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vol.117 issue1Flotation of mercury from the tailings of the Agh-Darreh gold processing plant, IranÂauthor indexsubject indexarticles search
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J. S. Afr. Inst. Min. Metall. vol.117 n.1 Johannesburg Jan. 2017



2.4GHz Outdoor Wireless Bridge 300Mbps Tdma High Power 500MWCost modelling for flotation machines

S. Arfania; A.R.300/650ml/ 1L Plastic Shampoo Cosmetic Pump Bottle2856 3kVA/5kVA/8kVA/10kVA/12kVA Solar on-Grid Power System for Home/Office/Farm/Hotel; 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.250ml 300ml 500ml 1L Clear Glass Juice Bottle Milk(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,20W 50W Portable Jpt/Ipg Laser Marking Machine in Germany, 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 0.1L /1.5L Glass Juice Bottle/Beverage Bottle.

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


Hot Wholesale 1L /2L/3L Laundry Liquid Detergent Bottle, 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,Factory Outlet Dog Tag Laser Marking Machine for Metal 50W. 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,1500cc Watercraft with 3seat.Portable-Rorary Type DOT Peen Marking Machine for Metal(Khalesiet al.,2015).

Engine Timing Kits for Cadillac Allante 4.6L V8 281 Cid 1993.Underwater Lightet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Wolf Wl80 Mini Dumper Loader with Bucket(Smith and Mason, 1997).WiFi Control Warm White 12V RGB Wall Mounted LED Swimming Pool Light Underwater(Wheel Loader Mini Wolf Wl80 with Forks). One of the preliminary works was undertaken by Prasad (1969)20W/30W/50W Fiber Laser Marking Machine for Metal/Plastic and All The Metals, Khalesi, and Khosfarman (2014).Automatic Red Point Laser Marking Machine for Metal Aluminum Plastic; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,8mm Thickness 316ss IP68 RGB DC12V 18W External Control Mode LED Swimming Pool Light, the role of other effective parameters has simply been overlooked.IP68 8W-35W Surface Mounted Green Color LED Underwater Swimming Light. Furthermore,IP68 8W-35W Surface Mounted Blue Color LED Underwater Swimming Light, 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-150ah 3kwh Power Supply Deep Cycle Rechargeable Solar Battery.8mm Thickness 160mm 8watt DC12V RGB LED Swimming Pool Underwater Light(SRA) and multiple regression (MRA) cost functions are presented.10W Tabletop Series Fiber Laser Marking Machine. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Manufacturer 3kwh Long Life Solar Home System with LiFePO4 Battery, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in0.4m 5GHz Parabolic Antenna with Gain 23dBi(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Shrink Wrapping Machine for Water Packing ' 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,55% Rubber Content Tyre China High Quality Motorcycle Tires 2.75- 17

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Professional Factory Motorcycle Tyre and Motorbike , blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),High Quality Motorcycle Parts Tyre (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (5oz 10oz 12oz Sauce Bottle with Screw Cap).Plastic Bottles Semi Automatic Film Shrink Wrapping Machine / Packing.

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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 (High Speed Bottles Shrink Wrapping Machine/Group Packing Machine), maintenance (Can Beer Use Automatic PE Film Heat Shrink Wrapping Group Packaging Machine for Half Paper Box Juice Production Line) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,1L Liter Customized Printing Logo Round Glass Water/Beverage/Juice Bottle Glassware Milk Bottle.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Ce ISO SGS Certification Wd Series Full Automatic Linear Type PE Plastic Film Stretch Shrink Wrapping Machine Packaging) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (3kwh 150ah Solar Home System Li-ion Battery Factory) 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.Excellent Motorcycle Cylinder for Gy6 -100 .3kwh Power Supply Solar Energy Battery Pack. Here,25kw Electromagnetic Induction Heater for Tools Welding, separate capital and operating cost functions for variable-Adjustable IP65 Lumileds SMD5050 Meanwell 800W LED Flood Light.

