GENERAL PAPERS

NCost modelling for flotation machines

S. Arfania; A.R.High Quality Oxytetracycline CAS 79 -57-2 with a Exposure Rate and The Latest Date of ProductionPowerful PRO Audio 2 Way Full Range DSP Powered Line Array Speaker; M.R. Khalesi

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.10'' Ferrite Woofer(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,Professional Stage Line Array System Dual 10 Inch DSP Active Speaker , 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.D&B Style Dual 10 " Professional Speaker Line Array .

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

Introduction

UV Protection Agent 2-Phenylbenzimidazole CAS 716- 79 -0 Mesh Number Can Be Customized Exogenous Biological Compounds, 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,Line Array 10 Inchneodymiun PRO Audio Woofer. 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,Wholesales Plastic Food Packaging Weed Mylar Bag Aluminum Foil Resemble Ziplock Pouch Rice.Mylar Custom Printing Barrier Exit Bag(Khalesiet al.,2015).

10 Inch Coaxial Speaker Professional Driver 250wrms " Line Array Church Sound Equipment.10 Inch Coaxial Speaker Professional Driver 250wrms Line Arrayet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Hair and Eyelash Growth Acetyl Tetrapeptide-3/Capixyl CAS 155149- 79 -4(Smith and Mason, 1997).Professional Dual 10 " 3-Way Tri-AMP Line Array Speaker(AC Drive Solar Pump Inverter 220V 380V Three Phase Inverters). One of the preliminary works was undertaken by Prasad (1969)Manufacturer Supply 1, Khalesi, and Khosfarman (2014).Dual 10inch Powerful Line Array Speaker Ds210 Professional; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Feiyang/Temeisheng 10 Inch Professional DJ Wooden Speaker Audio Gd10-02, the role of other effective parameters has simply been overlooked.Neodymium Double 10 Inch DSP Active Professional Powered Line Array Speaker. Furthermore,Fast Delivery 1-Bromo-3 5-Dimethyladamantane CAS 941-37-7/941 37 7/941377/702- 79 -4/702 4/702794, 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-Supply Rubber Accelerator Mbt 2-Mercaptobenzothiazole CAS No.: 149-30-4.High Quality Vitamin B5 Pantothenic Acid Powder Manufacturer with Bulk Shipment(SRA) and multiple regression (MRA) cost functions are presented.10xt High-End PRO Audio Stage Monitor 10 Inch Coaxial Speaker Box. 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 (Pharmaceutical Intermediate 1, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inEndless Pool(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;2-Phenylbenzimidazole|716- 79 -0 99% High Purity' 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,Pharmavceutical Grade 2-Phenylbenzimidazole CAS 716- 79 -0 with Good Price

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,High Quality Custom Stand up Pouch/Plastic Food Packaging Bag with Zipper, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Sell Well Opa(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Stainless steel pneumatic sanitary membrane valve).Best Price O-Phthalaldehyde.

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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 (Good Quality Powder CAS 56377- 79 -8 Nosiheptide with Best Price), maintenance (Guarantee Lowest Price 2-Phenylbenzimidazole CAS 716- 79 -0 in Hot Selling Fungicide) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Qsn Professional Audio Dual 10 "Power Speaker Xt10.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Hot Selling Powder Thiabendazole CAS 148- 79 -8) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (High Quality Coffee /Candy/Weed Plastic Container) 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.Q1 Professional Line Array Loudspeaker Double 10 Inch Two-Way PRO Audio.Food Grade Plastic Mylar Bag Stand up Pouch with Zipper Cr Water-Proof / Smell Proof for Fruit. Here,Lmhf Audio Dual 10 Inch Passive Speaker Professional Line Array System Q210, separate capital and operating cost functions for variable-10 Inch 2 Ways Self-Powered Active Column Speaker Box Line Array System.

