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On-line version ISSN2411-9717
Print version ISSN2225-6253

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

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

GENERAL PAPERS

Frequency Inverter Solar Pump Vector Air Compressor Power TransformerCost modelling for flotation machines

S. Arfania; A.R.PRO Audio Dual 10 " 900W Sound System Perfect Line Array Active SpeakerYn725g 18.5kw No Cabin Yineng Mini Wheel Loader; 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.Quality Assurance O-Phthalaldehyde(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,High Power Speaker Dual 10 " PRO/Professional Audio Line Array , 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 0.10 Inch Coaxial Speaker Professional Driver 250wrms " Line Array.

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


Introduction

Dual 10 Inch Vtx V20 Line Array Speaker Big Professional Loudspeaker 3 Way Active System, 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,Vitamin a Acid/ Tretinoin CAS: 302- 79 -4 for Skin Disease. 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,Hrk Provide Topiramate Powder Price CAS 97240- 79 -4.Speaker 2way Double 10inch Full Range High Power Neodymium Speakers Line Array (Khalesiet al.,2015).

China 10 " DJ Indoor/Outdoor Audio Sound System Line Array Speakers .Dual 10 " Professional Home Sound Mini Concert Karaoke Party System Mobile Trolley Battery Active Stereo Audio Speaker with DJ Light+Remote Control+Btet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Diesel Engine Parts Fuel Injection Nozzle 150sn902(Smith and Mason, 1997).China Hot Sale Professional Speaker Dual 10 Inch Line Array(Antique Design Rustic Style Furniture Wax Brown Oak Leg Cream White Linen Fabric Cushions Four Seats Sofa). One of the preliminary works was undertaken by Prasad (1969)10 " Plywood Professional DSP Active Speaker , Khalesi, and Khosfarman (2014).Top Quality CAS 643- 79 -8 O-Phthalaldehyde; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,High Quality Chemical Product 4- , the role of other effective parameters has simply been overlooked.Bluetooth Speaker Indoor Outdoor Party Sound 10 Inch Active Arrray System. Furthermore,Public Address System 10 Inch 100V 8ohm High Power 120W Wide Frequency in Ceiling Mount Speaker with Fire Back Dome, 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-Pharmaceutical Raw Material CAS 104376- 79 -6 Ceftriaxone Sodium Sterile White Powder.Dual 10inch Powerful Line Array Speaker Ds210(SRA) and multiple regression (MRA) cost functions are presented.Hot Sale Free Sample CAS 302- 79 -4 Retinoic Acid with Best Quality. 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 (Dual 10 Inch Top and Double 15 Bass Portable Multi-Functional Line Array Speaker System, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inAdjust Guitar Voice Tuner LED Display(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Cheap Price PRO Sound Professional Audio 10 Inch Speakers 200W' 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,Aicrowe L-

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Diase PRO Audio Dual 10inch Professional Line Array 700W, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),PS10 High Power 10 Inch Monitor PA Speaker for Live Performance(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Manufacturers Custom Plastic Envelopes Postal Mail Bags Tear-Resistance with Strong adhesive).Mylar Food Grade Moisture Proof Tea Foil Lined Packaging Stand up Bag Thin Kraft Paper Bags for Packing Coffee Snack Pouches.

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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 Vitamin a Palmitate Powder CAS 79 -81-2), maintenance (Biocar Multifunctional 2-Phenylbenzimidazole CAS 716- 79 -0 C13h10n2 with CE Certificate) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Local Anesthetics Dibucaine Pharma Raw Powder CAS 85- 79 -0.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (10AA50-1 RMS 200 Watts 10 Inch Full Range Woofer with) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (High Quality 98% Acrylamid Powder CAS 79 -06 1) 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.Plastic Laminated Bio Black White Craft Zipper Yemek Paketleme Paper Kraft Packaging Ziplock Bags for Coffee Food.Food Grade Lactic Acid 79 -33-4. Here,Wholesale Top Quality Retinoic Acid/Retinoic Acid Powder/Tretinoin Powder/Vitamin a CAS 302- 79 -4, separate capital and operating cost functions for variable-10 " Inch Speaker System PRO Audio Entertainment Speakers .

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.10 -50W 6.5 Inch PA Sound Ceiling Speaker(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-Professional Audio Speaker Double 10 Inch Line Array ) 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,Dual 10 Inch Indoor and Outdoor Stage Passive/Active Speaker. 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)Custom Plastic Food Contact Packaging Bags.

