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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.Tetracaine HCl CAS136-47-0(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,Factory Wholesales Painkiller Solutions Free Sample Novocaine CAS: 51-05-8 Canada Procaine Promotion, 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.CAS No.: 67-63-0 Isopropyl Alcohol 99.9% / Isopropanol 99.9%/ Ipa.

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

Introduction

Benzocaine CAS 94-09-7 Tetracaine HCl Lidocaine Sell 136-47-0, 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,Melamine Molding Powder for Making Tableware Dishware China. 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,Professional Self-Powered Active Bass Speaker Subwoofer Single 18inch PA Audio System 800W Vs18s20.8X4" Active Column PA Speaker(Khalesiet al.,2015).

Chinese Lidocaine Hydrochloride CAS 73-78-9 HCl.Professional Speaker with Hanging Hardware Parts Horizontal et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Speaker Wall Mount Bracket for PRO Audio Steel 134.8L*90W*160h (Smith and Mason, 1997).PA Power DJ Audio Speaker(Ceftriaxone Sodium 99% API CAS 104376- 79 -6 for Injection Grade). One of the preliminary works was undertaken by Prasad (1969)PA PRO Audio Stage 8 Ohm Speaker 12 Inch Neodymium Woofer 500W 2622HPL Loudspeaker, Khalesi, and Khosfarman (2014).Professional Two-Way Speaker 4X6.5inch 100dB 600W Line Array PA Audio System with L7; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,12nw76D- PA PRO Audio Stage 8 Ohm Speaker 12 Inch Neodymium Woofer 500W 2622HPL Loudspeaker, the role of other effective parameters has simply been overlooked.Double 12" 3-Way Line Array PA Speaker. Furthermore,Self-Powered Active Bass Speaker Professional Subwoofer Single 18inch PA Audio System 800W Vs18s20, 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-PA Speaker Parts&Accessories Back Plate Speakon Nl4 .Professional Speaker PRO Audio System Three-Way Large Line Array PA Mla8312/Mla8312da(SRA) and multiple regression (MRA) cost functions are presented.15 Inch PRO Audio Speaker Woofer with Dual Voice Coil Design Loudspeaker. 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 (Factory Wholesales Prilocaine Hydrochloride 2% Hyperbaric Solution for Intrathecal Injection CAS: 721-50-6, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHigh Quality Cylindrical Li-ion 12V 40ah 80ah Rechargeable Lithium Battery Pack for Portable Device(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;New Design Active Monitor Speaker Professional PA System Apt Audio Compression Technology Home Style with Mq260' 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,CAS No.: 67-63-0 Colorless Transparent Liquid Isopropyl Alcohol 99.9% / Isopropanol

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Food Grade L Selenomethionine Powder/L-Selenomethionine, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),120W 12" Portable Polywood Cabinet Trolley Speaker with 2 UHF Mics(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Ce UL Saso Screw Base E27 E40 40W Column Energy Saving LED Light Bulb Made in China for Office).Powersoft Professional Line Array Active Subwoofer Column System DSP PRO Audio Speaker PA Ml15SA.

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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 (Single 15 Inch PA Full Sound Systems Professional PRO Speaker), maintenance (Cheap Price PA Speaker of Line Array Rigging 8 Inch ) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Professional Self-Powered Subwoofer DSP Function Indoor Outdoor PA System Bass Speaker with Vk10SA19729.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (PA Speaker Horn for Stage 180L*180W*106h 1" ) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (6inch Bar PA Full Sound Speaker System Audio Muslims) 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.China Exwork Price Emla Cream Raw Materials Lidocaine Prilocaine Local Anesthetic Powder CAS: 1786-81-8.99% Amide Type Lidocaine Prilocaine Cream USP 2.5% Local Anesthetic Raw Powder CAS: 1786-81-8. Here,Aluminium Back Plate for PA Speaker , separate capital and operating cost functions for variable-Full Range Portable Multi-Fuction Speaker Box .

