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.K10 K20 P30 Tungsten Carbide Plate Strips for Cutting(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,Komastu PC60-6 Arm Cyl Oil Seal Kit, 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.Cat320b/C/D Arm Cyl Seal Kit Excavator Oil Kits.

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

Introduction

Pigment Violet 1 Toner for Ink, 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,Solvent Violet 59 . 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,Solvent Violet 13 for Plastic Application.Solvent Violet 11(Khalesiet al.,2015).

Solvent Violet G 49 for Plastic.Manufacturer ASTM 316L Uns S32205 Duplex Stainless Steel Tubeset al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for 1220X2440X9mm Carb P2 Glue Bleached Poplar Plywood for Furniture(Smith and Mason, 1997).Solvent Violet 10b 9(Pharmaceutical Industry CAS 643- 79 -8 O-Phthalaldehyde). One of the preliminary works was undertaken by Prasad (1969)Duplex Stainless Steel Sheet Super 2507, Khalesi, and Khosfarman (2014).ASTM A789 S32750 Uns Super Duplex Stainless Steel Pipe; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Uns S32750 2507 S32760 F55 1.4501 Super Duplex Stainless Steel Bar, the role of other effective parameters has simply been overlooked.Skycron® Disperse Violet 26/HFRL Dyestuff Fabric Dye. Furthermore,ASTM A790 Uns S31803 Seamless Stainless Steel Tube, 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-Manufacture High Quality PLA Silk Color Masterbatch.Ce Certification Plastic PP Blue Color Masterbatch(SRA) and multiple regression (MRA) cost functions are presented.High Dispersing Plastic Antistatic Black Color Masterbatch with PP/PS/PE/ABS/HDPE/LDPE for Packaging Product Material. 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 (Wireless Earbuds Headphones with Bluetooth 5.0 Earphones True Stereo Tws Charging Case for Sports Drive or Work, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in3D Ebony Veneneer Engineered Veneer Recomposed Okleiny Na Fizelinie for Plywood Door(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Bluetooth 5.0 Headset Mini Tws True Wireless Earbuds Stereo Bass in-Ear Earphone' 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,Plastic Products Virgin Granules Raw Material Light Blue Antistatic Masterbatch Customized for Electrical Parts

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),PP/PC Sheet Extrusion Machine(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Veneer Rotary Peeling Machine with Clipper Servo System Plywood).Water Treatment Disodium Phosphate .

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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 (Food Grade Addictive Disodium Phosphate DSP), maintenance (Disodium Phosphate Anhydrous CAS No 7558- 79 -4) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Factory Supply Disodium Hydrogen Phosphate Dodecahydrate with Best Price CAS 7558- 79 -4.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (K05/K10/ K20 /K30/K40 Tungsten Carbide Flat) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Changhong Film Stack Flexo Printing Machine) 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.Xft- 710 Axial Flow Fire Smoke Fan.Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors. Here,Disperse Violet 26 Dyes, separate capital and operating cost functions for variable-Skyzon® Cationic Violet 3R/Cationic Dyes/Cloth Dye.

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.Disperse Dyestuff Violet S3rl 200% C. I. 63(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-Pigment Violet 1 or Fast Rose Toner/Fast Lake) 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,Disperse Dyestuff Violet 200% P-CF for Textile. 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)Disperse Red/Blue/Orange/ Violet /Black.

Disperse Dyestuff Violet Recp-Hf 100% for Textile, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Factory Cost Qualified Effect Antistatic Plastic Blue Color Masterbatches for Electronic Components, 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.

Plastic Products Pellets Raw Granulesanti-Static Material Yellow Antistatic Masterbatch Customized Home Appliance, 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,Super Popular Endless Swimming Pool with Jacuzzi SPA for Market.

Massage Bathtub, 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 Filler Masterbatch for Injection Moulding. 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]).Swedish Soaking Bath Tubs Lowes Plastic Adult Freestanding Bathtub(PCs). As can be seen inSinopec Brand Chemical Fertilizer N21% with White Color, 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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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.910 Alicosolar 10kw on Grid Solar System with Power Inverter for Home CE/TUV/ISO Cretificateshows the main variables and the new generated PCs of the CSFM together, whileVelaslim Health Beauty Velashape Vacuum RF Cavitation LPG Body Slimming Equipments fordemonstrates the correlation matrix of the new PCs. As can be seen,2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA.

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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 inLakesea Brand 4X4 off Road Tires 4WD Muddy on Snow/Sand/Mud/Rock Light Truck Tyres 33X12.5r17lt), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromHot Selling X96 Mini Amlogic S905W 1GB 8GB TV Box Android 7.0 4K Full HD Quad Core Smart for Internet) 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.Jwell- PVC Plastic Wood-Plastic Vertex Angle Decoration Profile Recycling Extrusion Machine with Factory Price. 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.Portable Black Floor Tripod Speaker Stand Adjustable for 12 Inch PAdemonstrate 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,Jwell - Thermoplastic Polyurethane Film Extrusion Machine[9] were tested by different statistical approaches.Fast Shipping to Australia Quality 1.4 Butanediol Bdo 110-63-4shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Jwell - TPU Roll Car Paint Protection Matt Cast Film Machine(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 inBreathable Disposable Baby Pants Diaper Manufacturer.

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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].Diesel Engine Parts Fuel Injection Nozzle Dlla150p249/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.Polythene Plastic Sheet Making Machine; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Komastu PC60-6 Arm Cyl Oil Seal Kit, required air pressure, and power were considered as predictor variables simultaneously.

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1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower$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.Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q, 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%)Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189. 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.Xft- 710 Axial Flow Fire Extinguisher Fan. Moreover,Diesel Engine Parts Fuel Injection Nozzle Dlla155p274, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Diesel Engine Parts Fuel Injection Nozzle Dlla153p049, 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 (Food Grade Addictive Disodium Phosphate DSP), maintenance (Disodium Phosphate Anhydrous CAS No 7558- 79 -4), 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,Diesel Engine Parts Fuel Injection Nozzle Dlla155p273), and annual cost index of mineral processing equipment.Diesel Engine Parts Fuel Injection Nozzle Dlla154p332, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Diesel Engine Parts Fuel Injection Nozzle Dlla154pn006. Maximum MAER of 13.5% and minimum R²of 0.High Quality Nickel Alloy Monel 400 -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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