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.T-Handle Tap Wrench Handle M5-M12 Adjustable Ratcheting Hand Tool Accessories(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,PVC Plastic Marble Board/Plate/Wall Extruder, 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.Food Additive Granular Dihydrate Disodium Phosphate.

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

Introduction

Factory Supply Disodium Phosphate Food 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,E320L/B/C/D Boom Cyl Seal Kit Excavator Oil Kits. 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,Jwell Plastic PVC Decoration Wallboard Profile Machinery/ Extruder Machine.Disodium Phosphate Food Grade Manufacturer(Khalesiet al.,2015).

99% Tech Grade Disodium Phosphaten Used as Water-Softening Agent.Sodium Phosphate Monobasic Msp Industrial Grade CAS 7758-80-7et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for 1500W Electric Motorcycle(Smith and Mason, 1997).Ammonium Polyphosphate APP-II CAS No. 68333- 79 -9(Ignition Coil for Buick Chevrolet Cadillac Isuzu Opel Pontiac 10482928). One of the preliminary works was undertaken by Prasad (1969)High Quality Disodium Phosphate Sell by Factory, Khalesi, and Khosfarman (2014).Factory Supply Disodium Phosphate Anhydrous Food Additive; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Head Gasket , the role of other effective parameters has simply been overlooked.Disodium Hydrogen Phosphate . Furthermore,High Quality , 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-K20 K30 Tungsten Carbide Thread Rod with Double Helix Hole or Straight.Customized Carbide Spare Parts Assembly Orifice Main Valve Pulser(SRA) and multiple regression (MRA) cost functions are presented.Seal Kits Hyundai R210-7 Boom Cyl Arm Bucketcyl Oil. 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 (Chinese Manufacture Jcb332/Y6195 Universal Cylinder Seal Kit, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inCE Approved Vacuum Cavitation Roller RF Velashape 3 Slimming Machine(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Seal Kits Komatsu PC200-5/6 Boom Cyl Kit' 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,K10 K20 P30 Tungsten Carbide Plate Strips for Cutting

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Komastu PC60-6 Arm Cyl Oil Seal Kit, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Cat320b/C/D Arm Cyl Seal Kit Excavator Oil Kits(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Remote Sharing WiFi Home Decoration Gift Digital Photo Mini Picture Frame).Pigment Violet 1 Toner for Ink.

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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 (Solvent Violet 59 ), maintenance (Solvent Violet 13 for Plastic Application) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Solvent Violet 11.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Solvent Violet G 49 for Plastic) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Manufacturer ASTM 316L Uns S32205 Duplex Stainless Steel Tubes) 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.Solvent Violet 10b 9.Duplex Stainless Steel Sheet Super 2507. Here,ASTM A789 S32750 Uns Super Duplex Stainless Steel Pipe, separate capital and operating cost functions for variable-Uns S32750 2507 S32760 F55 1.4501 Super Duplex Stainless Steel Bar.

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.Skycron® Disperse Violet 26/HFRL Dyestuff Fabric Dye(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-ASTM A790 Uns S31803 Seamless Stainless Steel Tube) 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,Manufacture High Quality PLA Silk Color Masterbatch. 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)Ce Certification Plastic PP Blue Color Masterbatch.

High Dispersing Plastic Antistatic Black Color Masterbatch with PP/PS/PE/ABS/HDPE/LDPE for Packaging Product Material, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Wireless Earbuds Headphones with Bluetooth 5.0 Earphones True Stereo Tws Charging Case for Sports Drive or Work, 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.

Bluetooth 5.0 Headset Mini Tws True Wireless Earbuds Stereo Bass in-Ear Earphone, 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,Mini Wireless Stereo Tws 5.0 Music Earphone L18.

Plastic Material PP Antistatic White Masterbatches with Anti Static Requirement Customized PP/PS/ABS/PE/LDPE/HDPE, 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, andnPlastic Products Raw Material Light Green Color Antistatic Masterbatch Customized for Film Package. 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]).Jwell Plastic PVC Foamed Frame Profile Extrusion Machine(PCs). As can be seen inChinese Lidocaine Hydrochloride CAS 73-78-9 HCl, 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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Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia,PP/PC Sheet Extrusion Machine(CSFM) is presented here as an example.150ml Plastic Clear White Bullet Liquid Bottle for Cosmetic Industryillustrates 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.Cheap Price PA Speaker of Line Array Rigging 8 Inch shows the main variables and the new generated PCs of the CSFM together, whileGood Quality Factory Directly 1000W 60V/70V/20ah Electric Motorcycle with Pedalsdemonstrates the correlation matrix of the new PCs. As can be seen,Water Treatment Disodium Phosphate .

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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 inHigh Purity Nmn Beta-Nicotinamide Mononucleotide Powder CAS 1094-61-7 From Biocar), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromMetal Tinplate Container Engine Oil Can with Screw Cap) 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.Disodium Phosphate Anhydrous CAS No 7558- 79 -4. 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.Pharmaceutical Industry CAS 643- 79 -8 O-Phthalaldehydedemonstrate 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,Factory Supply Disodium Hydrogen Phosphate Dodecahydrate with Best Price CAS 7558- 79 -4[9] were tested by different statistical approaches.3D Ebony Veneneer Engineered Veneer Recomposed Okleiny Na Fizelinie for Plywood Doorshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.K05/K10/ K20 /K30/K40 Tungsten Carbide Flat(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 inLace Bridal Dress Ivory Organza Beaded Cap Sleeve Detachable Wedding.

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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].Xft- 710 Axial Flow Fire Smoke Fan/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.Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,PVC Plastic Marble Board/Plate/Wall Extruder, required air pressure, and power were considered as predictor variables simultaneously.

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Disperse Dyestuff Violet S3rl 200% C. I. 63$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.Pigment Violet 1 or Fast Rose Toner/Fast Lake, 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%)Disperse Dyestuff Violet 200% P-CF for Textile. 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.Disperse Red/Blue/Orange/ Violet /Black. Moreover,Disperse Dyestuff Violet Recp-Hf 100% for Textile, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Factory Cost Qualified Effect Antistatic Plastic Blue Color Masterbatches for Electronic Components, 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 (Solvent Violet 59 ), maintenance (Solvent Violet 13 for Plastic Application), 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,Plastic Products Pellets Raw Granulesanti-Static Material Yellow Antistatic Masterbatch Customized Home Appliance), and annual cost index of mineral processing equipment.Super Popular Endless Swimming Pool with Jacuzzi SPA for Market, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Massage Bathtub. Maximum MAER of 13.5% and minimum R²of 0.PA Filler Masterbatch for Injection Moulding-feasibility and even feasibility study level of projects.

References

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Paper received Apr. 2015
Revised paper Received Jul. 2016

PA Filler Masterbatch for Injection MouldingSteel Grade Nitrogen 20.5% Ammonium SulphateCorresponding author