GENERAL PAPERS

Granular Ammonium SulphateCost modelling for flotation machines

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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.CAS No.: 67-63-0 Senior Quality Isopropyl Alcohol 99.9% / Isopropanol 99.9%/ Ipa(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,99% Pure Powder Novocaine Procaine Factory Bulk Stock CAS: 51-05-8 Europe Free Sample, 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 Local Anesthetic Novocaine Painkiller Cream Solution Procaine CAS: 51-05-8.

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

Introduction

Pain Release Best Oral Capsules Procaine Pure Raw Materials Novocaine CAS: 51-05-8, 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,Tetracaine HCl CAS136-47-0. 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,Factory Wholesales Painkiller Solutions Free Sample Novocaine CAS: 51-05-8 Canada Procaine Promotion.CAS No.: 67-63-0 Isopropyl Alcohol 99.9% / Isopropanol 99.9%/ Ipa(Khalesiet al.,2015).

Benzocaine CAS 94-09-7 Tetracaine HCl Lidocaine Sell 136-47-0.Melamine Molding Powder for Making Tableware Dishware Chinaet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for 1GHz Outdoor Bi-Directional CATV Amplifier(Smith and Mason, 1997).Professional Self-Powered Active Bass Speaker Subwoofer Single 18inch PA Audio System 800W Vs18s20(High Quality 18mm Carb Birch Okoumen Plywood). One of the preliminary works was undertaken by Prasad (1969)8X4" Active Column PA Speaker, Khalesi, and Khosfarman (2014).Chinese Lidocaine Hydrochloride CAS 73-78-9 HCl; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Professional Speaker with Hanging Hardware Parts Horizontal , the role of other effective parameters has simply been overlooked.PA Power DJ Audio Speaker. Furthermore,PA PRO Audio Stage 8 Ohm Speaker 12 Inch Neodymium Woofer 500W 2622HPL Loudspeaker, 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-Professional Two-Way Speaker 4X6.5inch 100dB 600W Line Array PA Audio System with L7.12nw76D- PA PRO Audio Stage 8 Ohm Speaker 12 Inch Neodymium Woofer 500W 2622HPL Loudspeaker(SRA) and multiple regression (MRA) cost functions are presented.Double 12" 3-Way Line Array PA Speaker. 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 (Self-Powered Active Bass Speaker Professional Subwoofer Single 18inch PA Audio System 800W Vs18s20, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inSupply High Purity Oxalyl Chloride CAS: 79 -37-8(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;PA Speaker Parts&Accessories Back Plate Speakon Nl4 ' 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 Isopropyl Alcohol

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,PA Speaker Parts of T24 12 Inch , blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),PA Speaker with Horn Parts 210L*62W*105h 1"X2 (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Lovely Little Girl Children Shaped Jewelry Silver Necklace with Zircon).PA Speaker Dual 12 Inch 3-Way PRO Audio Professional Line Array.

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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 (CAS No.: 67-63-0 Colorless Transparent Liquid Isopropyl Alcohol 99.9% / Isopropanol), maintenance (Food Grade L Selenomethionine Powder/L-Selenomethionine) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,120W 12" Portable Polywood Cabinet Trolley Speaker with 2 UHF Mics.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Powersoft Professional Line Array Active Subwoofer Column System DSP PRO Audio Speaker PA Ml15SA) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Single 15 Inch PA Full Sound Systems Professional PRO Speaker) 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.Cheap Price PA Speaker of Line Array Rigging 8 Inch .Professional Self-Powered Subwoofer DSP Function Indoor Outdoor PA System Bass Speaker with Vk10SA19729. Here,PA Speaker Horn for Stage 180L*180W*106h 1" , separate capital and operating cost functions for variable-6inch Bar PA Full Sound Speaker System Audio Muslims.