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.Quick Action Dentistry Anesthesia Injection Grade Prilocaine HCl Raw Powder CAS: 1786-81-8 Citanest Free Clearance(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-Lidocaine Hydrochloride CAS 73-78-9 HCl) 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,PA Speaker Parts . 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)Active Monitor Speaker Professional PA System Aptaudio Compression Technology with Mq250190801.

Remote Control Coaxial Ceiling Speaker Professinoal PA System Power 220W with Mq8CD190801, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Line Array PA Speaker System Stage 12inch Monitor PRO Audio, Khalesi, and Khosfarman, 2014).

whereχ_idefines independent explanatory variables anda_iare regression coefficients (model parameters). As was mentioned, independency ofx_ivariables 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 Price Professional PA PRO Audio Sound System Loudspeaker, 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]:

whereX_obsis the observed value,x_ethe estimated value at time/placeI,and n,Full Range Speaker 4X4inch Professional PA Sound System Foh for Medium with Ml419731.

Music PA Speaker Double 12 Inch Full Range, 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).

whereC_eis the estimated cost,C_athe actual cost, andnPA Column Speaker Empty Alu. Cabinet 4.5" . 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]).PRO Audio Speaker 12 Inch Sub PA Passive Speakers(PCs). As can be seen inFactory Bulk Stock Pmk Intermediates BMK White Powder CAS: 16648-44-5, 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 andX_ias Equations [5] and [6]:

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In this research, main variables ofX₁, X₂... X_nwere 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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Professional Speaker Power Line-Array Actives Stage Loudspeaker PA System with Vs12,Line Array with Aluminum Rigging Parts for PA Speaker (CSFM) is presented here as an example.Professional Digital Audio Line Array System Dual 10 Inch Activeillustrates 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 Speed CKD SKD Pedals Disc Brake Electric Motorcycle Scooter for Olderly or Adultshows the main variables and the new generated PCs of the CSFM together, whileNew Generation Engine Er08 Wheel Loader with CE/Bucket for Saledemonstrates the correlation matrix of the new PCs. As can be seen,Outdoor Big Power Karaoke Trolley Loud 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)

whereX_iare main technical variables (like power or required air),a_iare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inIP66 LED Waterproof Luminaire), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromFood Grade Addictive Disodium Phosphate DSP) 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.PA System LED Light Trolley Tws Woofer Speaker Party Audio. 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.3840watts AC Output Built-in Inverter 80A Silent Power Portable Electric Storage and Generator with CE Certificatedemonstrate 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,Dual 12 Inch Fiver Drivers Passive/Active Line Array PRO Audio System[9] were tested by different statistical approaches.Nutrition Enhancer Hot Selling High Quality N-Glycyl-L-Tyrosine Powder CAS 658- 79 -7 White with Reasonable Price and Fast Deliveryshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.50W 8" Portable Polywood Cabinet Trolley Speaker with 2 UHF Mics(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 inIndoor Full Color P5/P6/P8/P10 LED Display for Advertising Screen Panel Sign.

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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].K2 Line Array Rigging Horn Metal Grill Waveguide Flare Sets /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.12 Inch Karaoke Bar KTV Speaker Professional PA Passive Stage; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Factory Wholesales Painkiller Solutions Free Sample Novocaine CAS: 51-05-8 Canada Procaine Promotion, required air pressure, and power were considered as predictor variables simultaneously.

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Sp215 Sound Prince Style Speaker Acoustic$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.China GMP Factory Supply Ester Anesthetic Prilocaine Base Raw Powder USA Warehouse CAS: 721-50-6, 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%)Cheap 500W Professional Audio Speakers Dual 15 Inch Speaker . 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.Best Sale Bulk Price1. Moreover,Passive Full Range 2-Way Speaker Line Array for Outdoor, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Free Sample Veterinary Drugs Xylazine Hydrochloride Powder CAS: 23076-35-9 USA Warehouse, 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 (Single 15 Inch PA Full Sound Systems Professional PRO Speaker), maintenance (Cheap Price PA Speaker of Line Array Rigging 8 Inch ), 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,High Power Horn Speaker H3), and annual cost index of mineral processing equipment.Horn Speaker L-Acoustics Kudo Line Array+ PA System Array Box, and over- extrapolation could result in misguiding estimates.

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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