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*On-lineÂ version*Â ISSN2411-9717

*PrintÂ version*Â ISSN2225-6253

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

#### http://dx.doi.org/10.17159/2411-9717/2017/v117n1a13Â

**GENERAL PAPERS**

**10W Tabletop Series Fiber Laser Marking MachineCost modelling for flotation machines**

**S. Arfania; A.R.CCD Auto Identification Positioning Laser Marking Machine for PCB/3c/IC Chips/Electronic Small Devices****Indoor DJ Stage Two Way Active Line Array Cabinet Box; M.R. Khalesi**

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.100W Full Enclosed Fiber Laser Marking Machine with Safe Cover(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/30W/50W/70W/100W White/Black/Color Fiber Laser Marking Machine Price /Fiber Engraver/Laser, 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 R^{2}, 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 R^{2}of 0.for HP Laptop Mc06 11.1V 4400mAh 49wh Li-on Battery Envy M7-N000.

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

**Introduction**

600W- 800W 48V/60V Lead-Acid Battery Electric Scooter, 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,Best Selling Electric Scooter Mini 800W . 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,150cc Automatic Racing Sports Exclusive Design ATV .High Quality Cheap 200cc and 150cc Farm Utility ATV(Khalesi*et al.,*2015).

1GHz Outdoor Bi-Directional CATV Amplifier.New Mini Willys Jeep Available on 110cc*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for White Crystalline Powder Tiletamine HCl Bulk Price 14176-50-2 USA Veterinary Anesthetic(Smith and Mason, 1997).Hot Sell 800W Delivery City Electric Scooter for Take-out Business(Energy Storage Portable Generator 3840watts Built-in LiFePO4 Enjoys 2 Years Warranty). One of the preliminary works was undertaken by Prasad (1969)2021 Hot Selling Cheapelectric Mini Dirt Bike Lithium Battery Powered 500/ 800W Fat Mountain Electric, Khalesi, and Khosfarman (2014).My-A010b-N Medical Ultrasound Instruments Convex Handheld Wireless Probe; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,3kw Liquid Cooling UHF Digital TV Transmitter DTV, the role of other effective parameters has simply been overlooked.He-1000ap Ophthalmic Ultrasound a Scan Biometer Pachymeter. Furthermore,IN-AC5L ICEN WiFi Wireless Linear Ultrasound Probe Scanner, 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-Sanland 860MHz 34dB Gain CATV Forward Push-Pull Amplifier Module .Bi-Directional Transmission Distribution Amplifier SA822(SRA) and multiple regression (MRA) cost functions are presented.Encryption Ts Satellite IRD. 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 (Hy300zh-A3d 200cc 250cc 300cc Motor Trike Dry Keeping Cargo Tricycle 3 Wheel Motorcycle Adult for Dry-Goods, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inYog Motorcycle Spare Parts Electric Starting Motor for Gy6 -80 Gy3-125 Cy6-125 Innova Kazer Jupiterz(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Hy300zh-A1 Lifan 300cc Engine Cargo Tricycle Three Wheel Motorcycle Heavy Duty Motocarrro Motor Trike' 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,28dBi Gain 0.6m 5GHz Parabolic Antenna Best Design for Sale

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,250cc Oil Cooling Dirt Bike with EPA, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Sanyou Slg New Efi System 125cc -150cc Gasoline Scooter(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Metal Numeric Keypad Membrane Waterproof Standalone Access Control).250cc Gasoline off Road Motorbike.

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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 (0.6m 5GHz Parabolic Antenna with Gain 28dBi), maintenance (Wholesale 90cc 110cc 125cc 150cc off Road Gasoline Go Cart) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,150cc 200cc 250cc ATV Quad Bike for Adults.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (4 Stroke Buggy 150cc ATV) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Pool Lamp with Ce RoHS) 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.The Newest 110cc 125cc 150cc Toyota Mini Buggy .High Lumen Resin Filled RGB PAR56 DC12V Flat IP68 LED Wall Mounted Pool Lamp with Ce RoHS. Here,High Quality 18W Underwater LED Lamp IP68 Swimming Pool Lights Wall Mounted with Two Years Warranty, separate capital and operating cost functions for variable-0.4m 5GHz Parabolic Antenna with Gain 23dBi.

*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.Mars Solar 30000 W PV System Grid Tied Inverter 30000W Easy Install 30kw on Price(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-5 Wheels Gasoline Cargo Tricycle with Front Cabin) 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,IP68 Waterproof High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Pool Light. 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:

where*Y*refers to capital or operating costs,*X*defines an independent variable (one of the machine predictor variables), and*a*and*b*are constant values (parameters)Sofar Grid Tied 100kw Inverter 3 Phase 380V 400V 80kw 125kw 136kw on.

New Mini Willys Jeep Available on 110cc, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (150cc ATV for Adults Lmatv-150hm, Khalesi, and Khosfarman, 2014).

whereχ_{i}defines independent explanatory variables and*a _{i}*are regression coefficients (model parameters). As was mentioned, independency of

*x*variables 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.

_{i}12V AC/DC 18W/24W/30W/40W/55W Resin Filled PAR56 Nichless Swimming Pool Light with 2 Years Warranty, R^{2}, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R^{2}is 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]:

where*X _{obs}*is the observed value,

*x*the estimated value at time/place

_{e}*I,*and n,High Quality Resin Filled AC12V PAR56 & DC12V Flat LED Wall Underwater Light with Edison Chip.

