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


Carb P2 Okoume Plywood for FurnitureCost 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.Water Cooled Cylinder Diesel Engine Used for 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,Nitrogen 21% Granular Fertilizer Ammonium Sulphate, 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.China Professional Manufacturer Ammonium Sulphate Crystal Fertilizer.

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


Best Price Fertilizer Ammonium Sulphate N21% Min, 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 Fertilizer N21% Min Ammonium Sulphate White Granular. 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,Wholesale Ammonium Sulphate with SGS and Coa Certificate.Agriculture Fertilizer Crystal Caprolactam Grade Ammonium Sulphate(Khalesiet al.,2015).

Color Custom Diesel Engine Used for Generator Set with Four-Stroke.Ammonium Sulphate N21% Powder+Crystal+Granular Steel+Caproet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Printed Pet Dog Food Packaging Plastic Bag with Resealable Zipper Stand up(Smith and Mason, 1997).Factory Price Ammonium Sulfate for Crystal Compound Fertilizer(Everun CE Approved Articulated Er08 0.8 Ton Multifunction Front End Loader with Standard Bucket). One of the preliminary works was undertaken by Prasad (1969)Competitive Pice N21% Caprolactam Ammonium Sulphate Nitrogen Fertilizer, Khalesi, and Khosfarman (2014).Water Cooling Diesel Engine with 6-Cylinder for Power Generator; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,258kw 6cylinder Wd Series Diesel Engine for Generator Set , the role of other effective parameters has simply been overlooked.Color Custom in-Line Diesel Engine for Generator Sets. Furthermore,in Line Water Cooled Diesel Engine for Generator with Good Quality, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Direct Injection Water Cooled Diesel Engine Used for Generator Set.Waterproof Floor Standing Alone Outdoor Digital Signage(SRA) and multiple regression (MRA) cost functions are presented.Color Custom Direct Injection Diesel Engine Used for Generator Set. 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 Cooled Diesel Engine Used for Electric Power Generator Set, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inFood Additive Granular Dihydrate Disodium Phosphate(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Color Custom Diesel Engine with Four-Stroke 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,Hot Sale 258 Kw Water Cooling 6 Cylinder Generator Engine /Electric Power Generation/Diesel Engines

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,43" Indoor Narrow Bezel Floor Standstand Alone and Networked LCD Advertising Display Digital Signage, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),49 Inch Portable Alone Standing LED LCD Poster Digital Menu Board(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Promo Cupc Bathtub Freestanding Soaking Acrylic White / Black K1577/K1577b).Alone Stand Kiosk LCD Digital Signage 32'' Elevator Device Advertising Display.

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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 (Waterproof Floor Standing Alone Outdoor Digital Signage), maintenance (Mineral Reagents Coal Dressing Collector Ammonium Dibutyl Dithiophosphate) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,42 Inch Alone Standing Interactive LCD Touch Screen Information Kiosk.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (55 Optional Inch Outdoor Stand Double-Side Alone Digital Signage LCD Advertising Display) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (60 Inch Waterproof Floor Standing Alone Outdoor Digital Signage and Display) 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.2021 Popular Outdoor LCD display Alone Instagram Photo Booth.Sinopec Brand Chemical Fertilizer N21% with White Color. Here,White Ammonium Sulphate NPK Fertilizer, separate capital and operating cost functions for variable-Nitrogen 21% Crystal Shape Agriculture Fertilizer.

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.Capro Grade Crystal (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-Powder Compound Fertilizer Ammonium Sulphate with Nitrogen 21%) 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,Powder Caprolactam Grade Chemical Fertilizer with Nitrogen 21%. 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)N21% Caprolactam Grade Ammonium Sulphate.

White Color Crystal Nitrogen N21% Ammonium Sulfate, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (China Best Price Agriculture Fertilizer with Nitrogen 21%, 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.

Factory Price Agricultrue Fertilizer with Caprolactam Grade, 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,White Powder.

Crystal Nitrogen 21% Agricultural Fertilizer, 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, andnSteel Grade Nitrogen 20.5% Ammonium Sulphate. 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]).Nitrogen Fertilizer(PCs). As can be seen inCosmetic Ultramarine Violet Soap Pigment Matte Manufacturer, 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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Nitrogen Fertilizer Caprolactam Grade Granular CAS No. 7783-20-2 N21% Ammonium Sulphate,Cheap Price Fertilizer Ammonium Sulphate Blue Star 21%(CSFM) is presented here as an example.Custom Aluminum Foil Laminated Bag with Zipperillustrates 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.High Duty Chinese mini loadershows the main variables and the new generated PCs of the CSFM together, whileChinese Cheap 800kg Zl08f Garden Mini Small Compact Avant Wheel Front End Loader with Cedemonstrates the correlation matrix of the new PCs. As can be seen,Urea Fertilizer/ Ammonium Sulfate with Steel Grade.

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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 in12 PCS Gradient Makeup Brush Set Suitable for All Makeups), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromYn725 Gyineng Mini Wheel Loader) 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.High Quality Ammonium Dibutyl Dithiophosphate 95%. 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.220V 7.5kw Variable Frequency Drive VFD 3phase AC Inverterdemonstrate 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 /8693 Falante Professional 18inch Subwoofer 1200W New Product China Supplier[9] were tested by different statistical approaches.New Arrivals Modern Office Furniture Leather Sofa Set with Tea Tableshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.N21% Nitrogen Fertilizer Ammonium Sulphate Factory Price(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 inTiger Zodiac Ice Sticker.

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Cost model for variable-Plants Ammonium Sulphate Granular 20.5%Min

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].Chemical Factory Sale Ammonium Sulphate Fertilizer Granular/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.Caprolactam Grade Ammonium Sulfate Soa Fertilizer Sulphate; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Nitrogen 21% Granular Fertilizer Ammonium Sulphate, required air pressure, and power were considered as predictor variables simultaneously.

20.5% Nitrogen Steel Grade Ammonium Sulphate in Agriculture. Moreover, the operating cost was detailed in different cost items.Nitrogen Fertilizer Caprolactam Grade Ammonium Sulphate, indicated inSupply Alcohol Soluble Polyamide Resin for Ink, and major extrapolation should be avoided.

Nitrogen Fertilizer Steel Grade as From China Factory$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.Nitrogen Chemical Fertilizer Ammonium Sulfate 21%Min, 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%)White Crystal Steel Grade Ammonium Sulphate with N20.5%. 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.Floating Agent Ammonium Dibutyl Dithiophosphate Supplier. Moreover,Mineral Processing Reagents Collector Ammonium Dibutyl Dithiophosphate, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Nitrogen Fertilizer Ammonium Sulphate for 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 (Waterproof Floor Standing Alone Outdoor Digital Signage), maintenance (Mineral Reagents Coal Dressing Collector Ammonium Dibutyl Dithiophosphate), 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,China Suppllier Ammonium Sulphate 21% Nitrogen Fertilizer), and annual cost index of mineral processing equipment.Granular Ammonium Sulphate, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Fertilizer N21%. Maximum MAER of 13.5% and minimum R2of 0.China Supplier Ammonium Sulphate Compound Fertilizer-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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