 6-Cylinder for Power Generator,258kw 6cylinder Wd Series Diesel Engine for Generator Set (CSFM) is presented here as an example.Adult 800W Power Electric Scooter Suit for Womanillustrates 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.10 Inch Sound System Speaker Box China Line Array Audio Systemsshows the main variables and the new generated PCs of the CSFM together, whileTransparent Ceramics Hot Press Sintering Furnacedemonstrates the correlation matrix of the new PCs. As can be seen,Color Custom in-Line Diesel Engine for Generator Sets.

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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 inOriginal Lens Strips 42 Inch for LG Assembly), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromWhite Color Crystal Nitrogen N21% Ammonium Sulfate) 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.Direct Injection Water Cooled Diesel Engine Used for Generator Set. 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.Alone Stand Kiosk LCD Digital Signage 32'' Elevator Device Advertising Displaydemonstrate 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,Waterproof Floor Standing Alone Outdoor Digital Signage[9] were tested by different statistical approaches.Chinese Supplier of Variable Frequency Drive/AC/DC Motor Speed Controllershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Color Custom Direct Injection Diesel Engine Used for Generator Set(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 inFast Delivery Anti Virus Safety Mouth Cover Disposable Respirator En149 Face Mask FFP2 for Medical Doctor Surgical.

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Cost model for variable-Water Cooled Diesel Engine Used for Electric Power Generator Set

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].Color Custom Diesel Engine with Four-Stroke for Generator Set/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.Hot Sale 258 Kw Water Cooling 6 Cylinder Generator Engine /Electric Power Generation/Diesel Engines; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,100% Copper Wire St-7.5kw Single Phase Alternator Factory Price, required air pressure, and power were considered as predictor variables simultaneously.

Diesel Engine Used for Silent Generator Set with Multy-Cylinder. Moreover, the operating cost was detailed in different cost items.Waterproof Floor Standing Alone Outdoor Digital Signage Display, indicated inChanning Small Stand Alone Bath White Best Hot Tub Acrylic Freestanding Baby Tubs , and major extrapolation should be avoided.

Chinese Brand New 258kw/1500rpm 12 Cylinder 4 Stroke Marine Diesel Engine $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.Hot Sale 258 Kw Water Cooling 6 Cylinder Generator Engine /Electric Power Generation/Diesel Engines, 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%)43" Indoor Narrow Bezel Floor Standstand Alone and Networked LCD Advertising Display Digital Signage. 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.49 Inch Portable Alone Standing LED LCD Poster Digital Menu Board. Moreover,Alone Stand Kiosk LCD Digital Signage 32'' Elevator Device Advertising Display, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Waterproof Floor Standing Alone Outdoor Digital Signage, 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 (China Weichai Steyr 258 -450kw Marine Diesel Engine Wp6 Boat with High Quality), maintenance (White Crystalline Ammonium Sulphate for Compound Fertilizer), 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,Mineral Reagents Coal Dressing Collector Ammonium Dibutyl Dithiophosphate), and annual cost index of mineral processing equipment.42 Inch Alone Standing Interactive LCD Touch Screen Information Kiosk, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,55 Optional Inch Outdoor Stand Double-Side Alone Digital Signage LCD Advertising Display. Maximum MAER of 13.5% and minimum R2of 0.60 Inch Waterproof Floor Standing Alone Outdoor Digital Signage and Display-feasibility and even feasibility study level of projects.


Camm, T.W. 1994.2021 Popular Outdoor LCD display Alone Instagram Photo Booth.Sinopec Brand Chemical Fertilizer N21% with White Color,vol. 46, no.6. pp. 559-562.         [Carb P2 Okoume Plywood for Furniture]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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