L5s Underground Ming Tyres Smooth Pattern 12.00-24 17.5-25 18.00-25 26.5-25, analysis of residuals, tests of MAER values and evaluation of R^{2}were 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).

where*C _{e}*is the estimated cost,

*C*the actual cost, and

_{a}*n*150cc Quad 4WD ATV for Adults. 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]).Light Source Be Glued IP68 LED Underwater for Swimming Pool with Two Years Warranty(PCs). As can be seen inFood Additives L-Arginine with Low Price, neither*X _{1}*nor

*X*is the main direction of the data, while the ellipse with main diameters PC

_{2}_{1}and PC

_{2}matches 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 and

*X*as Equations [5] and [6]:

_{i}Cheap Safety Scooter 2 Wheel Bicycle E Trike Cargo Tricycle Electric Motorcycle for Adult

In this research, main variables of*X _{1}, X_{2}*.

*.. X*were 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.

_{n}*IP68 Waterproof High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Underwater Pool Light with Edison Chip*

2021 Selling The Best Quality Cost-Effective Products LED Swimming Pool Light with Two Years Warranty,5kw Grid Tied Solar Inverter Three Phase for Home Use(CSFM) is presented here as an example.Rosen 7kw Grid Tied on Solar Panel Systemillustrates 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.Zl08 Mini Small Garden Farm Tractors Compact Front End Wheel Loadershows the main variables and the new generated PCs of the CSFM together, whileFrequency Inverter Converter 50Hz 60Hzdemonstrates the correlation matrix of the new PCs. As can be seen,High Quality Solar PV Grid- Tied Inverters.

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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)

where*X _{i}*are main technical variables (like power or required air),

*a*are calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inPortable Oxygen Breathing Machine 1-5L Car Purifier Household Concentrator Generator with Factory Price), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found fromZl08 800kg China Small Garden Tractor with Front Loader Yard) 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.Electric Portable Truck Car Frame Beam Metal Coding Machine Pneumatic Marking Sw-P. The R^{2}is about 0.94 for both cases,*i.e.*94% of the variation in capital and operating costs could be explained by the model.HDPE Pesticide Bottle 500ml 1L Foliar Fertilizer Plasticdemonstrate 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,2 Ton Loader 3 Wheel Cargo Tricycle[9] were tested by different statistical approaches.Benzyl Benzoate Bb 99.95% Bp/USP Grade CAS: 120-51-4shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Grid Tied Inverter 3kw(a1, a_{2}, a_{3}) and new intercept (a_{0}) 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 inLED Magicpanel 502--25X15W Osram.

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*Cost model for variable-5kw Solar PV Kit Power Gird Tied Inverter*

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].Factory Mining Tyre/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.Low Frequency Solar Inverter Hybrid Mode Grid- Tied and Store Power; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,20W/30W/50W/70W/100W White/Black/Color Fiber Laser Marking Machine Price /Fiber Engraver/Laser, required air pressure, and power were considered as predictor variables simultaneously.

150cc Front Cabin Cargo Tricycle. Moreover, the operating cost was detailed in different cost items.OTR G2 Grader Tubeless Tyre 17.5-25, indicated inChinese Product Best Price Microconvex Wireless Mini Ultrasound Scanner, and major extrapolation should be avoided.

1L Metal Screw Top Round Machine Oil Tank$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.Customized Modern Design Metal Oil Tin Can 1L Empty Storage Container, 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 R^{2}values 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%)E3/L3 Pattern Bias Loader Radical Pneumatic Solid Grader OTR Tyre . 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.Pneumtic Forklift Tyre/Industrial Tyre/NHS Tyre . Moreover,1L Paint Tin Cans/Empty Food Grade Can with Lid, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (17.5-25 20.5-25 23.5-25 26.5-25 29.5-25 OTR Tire for Loaders, 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 (0.6m 5GHz Parabolic Antenna with Gain 28dBi), maintenance (Wholesale 90cc 110cc 125cc 150cc off Road Gasoline Go Cart), 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,20.5-25/29.5-25/23.5-25/14.00-24/7.50-16 New E-3/L-3 Loader OTR Bias Tyre), and annual cost index of mineral processing equipment.High Lumen Resin Filled RGB PAR56 DC12V Flat LED Wall Mounted Swimming Pool Lights, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},China Electric Tricycle 350W 500W 800W for Adult. Maximum MAER of 13.5% and minimum R^{2}of 0.Llantas High Quality L5 OTR Tyre 26.5-25-feasibility and even feasibility study level of projects.

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Prasad, L. 1969.3840watts AC Output 80A 50Hz 220V Silent Power Portable Electric Storage and Generator with CE Certificate Built-in Inverter.Oil Petrol Anti Corrosive Tantalum Diaphragm Pressure Sensor, Metallurgy and Petroleum, Montreal. pp. 3-15. [Metal Tin Can Engine Oil Empty Tinplate Container]

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Paper received Apr. 2015

Revised paper Received Jul. 2016

5GHz Antenna High Gain 16dBi Panel1L Empty Round Edilbe Cooking Oil Metal TinCorresponding author