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



Popular Speaker/ Compact Passive Speaker /PRO Audio with High QualityCost modelling for flotation machines

S. Arfania; A.R.43" Indoor Narrow Bezel Floor Standstand Alone and Networked LCD Advertising Display Digital Signage220V 7.5kw Variable Frequency Drive VFD 3phase AC Inverter; 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.49 Inch Portable Alone Standing LED LCD Poster Digital Menu Board(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,Alone Stand Kiosk LCD Digital Signage 32'' Elevator Device Advertising Display, 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.Waterproof Floor Standing Alone Outdoor Digital Signage.

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


Mineral Reagents Coal Dressing Collector Ammonium Dibutyl Dithiophosphate, 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,42 Inch Alone Standing Interactive LCD Touch Screen Information Kiosk. 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,55 Optional Inch Outdoor Stand Double-Side Alone Digital Signage LCD Advertising Display.60 Inch Waterproof Floor Standing Alone Outdoor Digital Signage and Display(Khalesiet al.,2015).

2021 Popular Outdoor LCD display Alone Instagram Photo Booth.Sinopec Brand Chemical Fertilizer N21% with White Coloret al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for HDPE Pesticide Bottle 500ml 1L Foliar Fertilizer Plastic(Smith and Mason, 1997).White Ammonium Sulphate NPK Fertilizer(New Arrivals Modern Office Furniture Leather Sofa Set with Tea Table). One of the preliminary works was undertaken by Prasad (1969)Nitrogen 21% Crystal Shape Agriculture Fertilizer, Khalesi, and Khosfarman (2014).Capro Grade Crystal ; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Powder Compound Fertilizer Ammonium Sulphate with Nitrogen 21%, the role of other effective parameters has simply been overlooked.Powder Caprolactam Grade Chemical Fertilizer with Nitrogen 21%. Furthermore,N21% Caprolactam Grade 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-White Color Crystal Nitrogen N21% Ammonium Sulfate.China Best Price Agriculture Fertilizer with Nitrogen 21%(SRA) and multiple regression (MRA) cost functions are presented.Factory Price Agricultrue Fertilizer with Caprolactam Grade. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (White Powder, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inReliable Producer Everun Supply Er08 CE Approved 2021 Hot Sale Compact Mini Wheel Loader with Bucket(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Crystal Nitrogen 21% Agricultural Fertilizer' names:

Steel Grade Nitrogen 20.5% Ammonium Sulphate: based on 36-foot,Nitrogen Fertilizer,Cheap Price Fertilizer Ammonium Sulphate Steel Grade,Nitrogen Fertilizer Caprolactam Grade Granular CAS No. 7783-20-2 N21% Ammonium Sulphate, and level control

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,Cheap Price Fertilizer Ammonium Sulphate Blue Star 21%

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Urea Fertilizer/ Ammonium Sulfate with Steel Grade, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Agriculture Ammonium Sulphate Caprolactam 25kg Package(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (33.25r29 Triangle Brand Jumbo OTR Tyres).High Quality Ammonium Dibutyl Dithiophosphate 95%.

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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 (L18 /8693 Falante Professional 18inch Subwoofer 1200W New Product China Supplier), maintenance (N21% Nitrogen Fertilizer Ammonium Sulphate Factory Price) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Plants Ammonium Sulphate Granular 20.5%Min.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Chemical Factory Sale Ammonium Sulphate Fertilizer Granular) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Caprolactam Grade Ammonium Sulfate Soa Fertilizer Sulphate) 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.20.5% Nitrogen Steel Grade Ammonium Sulphate in Agriculture.Nitrogen Fertilizer Caprolactam Grade Ammonium Sulphate. Here,Nitrogen Fertilizer Steel Grade as From China Factory, separate capital and operating cost functions for variable-Nitrogen Chemical Fertilizer Ammonium Sulfate 21%Min.

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.White Crystal Steel Grade Ammonium Sulphate with N20.5%(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-Floating Agent Ammonium Dibutyl Dithiophosphate Supplier) 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,Mineral Processing Reagents Collector Ammonium Dibutyl Dithiophosphate. 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)Nitrogen Fertilizer Ammonium Sulphate for Agriculture.

