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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017



2-Carboxybenzaldehyde/Phthalaldehydic Acid CAS 119-67-5Cost modelling for flotation machines

S. Arfania; A.R.1L Paint Tin Cans/Empty Food Grade Can with LidMetal Tin Can Engine Oil Empty Tinplate Container; M.R. Khalesi

Tarbiat Modares University, Iran


Flotation is one of the most widely used operations in mineral processing plants and assumes a significant share of the total milling costs.17.5-25 20.5-25 23.5-25 26.5-25 29.5-25 OTR Tire for Loaders(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,20.5-25/29.5-25/23.5-25/14.00-24/7.50-16 New E-3/L-3 Loader OTR Bias Tyre, 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.High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Swimming Pool Lights.

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


China Electric Tricycle 350W 500W 800W for Adult, 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,Llantas High Quality L5 OTR Tyre 26.5-25. 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,1L Empty Round Brake Fluid Can Boxes.Pneumatic Electric Portable Truck Car Frame Beam Metal Coding Machine Marking Coder(Khalesiet al.,2015).

Motor King Rear Double Axle Tricycle for Heavy Loader.Pneumatic Frame Number Marking Machine Metal Cutting Plotter Plate Beam Codinget al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for MPPT Function Variable Frequency Drive Motor Controller Power Supply Generator(Smith and Mason, 1997).1L Custom Metal Round Tin Cans Box Packaging for Glue Coating Slovent(Softel 5-1000MHz Outoodr Bi-Directional CATV RF Amplfier with 2 Outputs and Return Path). One of the preliminary works was undertaken by Prasad (1969)1L /1000ml Extra Virgin Olive Oil Metal Can, Khalesi, and Khosfarman (2014).1L Olive Oil Can Cooking Empty Tin Can/Pot Metal; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Heavy Loader 5wheel Cargo Tricycle with Cabin, the role of other effective parameters has simply been overlooked.High Precision and Fast Speed Nonmetal CO2 Laser Marking Machine. Furthermore,Motor Cargo Tricycle for 2-3ton Loader, 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-1L Empty Round Tin Can with Plastic Lid Manufacturer.1L Extra Virgin Olive Oil Metal Can with Cover(SRA) and multiple regression (MRA) cost functions are presented.Solar & Mains 3840wh 80A 220V Outlet Battery for Appliances with Rated Power Under 1500W. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Gy6 -125/ 150ccformaular, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inMotorcycle Spare Part Turn Light for Gy6 -150(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Double Chasis Cargo Tricycle' names:

Euro 5 Gy6 -50cc 4t Moped: based on 36-foot,Chinas Motos Electricas 500W/ 800W /1200W/1000W Electrical Electric Scooter ,Water Proof Closed Box Delivery Tricycle,3840watts 50Hz 80A Built-in Inverter Silent Power Portable Electric Storage and Generator with CE Certificate, and level control

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,Barrow Mini Dumper with Three Wheels

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,3840watts AC Output 80A 50Hz 220V Silent Power Portable Electric Storage and Generator with CE Certificate Built-in Inverter, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Oil Petrol Anti Corrosive Tantalum Diaphragm Pressure Sensor(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Professional design vinyl plastic flooring Spc PVC).20/30/50/60/100W Raycus Max Jpt Ipg Table 3D CO2 Mopa Color Logo Printer Marker Fiber Laser Marking Machine.

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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 (Gy6 150cc EEC Scooter), maintenance (250W- 800W Handicapped Mobility Scooter for Old People with Basket) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,with Built-in LiFePO4 Energy Storage Portable Generator 3.8kwh 80A Enjoys 2 Years Warranty.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Camping Power / RV LiFePO4 Energy Storage Portable Generator 3.8kwh 80A 220V AC Output Enjoys 2 Years Warranty) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (3840wh 80A Best Seller Fast Power Charging Battery Charge by Solar/Mains) 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.Pedal E-Bike / Scooter Electric Bicycle 500W/ 800W.Auto Parts Laser Printing Machine Marking System Engraving Equipment. Here,Water-Proof Cover 3 Wheel Cargo Gasoline Trike, separate capital and operating cost functions for variable-Jpt Mopa Color Fiber Laser Cutter Raycus Max Ipg 20W 30W 50W Metal Marking Engraving Cutting Machine.