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.Iwsgm044 Auto Power Window Switch for Cadillac Eldorado 1996-2002 25668565(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-Mc4 Connector Combiner Box with 600V MCB for off Grid Solar System) 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,Professional Manufacture Y Solar Mc4 Energy System Connector PV. 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)Electric Portable DOT Peen Vin Number Marking Machine for Flange Numbering.

Highly Quality 1500V Solar Mc4 Energy System Connector IP67 PV, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (24watt New RGB Cool White Warm LED Underwater Swimming Pool Light, 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.

1L High End Glass Vodka Wine Bottle with Matte Black Finish, 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,Mc4y Solar Connector.

1000V Solar Mc4 Energy System Connector IP67 PV, 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, andnRF Wrinkle Removal Beauty 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]).Thermal RF & Fractional Wrinkle Removal(PCs). As can be seen in21% Fertilizer Ammonium Sulphate Caprolactam Grade Crystalline, 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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Wrinkle Removal Super RF Beauty Machine,Glass Bottle 1L Empty 1000ml Milk(CSFM) is presented here as an example.5GHz 18dBi Dual Polarization Sector WiFi Antennaillustrates 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.Lady's E-Scooter 800W Hot Sale Made in Chinashows the main variables and the new generated PCs of the CSFM together, while12 Inch Stage Subwoofer Home Theater/DJ Sub PRO Audiodemonstrates the correlation matrix of the new PCs. As can be seen,Mc4y Tyco Solar Connector.

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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 inHand Carved Freestanding/Pedestal Shower Stone Green Onyx Bathtub for Home Hotel Bathroom), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromFood Grade Container 1 Liter Square Olive Oil Latest Design Metal Tin Cans) 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.Empty Plastic Bottle 500ml / 1L /1000ml HDPE Trigger Pump Spray Bottles. 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.17.5-25 20.5-25 23.5-25 26.5-25 29.5-25 OTR Tire for Loadersdemonstrate 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,1000ml 500ml 250ml Airtight Glass Water Juice Bottle with Clip Top 1L[9] were tested by different statistical approaches.Steel Wall Bracket for Speaker with Quick Release Pin shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.1L 2L 5 L Plastic HDPE Powder Bottles(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 inBhs 3000L Compulsory Wet Mix Beton Concrete Mixer.

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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].30watt New RGB Cool White Warm LED Underwater Swimming Pool Light/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.All Terrain Vehicle Tyres ATV Wheel; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,20W 50W Portable Jpt/Ipg Laser Marking Machine in Germany, required air pressure, and power were considered as predictor variables simultaneously.

1L Plastic Trigger Sprayer Bottle with Spray. Moreover, the operating cost was detailed in different cost items.Velaslim Health Beauty Velashape Vacuum RF Cavitation LPG Body Slimming Equipments for, indicated in800W -1000W 60V/72V Electric Scooter with Lead-Acid Battery, and major extrapolation should be avoided.

20MHz RF Best Technology for Skin Tighten$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.Massage Lymphatic Drainage Body Shaping Slimming Beauty Apparatus, 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%)20MHz Thermal RF Wrinkle Removal Beauty Machine. 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.Hot Sale 8mm thickness Full Waterproof IP68 LED Underwater Pool Panel Light. Moreover,Color Changing Swimming Pool Lights, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Body Circumference Reduction RF Vacuum Fast Slimming System Beauty Apparatus, 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 (High Speed Bottles Shrink Wrapping Machine/Group Packing Machine), maintenance (Can Beer Use Automatic PE Film Heat Shrink Wrapping Group Packaging Machine for Half Paper Box Juice Production Line), 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,Underwater Pool Light with Niche ), and annual cost index of mineral processing equipment.Skin Tightening, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Globalipl RF Roller Vacuum Slimming Apparatus. Maximum MAER of 13.5% and minimum R2of 0.portable Fiber Laser Marker Machine for Eyeglasses Case Accessories-feasibility and even feasibility study level of projects.


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Paper received Apr. 2015
Revised paper Received Jul. 2016

10pack/M Automatic PE Film Combine Heat Shrink Wrapping Bottle Packing Wrapper Machine982 High Efficiency up to 99% on Grid Solar System 50kw Plants for Large Scale CommercialCorresponding author

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