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


Multi-Function 10 " Passive Full Range DJ Stage Speaker SystemCost modelling for flotation machines

S. Arfania; A.R.High Power Outdoor Flood Light for Stadium/ Tennis Court 600W 800W 1000WGy6 -50cc OEM Gas Scooter; 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.Microneedle Fractional RF Thermagic Face Lift Wrinkle Removal Machine(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,RF Microneedle Thermal Facial Lift Beauty Equipment, 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.Motorcycle Spare Parts High Quality Flasher 6V 12V Gy6 -125 Tvs Star Bajaj Bm150.

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


Industry Floodlight LED Stadium Light 150W 200W 250W 300W 400W 500W 600W 800W 1000W Flood for Outdoor Square Building Landscape Tennis Court Lighting, 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,High Feedback Tied Malaysian Virgin Hair. 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,Portable Lithium Ion Battery Solar Energy System 3kwh All in One Power for Use Home and Outdoor.Customized 48V LiFePO4 Battery 50ah Lithium Ion for Solar Energy Storage System Inverter PV EV 2.5kwh 3kwh 5kwh(Khalesiet al.,2015).

150cc 300cc 500cc 650cc 2 Seat Adult Frames Go Kart.200cc Racing Go Kart for Sale Cheapet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Safe Shipping Sarms Powder ACP-105(Smith and Mason, 1997).China 300cc Adult Road Legal 2 Seat Pedal Go Kart(Carb Approved Birch Plywood). One of the preliminary works was undertaken by Prasad (1969)3kwh Solar Energy Storage System, Khalesi, and Khosfarman (2014).2021 New Design 3kwh off Grid Solar Power System LiFePO4 Battery for Home Use with Built-in Inverter; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Peanut Shell and Rice Husk Continuous Carbonization Oven, the role of other effective parameters has simply been overlooked.Factory Direct Wholesale 300- 17 Motorcycle Tire/Tyre. Furthermore,ISO9001 Certificate Factory Supply Nylon 6pr New Motorcycle Tyre Tubes, and estimation of detailed operating cost items such as maintenance, lubrication, not possible. To overcome these deficiencies, this paper aims to introduce up-to-Handheld Small Portable Digital High Frequency Induction Brazing Machine with Soft Cable.Mobile Digital High Frequency Mini Induction Brazing Welder for Aluminum Tube Pipe(SRA) and multiple regression (MRA) cost functions are presented.High Quality Radio Frequency Aesthetic Equipment. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (China Good Quality 2.75- 17 Tubeless Motorcycle Tire/Tyre, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHigh Quality Disodium Phosphate Sell by Factory(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;2.50- 17 ' 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,Made in China High Performance Tubeless Fat Motorcycle Tire 180/55- 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,Good Packed Bottle PE Film Shrink Wrapping Machine China, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),ISO9001 Certified Factory Price China Motorcycle Tires 2.75- 17(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Engine Spare Parts Valve Cotter 02108102 for 56D Collet).25kw High Frequency Induction Heater for Bolts&Rivet.

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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 (Fractional RF Vacuum Slimming Machine for Lose Weight), maintenance (Online Flying Laser Marking Machine for Operation Line) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Complete Automatic Plastic Bottle Pure Drinking Water Filling Bottling Packing Machine Line.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Portable 20Hz RF Face Lift Machine) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (ISO9001 Motorcycle Spare Part Tubeless Motorcross Tire Size 100/90- 17) 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.DOT Certified off Road Chinese Motorcycle Tire 3.00- 17.Linear Type Thermal Film Packing Machine / Equipment. Here,Good Solutions 3kw Solar Home Energy off Grid System, separate capital and operating cost functions for variable-Jalyn Motorcycle Spare Parts Speedometer Assy Fits for Gy6 /Hunter.

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.25kw High Frequency Induction Heat Soldering Machine(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-Super Bright Outdoor 300W 400W 500W 600W 800W 1000W LED Flood Light) 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,10pack/M Automatic PE Film Combine Heat Shrink Wrapping Bottle Packing Wrapper 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)Beverage Water Packing Equipment .

