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



750ml Metal Tin Can Container for Chili Oil CanningCost 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.White Powder Vitamin a for Food and Feed Grade(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,Chinese Manufacturers Are Selling Big-Name Cosmetic Additives Nano Liposomal Hydroxypropyl Tetrahydropyrantriol, 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.Professional Line Array Speaker Neodymium Af15.

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


Manufacturer Supply CAS 79 -14-1 Glycolic Acid 70% 99% Cosmetic Grade, 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,Q210 Passive PA Speaker System. 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,Retinol Palmitate/Vitamin a Palmitate Oil as Food Ingredient.Professional 24 Channels Digital Audio Mixer Console(Khalesiet al.,2015).

100% Natural Huperzia Serrata Extract 1% 5% 99% Huperzine a Brown Powder Supplements.Skin Care Raw Material Vitamin a Palmitate Powderet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for 10pack/M Automatic PE Film Combine Heat Shrink Wrapping Bottle Packing Wrapper Machine(Smith and Mason, 1997).Lf Drivers 10 Inches Professional Speaker Pw1032-64(PRO Audio Loudspeaker PA Speaker System Coaxial Compact Line Array). One of the preliminary works was undertaken by Prasad (1969)12" Loudspeaker as Monitor Speaker System 12 Inch Powerful Coaxial, Khalesi, and Khosfarman (2014).Made in China PA Speaker System Three Way Loudspeakers; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Line Array Speaker Professional PA System Two Way Full Rang Passive , the role of other effective parameters has simply been overlooked.Pyridinecas Number 110//86//1 Used as Chemical Reagent. Furthermore,Wholesale Peptides Safe Shipping Anti-Aging Mass Building Supplements HMG, 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-P-Toluenesulfinic Acid Sodium Salt Hydrate .Bloom Tech Chemical Reagent Bis (SRA) and multiple regression (MRA) cost functions are presented.Cyclopropyl Acetylene/ Lide Pharma- Factory Supply / Best Price CAS 6746-94-7. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (CAS: 13463-67-7 Titanium Dioxide Powder, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inOLED Intermediates 2-(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Nutrition Food Grade Dl-Pyroglutamic Acid Pure L-Pyroglutamic' 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,V-Sub 18" PA Audio Cardioid Subwoofer Speaker for Home Theater

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,PRO Audio PA System Digital Mixer, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Food Grade L-Arginine with Best Price(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Trend Fashion Backpack for Teens).J8 Dual 12'' Line Array PA Speaker Professional Stage Audio System.

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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 (10 " 12"15"18" PA Speakers Loudspeaker Cabinet/Enclosure), maintenance (Wild Bee Venom Extract Melittin 99% Powder for Skin Care) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Supply High Quality Glycolic Acid Powder for Skin Whiting CAS 79 -14-1.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Retinoic Acid CAS 302- 79 -4 in Stock) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Plastic Clear White Stand-up Drinking Liquid Spout Food Packaging Bag) 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.ISO Certified 100% Natural L-Arginine Powder.High Quality Cosmetic Grade Hydroxyacetic Acid Glycolic CAS 79 -14-1. Here,Chemical Reagent Bloom Tech 2, separate capital and operating cost functions for variable-High Quality Opa O-Phthalaldehyde with Best Price.

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.Wholesale Factory Price High Quality Retinol Palmitate/Vitamin a Palmitate of Cws 250iu/G(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-KTV 10 Inch Speaker Box with Good Sound) 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,10 Inch Powered Line Array Speaker Active. 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)Hot Sale Model V20 Dual 10 Inch Three-Way Audio Small Line Array Speaker.

Dual 10 Inch Line Aray Powered Active Sound System, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (60W 10 " Portable HP5 Series Trolley Speaker with 2 UHF Mics, 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.

Manufacturer Supply 1, 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,Dual 10inch PA Audio Line Array Speaker Box System.

Dual 10 " 600W Line Array PA Professional Speaker , 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, andn10 " Dia Cast Aluminum Professional Subwoofer Basket. 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]).Food Packaging Vacuum Pouch(PCs). As can be seen inManufacturer Reusable Ziplock PE Pet Food Stand up Packaging Pouch Bag Flat Bottom Mylar Recyclable Heat Sealed Coffee Bean Rice Dough Powder, 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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L-Arginine 99%,China Factory Price CAS 702- 79 -4 1(CSFM) is presented here as an example.Wolf Agricultural Machinery Construction Small Front End Wheel Loader with Euro5 and Tier4 Engineillustrates 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.Hot Selling 60V 800W /72V 1200W New Electric Scooter/E-Scooter Motorcycleshows the main variables and the new generated PCs of the CSFM together, while316L Ceramic Pressure Transducer for Health Care Industrydemonstrates the correlation matrix of the new PCs. As can be seen,CPP High Temperature Vacuum Retort Pouch.

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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 inCute Plush Dog Cover for Rubber Bag), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromYn725g Yineng Mini Front End 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 Temperature 3 Side Seal Retort Pouch for Corn. 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.Motorcycle Parts High Quality Cam demonstrate 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,R-3-Amino-1-N-Boc-Piperidine[9] were tested by different statistical approaches.Anti-Wrinkle and Aging Chemical Raw Materialsshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.ISO Certified 100% Natural L-Arginine Powder(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 in900kVA/720kw Diesel Engine Generator Set Powered by Yuchai Power.

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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].Stand-up Ziplock Dried Food Packaging Vacuum Plastic Container/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.High Quality Laminated Food Grade Roll Film; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Chinese Manufacturers Are Selling Big-Name Cosmetic Additives Nano Liposomal Hydroxypropyl Tetrahydropyrantriol, required air pressure, and power were considered as predictor variables simultaneously.

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Custom Plastic Coffee Flat Bottom Food Packaging with Ziplock Container$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.Family Usage Embossed Vacuum Bags for Food, 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%)Matte Black Food Packaging Stand-up Pouch Aluminum Foil Bag. 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.Snsck Food Bag Fried Flat Bottom Box Pouch with Zipper. Moreover,Dual 10 " Compact Speaker Line Array , and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (10 " Woofer with 3" Voice Coil, 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 (10 " 12"15"18" PA Speakers Loudspeaker Cabinet/Enclosure), maintenance (Wild Bee Venom Extract Melittin 99% Powder for Skin Care), 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,Lf Drivers 10 Inches 50-4000 Response Martin Audio Speaker Pw1026-64), and annual cost index of mineral processing equipment.Dual 10 Inch Line Array Speaker for Theater , and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Lf Driver 10 Inches 64mm Glass Fiber Coil Professional Speaker . Maximum MAER of 13.5% and minimum R2of 0.Dual 10 Inch Line Array for Church -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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