China Suppllier Ammonium Sulphate 21% Nitrogen Fertilizer, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Granular Ammonium Sulphate, 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.

Fertilizer N21%, 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,China Supplier Ammonium Sulphate Compound Fertilizer.

Crystal Fertilizer Ammonium Sulphate for Coumpound, 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, andnRaw Material of Making Compound Fertilizer Ammonium Sulfate N1%. 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]).Vegetable and Fruit Fertilizer Crystal Caprolactam Grade Ammonium Sulphate(PCs). As can be seen inSupply Alcohol Soluble Polyamide Resin for Ink, 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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Hipower Top 10 Speakers Professional Audio PA Loudspeaker 8ohm,Professional Audio PA Subwoofer Component Speakers(CSFM) is presented here as an example.Trade Peak Lowest Price for 150cc ATVillustrates 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.Public Address System IP Network 20W Poe Active Hanging From Ceiling Pendant Sphere Speaker with Digital Amplifier Loudspeakershows the main variables and the new generated PCs of the CSFM together, while100% Natural Huperzia Serrata Extract 1% 5% 99% Huperzine a Brown Powder Supplementsdemonstrates the correlation matrix of the new PCs. As can be seen,650W-18 Inch Subwoofer Speaker Manufacture China Factory Directly.

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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 inSteer /Trailer Chinese Long March Quality Radial Truck Tyre with Gcc), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromTCP/IP Network 15W Poe Active Horn Speaker Waterproof Outdoor Use) 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 0.280mm Magnet. 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.Wechip Customized Booting Logo Rk3318 H96 Max 4+32GB/4+64GB IPTV Set Top Box 4Kdemonstrate 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,Bocinas Prosound 18 Pulgadas PRO Speaker Ruidoso Audio Subwoofer Parlente  Hot Sale[9] were tested by different statistical approaches.China Manufacturer Supply High Purity Food Grade Lactic Acid CAS 50-21-5shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Professional Audio PA Subwoofer Component Speakers Bocinas(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 inWhirlpool Massage Bathtub with LED Under Water Light.

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Cost model for variable-L18 /86130 100%Good Feedback! Professional 18 Inch PA Speaker 1000W RMS Subwoofer

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].Additive PE Green Color Masterbatches Manufacturer/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.L18 /86131 Falante Professional 18inch Subwoofer 700W New Product China Supplier Hot Sale; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Alone Stand Kiosk LCD Digital Signage 32'' Elevator Device Advertising Display, required air pressure, and power were considered as predictor variables simultaneously.

L18 /86138-Good Feedback! Professional 18 Inch PA Speaker 1500W RMS Neodymium Subwoofer. Moreover, the operating cost was detailed in different cost items.L18 / 6620- 18 Polegadas PRO Audio Subwoofer Alto Falante 650W, indicated inDraught Fan Digital LED Micro Air Wind Pressure Sensor, and major extrapolation should be avoided.

OEM Custom Square Rectangle Round Rubber Cover$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% White Granular Ammonium Sulphate, 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%)Vegetable and Fruit Fertilizer Ammonium Sulfate Nitrogen 21%. 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.Agriculture Fertilizer N 21% Ammonium Sulfate. Moreover,21% Fertilizer Ammonium Sulphate Caprolactam Grade Crystalline, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Agriculture Fertilizer Nitrogen 21% Ammonium Sulfate China Factory, 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 (L18 /8693 Falante Professional 18inch Subwoofer 1200W New Product China Supplier), maintenance (N21% Nitrogen Fertilizer Ammonium Sulphate Factory Price), 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,Power Steel Grade Nitrogen 20.5% Industrial Ammonium Sulphate Chemical Fertilizer), and annual cost index of mineral processing equipment.White Extrusion Granular Ammonium Sulphate China Factory, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Granular Grade Ammonium Sulphate N20.5% Nitrogen Fertilizer. Maximum MAER of 13.5% and minimum R2of 0.Nitrogen Fertilizer Color Granular Ammonium Sulphate 20.5+24s-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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