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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. 2017

http://dx.doi.org/10.17159/2411-9717/2017/v117n1a13Â

GENERAL PAPERS

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Tarbiat Modares University, Iran


SYNOPSIS

Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.100% Safe Arriving Australia GB-B L 1.4 Butanediol Bdo 110-63-4(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,High Purity Levamisole Manufacturer CAS 14769-73-4 with Best 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.Free Sample Organic Chemicals 1.

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


Introduction

High Quality Phena, 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,Manufacturer Supply Raw Material Levamisole Powder CAS 14769-73-4. 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,18" Fane Style Aluminum Speaker Frame.18" Die Cast P-Auido Style Aluminum Frame(Khalesiet al.,2015).

Professional Stage Active Line Array Speaker with DSP.Single 18" Subwoofer Speaker Boxet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for China Heavy Load Inverter 220V 380V Three Phase Converter DC to AC(Smith and Mason, 1997).Wholesales Veterinary Drugs Tiletamine HCl 14176-50-2 USA Warehouse(Electric Motorcycle ). One of the preliminary works was undertaken by Prasad (1969)12" Professional Rcf Style Speaker Frame, Khalesi, and Khosfarman (2014).Horn Professional Speaker H3; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Coaxial Loudspeaker TD12, the role of other effective parameters has simply been overlooked.18'' Subwoofer Speaker Box Ls1200. Furthermore,Dual 12" Subwoofer Speaker Box, 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-DV Portable Speaker 12 Inch 1600W Subwoofer Box Audio Professional.Fast Delivery 1(SRA) and multiple regression (MRA) cost functions are presented.Professional Speaker Box F12+. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.

Methodology

Data

Thirty-seven major flotation machines (Df B&C Trees Speaker Subwoofer Audio Professional, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in5GHz Dual Polarization Enclosure WLAN Antenna(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;15'' Coaxial 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,Tetracaina HCl Tetracaine Base Depuracao Segura Mercado 100% Brasileiro

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The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),China Factoty Supply Levamisole HCl CAS16595-80-5 Hydrochloride Tetramisole(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Sea Shipping FCL Freight Forwarder From China to Buenos Aires Argentina Professional Fast Reliable Logistics Services).400 Watt Portable Music Player Speaker Professional Audio.

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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 (Dual 6inch Loudspeaker for Coffee Room Restaurant Conference Speakers), maintenance (Dm 15 Inch PA Full Sound Systems Professional PRO Speaker) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,12inch KTV Bar PA Full Sound Speaker System Audio.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Dare Dual 8" Neodymium Active Line Array Set PA System) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (12" Die Cast Aluminum PA Speaker Frame) 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.PA Speaker Dual 18" Subwoofer System.PA Speaker with Line Array Tweeter Horn . Here,Active Mini Line Array Speaker with DSP Amplifier Module, separate capital and operating cost functions for variable-Quality Certified Product Ethyl 2-Phenylacetoacetate CAS: 5413-05-8 BMK Powder.

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.High Quality Karaoke Loudspeaker with B&C Compression Driver(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-99% Tetracaine Hydrochloride/ HCl Powder CAS 136-47-0) 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,Factory Supply BMK Powder Glycidate CAS: 5413-05-8. 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 Factory Supply CAS 99-93-4 4-Hydroxyacetophenone.

Chinese Manufacturer Bulk Stock Pmk Intermediates16648-44-5 BMK White Powder, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (99.9% High Purity Prilocaine Hydrochloride/Prilocaine HCl CAS 1786-81-8, 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.

High Quality 4'-Hydroxyacetophenone CAS 99-93-4 4-Hydroxyacetophenone with Best Price, 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,Factory Bulk Stock Pmk Intermediates BMK White Powder CAS: 16648-44-5.

99% BMK White Powder Glycidate Bulk Sales CAS: 16648-44-5, 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, andn99% 4'-Hydroxyacetophenone CAS 99-93-4 100% Pass Customs. 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]).62442 Shiny and Non Phena Powder 62 44 2(PCs). As can be seen inDiesel Engine Parts Fuel Injection Nozzle Dlla153p049, 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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Hair Loss Treatment Acetyl Tetrapeptide-3/Capixyl CAS 827306-88-7 Purity Min 99% Powder,100% Passing The Customs Europe Free Shipping BMK Glycidate 16648-44-5(CSFM) is presented here as an example.Lucky Tone SIP PA System 15W Poe Ceiling Speaker with Built-in Amplifier and Fire Dome for Public Addressillustrates 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.St 5kw Single Phase AC Electric Alternator Generatorshows the main variables and the new generated PCs of the CSFM together, whileHigh Quality 5dBi 4G Lte Antenna for Huawei B593 B880 B310 B2000 Router External SMA-Male Connectordemonstrates the correlation matrix of the new PCs. As can be seen,Trolley Large Audio Loudspeaker Box Professional Stage Active PA Speaker.

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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 inWholesale Manufacturer Classic Printing Picnic Cooler Bag), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromHot Sells Solar Power System for Home 3kwh with Both AC&DC Output) 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.Portable 15inch PA Speaker F15+. 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.New Arrival 4K Smart S905X2 TV Box 4+64GB X96 Minidemonstrate 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,Pharmaceutical Chemical CAS 236117-38-7[9] were tested by different statistical approaches.1220X2440X9mm Carb P2 Glue Bleached Poplar Plywood for Furnitureshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Speaker 12 Inch SA-212 Professional Sound Box Portable Passive(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 inSuper Silent Electric Portable Power Diesel Generator Used with Cummins Engine at 60Hz.

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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].PA Woofer Speaker T- 10 12 15/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.

Discussion

Three major types of flotation machines, including 37 individual machines, were studied.Passive Double 10 Inch Proal Audios Sound System Line Array Speakers for Direct Sale; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,High Purity Levamisole Manufacturer CAS 14769-73-4 with Best Price, required air pressure, and power were considered as predictor variables simultaneously.

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Wholesale Factory Price CAS: 16648-44-5 BMK Glycidate Powder$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.Buy Real Pharmaceutical Intermediates BMK Glycidate Powder 16648-44-5, 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%)10 " PRO Sound PA Line Array Loudspeaker Audio Speaker System. In the MRA cases, this property is owed to the SFM (3.05%).

Conclusion

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.Big Outdoor Sound Equipment Active Dual 8" Line Array Speaker. Moreover,Professional Powered Line Array Selfpowered Speakers Active System, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (MBN1503 PA Woofer , 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 (Dual 6inch Loudspeaker for Coffee Room Restaurant Conference Speakers), maintenance (Dm 15 Inch PA Full Sound Systems Professional PRO Speaker), 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,Best Quality BMK Glycidate Raw Materials Fororganic Intermediates Bulk Price), and annual cost index of mineral processing equipment.Self Powered Generator Double 8 Inch Outdoor Sound Indoor Line Array, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Light and Durable Mixing Console Mg124cx Audio Mixer. Maximum MAER of 13.5% and minimum R2of 0.Chassis/Dolphin/Powerful Speaker for Stadium-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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