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.2021 Most Hot Selling Electric Mope E-Motorcycle 500W- 800W(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-Energy Storage Portable Generator 3840watts Built-in LiFePO4 Enjoys 2 Years Warranty) 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,30W CO2 Touch Screen Laser Marking Coding Engraving Machine. 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)with Built-in LiFePO4 Energy Storage Portable Generator 3.8kwh Enjoys 2 Years Warranty.

Solid State Inductive Heating Furnace for Tyre Cord Wire, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Factory Supply Biomass Rice Husk Charcoal Making Machine, Khalesi, and Khosfarman, 2014).

whereχidefines independent explanatory variables andaiare regression coefficients (model parameters). As was mentioned, independency ofxivariables 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.

Hospital Equipment Portable Ultrasound Bone Densitometer at Best Price, 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]:

whereXobsis the observed value,xethe estimated value at time/placeI,and n,Ce Approved Ho-100 Eyes Hospital Use Ophthalmic Ultrasound Scanner.

Outdoor/Home Use Built-in LiFePO4 Energy Storage Portable Generator 3.8kwh 80A Enjoys 2 Years Warranty, 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).

whereCeis the estimated cost,Cathe actual cost, andnLow Failure Rate High Efficiency Induction Metal Heating Machine . 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]).Portable Ultrasonic Ophthalmology Ophthalmic a/B Scan(PCs). As can be seen inSulfasalazine CAS No. 599- 79 -1, 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 andXias Equations [5] and [6]:

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In this research, main variables ofX1, X2... Xnwere 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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Camping Power / RV LiFePO4 Energy Storage Portable Generator 3.8kwh 80A Enjoys 2 Years Warranty,Hot Sale Mini High Frequency 25kw Induction Heater Price(CSFM) is presented here as an example.Solar Energy System 3kwh Power Home Built in Inverterillustrates 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.5GHz Antenna High Gain 16dBi Panelshows the main variables and the new generated PCs of the CSFM together, while1L Empty Round Edilbe Cooking Oil Metal Tindemonstrates the correlation matrix of the new PCs. As can be seen,Convex Series Probe Type Wireless Mini Ultrasound Scanner.

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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)

whereXiare main technical variables (like power or required air),aiare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inIron Die Struck Plating Gold&Soft Enamel Lapel Pin), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromKraft Paper LDPE Supermarket Vegetable Cosmetic Fruit Packaging Bag) 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.Hot Selling 2ND Generation Ultrasound Bone Densitometer. 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.2021 Best Selling Dual Battery Pedal Assisted Electric Scooter Bicycledemonstrate 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,Real Mink 3D 5D New Fashion Fast Shipping High Quality Best Seller Eyelash[9] were tested by different statistical approaches.Wall Mounted Swimming Pool Lamp Underwater LED Light 18watt 12V RGB with Two Years Warrantyshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.High Quality Economic Ultrasound a/B Scan for Ophthalmology (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 inQtj4-25 PLC Control Automatic Fly Ash Sand Stone Cement Paving Solid Curbstone Hollow Concrete Block Brick Production Line Without Hydraulic System.

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Cost model for variable-Ut-O500 Diagnosis System Portable Full Digital Ophthalmic Ultrasound a/B Scan for Eye

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].Ophthalmic a Scan and Pachymeter Combined Unit/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.


Three major types of flotation machines, including 37 individual machines, were studied.Ophthalmic Optical Pachymeter & Biometer / a Scan ; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,20.5-25/29.5-25/23.5-25/14.00-24/7.50-16 New E-3/L-3 Loader OTR Bias Tyre, required air pressure, and power were considered as predictor variables simultaneously.

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SA831r Outdoor Return Path CATV Trunk Amplifier$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 0.2200 Degree Vacuum Hot Pressing Furnace High-Temperature for Cim, 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%)Portable Induction Heater for Crystal Growth. In the MRA cases, this property is owed to the SFM (3.05%).


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.Dry diaphragm membrane sanitary pressure transducer. Moreover,Mobile Digital High Frequency Mini Induction Brazing Welding Equipment for Sale, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (High Frequency Induction Heater , 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 (Gy6 150cc EEC Scooter), maintenance (250W- 800W Handicapped Mobility Scooter for Old People with Basket), 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,Industrial Vacuum Atmosphere Hot Pressing Sintering Furnace), and annual cost index of mineral processing equipment.Softel 4u 12 Channel Agile CATV Analog RF Modulator, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Maintence Grease Gun 21V LCD Real Time Information Reading Hand Tool. Maximum MAER of 13.5% and minimum R2of 0.Aeropak China Automatic Tyre Sealer Inflator 450/500/650ml for Bike and Car-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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