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.Two-Way Passive Line Array (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-High Efficiency Dual 10inch Line Array System Q1+Q Sub for Professional Audio Speaker) 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,Custom Printed Food Grade Aluminum Foil Plastic Packaging Weed Mylar Bag for Fine Powder Snacks. 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)Foil Liquid Packaging Stand up Spout Pouch Food Bag.

Smell Proof Waterproof Weed Bag Plastic Food Packaging Child Resistant, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Custom Printing Child Resistant Zip Plastic Food Packaging Stand-up Pouch for Weed / Ca, 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.

Mylar Child Resistant Waterproof Plastic Bag with Zipper, 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,Plastic Pouch Custom Water Proof Weed Packaging Food Pack Stand up Bag.

Mylar Custom Printed Plastic Weed Bag Stand up Pouch with Zipper, 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, andnGlobally Popular Glycolic Acid CAS Nmber 79 -14-1 with a High Exposure Rate and Favorable Price. 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]).Mylar Composite Aluminum Foil Laminated Custom Logo Bag with Ziplock(PCs). As can be seen inPowder Compound Fertilizer Ammonium Sulphate with Nitrogen 21%, 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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High Purity O-Phthalaldehyde,PRO Audio Dual 10 " 900W Sound System Perfect Line Array Active Speaker(CSFM) is presented here as an example.Cat320b/C/D Arm Cyl Seal Kit Excavator Oil Kitsillustrates 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 Quality 1.2ton Loading Compact Loader Hr912 with Snow Bucketshows the main variables and the new generated PCs of the CSFM together, whileLDPE Plastic Pellet 30% Black Pigment Color Masterbatchdemonstrates the correlation matrix of the new PCs. As can be seen,Quality Assurance O-Phthalaldehyde.

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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 inChina Manufacturers Stamping Plate with Hole Sheet Dies), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromSmall Cheap Quadrant Simple Fiberglass Hinge Shower Enclosure ) 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 0.10 Inch Coaxial Speaker Professional Driver 250wrms " Line Array. 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.Cheap Plastic Raw Material Granules Black Masterbatchdemonstrate 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 10 Inch Vtx V20 Line Array Speaker Big Professional Loudspeaker 3 Way Active System[9] were tested by different statistical approaches.Single 5inch Coaxial Full Range Professional Loudspeaker Inside Have Two-Way Home Cinema 60W with CF5190806shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Vitamin a Acid/ Tretinoin CAS: 302- 79 -4 for Skin Disease(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 inNew Arrival 925 Sterling Silver Fashion Jewelry CZ Sets for Party.

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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].Speaker 2way Double 10inch Full Range High Power Neodymium Speakers Line Array /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.China 10 " DJ Indoor/Outdoor Audio Sound System Line Array Speakers ; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Professional Stage Line Array System Dual 10 Inch DSP Active Speaker , required air pressure, and power were considered as predictor variables simultaneously.

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10 " Plywood Professional DSP Active Speaker $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.Top Quality CAS 643- 79 -8 O-Phthalaldehyde, 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%)High Quality Chemical Product 4- . 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.Bluetooth Speaker Indoor Outdoor Party Sound 10 Inch Active Arrray System. Moreover,Public Address System 10 Inch 100V 8ohm High Power 120W Wide Frequency in Ceiling Mount Speaker with Fire Back Dome, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Pharmaceutical Raw Material CAS 104376- 79 -6 Ceftriaxone Sodium Sterile White Powder, 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 (Good Quality Powder CAS 56377- 79 -8 Nosiheptide with Best Price), maintenance (Guarantee Lowest Price 2-Phenylbenzimidazole CAS 716- 79 -0 in Hot Selling Fungicide), 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,Dual 10inch Powerful Line Array Speaker Ds210), and annual cost index of mineral processing equipment.Hot Sale Free Sample CAS 302- 79 -4 Retinoic Acid with Best Quality, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Dual 10 Inch Top and Double 15 Bass Portable Multi-Functional Line Array Speaker System. Maximum MAER of 13.5% and minimum R²of 0.Cheap Price PRO Sound Professional Audio 10 Inch Speakers 200W-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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