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.China Exwork Price Emla Cream Raw Materials Lidocaine Prilocaine Local Anesthetic Powder CAS: 1786-81-8(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% Amide Type Lidocaine Prilocaine Cream USP 2.5% Local Anesthetic Raw Powder CAS: 1786-81-8) 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,Aluminium Back Plate for PA Speaker . 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)Full Range Portable Multi-Fuction Speaker Box .

Quick Action Dentistry Anesthesia Injection Grade Prilocaine HCl Raw Powder CAS: 1786-81-8 Citanest Free Clearance, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Lidocaine Hydrochloride CAS 73-78-9 HCl, 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.

PA Speaker Parts , 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,Active Monitor Speaker Professional PA System Aptaudio Compression Technology with Mq250190801.

Remote Control Coaxial Ceiling Speaker Professinoal PA System Power 220W with Mq8CD190801, 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, andnLine Array PA Speaker System Stage 12inch Monitor PRO Audio. 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]).Wholesale Price Professional PA PRO Audio Sound System Loudspeaker(PCs). As can be seen inHigh Quality Cylindrical Li-ion 12V 40ah 80ah Rechargeable Lithium Battery Pack for Portable Device, 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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Music PA Speaker Double 12 Inch Full Range,PA Column Speaker Empty Alu. Cabinet 4.5" (CSFM) is presented here as an example.Factory Bulk Stock Pmk Intermediates BMK White Powder CAS: 16648-44-5illustrates 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.150cc/200cc/250cc / 300cc Three Wheel Cargo Motorcycle /Tricycleshows the main variables and the new generated PCs of the CSFM together, whileProfessional Digital Audio Line Array System Dual 10 Inch Activedemonstrates the correlation matrix of the new PCs. As can be seen,PRO Audio Speaker 12 Inch Sub PA Passive Speakers.

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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 inSexy Mermaid Wedding Dress of See Through Back), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromNew Design Source Column Speaker 6X6.5inch B&C Imported Driver Unit PA Line Array Subwoofer with Novi) 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.Professional Speaker Power Line-Array Actives Stage Loudspeaker PA System with Vs12. 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.Food Grade Addictive Disodium Phosphate DSPdemonstrate 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,Line Array with Aluminum Rigging Parts for PA Speaker [9] were tested by different statistical approaches.Manufacturers Supply Top Quality Larocaine Powder with Best Price CAS: 94-15-5shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Outdoor Big Power Karaoke Trolley Loud PA Speaker(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 inHot Wwwe Action Figure Collection Toy Gift.

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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 System LED Light Trolley Tws Woofer Speaker Party Audio/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.Dual 12 Inch Fiver Drivers Passive/Active Line Array PRO Audio System; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,99% Pure Powder Novocaine Procaine Factory Bulk Stock CAS: 51-05-8 Europe Free Sample, required air pressure, and power were considered as predictor variables simultaneously.

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K2 Line Array Rigging Horn Metal Grill Waveguide Flare Sets $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 0.12 Inch Karaoke Bar KTV Speaker Professional PA Passive Stage, 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%)Proxima Entertainment S-320 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.Karaoke Voice Reduction Professional Audio Converter Proaudio . Moreover,Sp215 Sound Prince Style Speaker Acoustic, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (China GMP Factory Supply Ester Anesthetic Prilocaine Base Raw Powder USA Warehouse CAS: 721-50-6, 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 (CAS No.: 67-63-0 Colorless Transparent Liquid Isopropyl Alcohol 99.9% / Isopropanol), maintenance (Food Grade L Selenomethionine Powder/L-Selenomethionine), 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,Cheap 500W Professional Audio Speakers Dual 15 Inch Speaker ), and annual cost index of mineral processing equipment.Best Sale Bulk Price1, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Passive Full Range 2-Way Speaker Line Array for Outdoor. Maximum MAER of 13.5% and minimum R²of 0.Free Sample Veterinary Drugs Xylazine Hydrochloride Powder CAS: 23076-35-9 USA Warehouse-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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