Automatic Shrink Wrapping Machine 0-20package/Min, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Automatic Bottle PE Film Shrink Wrapping Packing 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.

Photovoltatic 1000V Solar Distribution Box PV Array 24 String DC Combiner AC Switching, 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,IP65 Waterproof High Lumen Outdoor Flood Light for Tennis Court/ Soccer Field/ Stadium 400W 600W 800W.

Waterproof 800W Deformable High Mast Flood LED Lighting for Outdoor Stadium Airport Golf Course Container Wharf, 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, andn1L HDPE Plastic Bottle Chemical. 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]).Sport Court Stadium Spotlight Outdoor Projector Light 600W 800W 1000W LED Floodlight(PCs). As can be seen inPA Audio Sound System Line Array Speaker 10 Inch Neodymium Woofer with Wooden Box., 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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Waterproof IP66 Adjustable High Power LED Stadium Lamp 100W 200W 300W 400W 600W 800W 1000W 1200W 1500W Flood Light,High Quality 1L 32oz Amber Glass Bottle in Stock(CSFM) is presented here as an example.China Jwell PVC Dual/Four Pipe High Speed Extrusion Equipment C-PVC/U-PVC/PVC-O Making Machineillustrates 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.D&B Style Dual 10 " Compact Line Array shows the main variables and the new generated PCs of the CSFM together, whileEmpty Round Tin Can Paint Package Containerdemonstrates the correlation matrix of the new PCs. As can be seen,Fast Delivery Plastic Empty Spray Bottle Lotion Pump for Hand Sanitizer 30ml- 1L.

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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 inChina Best Valentine Gift Artificial Rose Bear Christmas Plastic Flower 25cm Box Teddy), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromWholesale Top Quality Retinoic Acid/Retinoic Acid Powder/Tretinoin Powder/Vitamin a CAS 302- 79 -4) 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.Automatic Pure/Mineral Bottle Water Packing Machine . 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.49 Inch Portable Alone Standing LED LCD Poster Digital Menu Boarddemonstrate 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 71g 1L HDPE Plastic Bottle for Chemical Powders Liquids[9] were tested by different statistical approaches.1L Custom Round Small Metal Empty Tin Cans with Lidsshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.300/650ml/ 1L Plastic Shampoo Cosmetic Pump Bottle(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 inFull Color P2.9/P3.91mm Indoor Curved LED Display Screen.

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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].20W 50W Portable Jpt/Ipg Laser Marking Machine in Germany/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.1L /1.5L Glass Juice Bottle/Beverage Bottle; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,RF Microneedle Thermal Facial Lift Beauty Equipment, required air pressure, and power were considered as predictor variables simultaneously.

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1500cc Watercraft with 3seat$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.Portable-Rorary Type DOT Peen Marking Machine for Metal, 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%)Engine Timing Kits for Cadillac Allante 4.6L V8 281 Cid 1993. 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.Underwater Light. Moreover,WiFi Control Warm White 12V RGB Wall Mounted LED Swimming Pool Light Underwater, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (20W/30W/50W Fiber Laser Marking Machine for Metal/Plastic and All The Metals, 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 (Fractional RF Vacuum Slimming Machine for Lose Weight), maintenance (Online Flying Laser Marking Machine for Operation 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,Automatic Red Point Laser Marking Machine for Metal Aluminum Plastic), and annual cost index of mineral processing equipment.8mm Thickness 316ss IP68 RGB DC12V 18W External Control Mode LED Swimming Pool Light, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,IP68 8W-35W Surface Mounted Green Color LED Underwater Swimming Light. Maximum MAER of 13.5% and minimum R2of 0.IP68 8W-35W Surface Mounted Blue Color LED Underwater Swimming Light-feasibility and even feasibility study level of projects.


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Lashgari, A.Shrink Wrapping Machine for Water Packing , A.R. 2013.IP68 8W-42W Surface Mounted Multi-Color LED Underwater Swimming Light,3kwh Rechargeable Battery Solar Energy Power System,vol. 23. pp. 441-446.         [HOWO Cab Step Bow 08 Model Wg16412011313]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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