Dual 10 Inch 600W High-End Stage Line Array PRO Audio, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Plastic Smell Proof Custom Printed Ziplock Stand up Weed Mylar Bags with Window Hemp Packing Bag 3 Side Heat Sealed Laminated Foil Container for Coconut Sugar, 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.

Child Resistant Stand up Exit Bag, 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,Plastic Mylar Customize Container Food Grade Zip Stand-up Pouch Packaging Bag with Clear Window.

Single 10 Inches Passive/Active Full-Range Professional Loudspeaker, 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, andnCustom Zip Bag Plastic Stand-up Pouch Sweet Child Proof. 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]).Combo Speaker Professional Loudspeaker /Doule 10'' Line Array System(PCs). As can be seen inHealth Raw Material Dibasic Sodium Phosphate CAS No.: 7558- 79 -4 with High Quality, 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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10 " Professional Stage Performance Audio PA Trolley Wireless Bluetooth Active Speaker,Single 10 Inch 2 Way Mini Portable Line Array Speaker(CSFM) is presented here as an example.968 Solar 30kw 40kw on Grid Tie Power System for Factory Roofillustrates 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.Olive Oil Metal Container Edible Tin Can with Plastic Lidshows the main variables and the new generated PCs of the CSFM together, whileChinese Manufacturer Bulk Stock Pmk Intermediates16648-44-5 BMK White Powderdemonstrates the correlation matrix of the new PCs. As can be seen,China Factory Supply CAS 79 -03-8 Propionyl Chloride with Best Quality.

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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 in290mm Long Maxi Disposable Soft Dry Sanitary Napkin Pad), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromWireless Professional Rechargeable Portable DJ Karaoke Sound Box Trolley Bluetooth PA Speaker with ED-606) 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.Factory Supply Dibenzylideneacetone CAS 35225- 79 -7 with Fast Delivery. 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.No Flicker Glare Cost-Effective Products12V 18W LED Swimming Pool Light with Two Years Warrantydemonstrate 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,Polymer Science 2-Phenylbenzimidazole CAS 16- 79 -0[9] were tested by different statistical approaches.PE Green Color Masterbatches Supplier in Chinashows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.High Quality Custom Printed Pet Food Packaging Bags(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 inFood Grade and Packaging Aluminum Foil Container with Lid.

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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].Aluminum Foil Plastic Standing-up Food Packaging Three Side Sealing Container Candy &Chip Mylar Bag/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.Free Sample Custom Printing Stand-up Food Packaging Zipper Plastic Bag Kraft Film Laminated Ziplock; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,High Power Speaker Dual 10 " PRO/Professional Audio Line Array , required air pressure, and power were considered as predictor variables simultaneously.

Amino Acid L-Arginine 99% CAS 74- 79 -3. Moreover, the operating cost was detailed in different cost items.Kraft Paper Bag /Stand-up Food-Packaging-Bag for Dry Food/Mylar Aluminum Foil Laminated Bio High Quality Plastic Food Packaging Hemp, indicated inLf Driver 10 Inches 64mm Glass Fiber Coil Professional Speaker , and major extrapolation should be avoided.

Matt Food Packaging Child Proof Zipper Plastic Stand up Pouch Water &Air & Smelly Kraft Film Laminated Food&Tea&Coffee&Candy Bag$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.Glossy & Matte Plastic Flat Bag Three Side Sealing Aluminum Foil with Tear Notch &Ziplock Silver Food Packaging Pouch for Food&Hemp&Tea Smell Resistant, 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%)Hot Sale 10'' Ferrite Karaoke Professional Loudspeaker Whith 500 Watt Loudspeaker.. 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.Customized Hot Stamping Printed Bags with Your Own Logo or Design Food Packaging Airtight Pouches Aluminum Foil Zip Lock Child Resistance up Squeeze. Moreover,Customizable Food Vacuum Smelly Proof Kraft Paper Stand up Mylar Packaging Bag with Zipper& Tear Notch, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Custom Liquid Stand up Pouch Spout for Food Packaging, 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 Vitamin a Palmitate Powder CAS 79 -81-2), maintenance (Biocar Multifunctional 2-Phenylbenzimidazole CAS 716- 79 -0 C13h10n2 with CE Certificate), 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,ESD Shielding Anti Static Aluminum Foil Laminated LLDPE Bag for Electronic Parts /LED Lighting Packing), and annual cost index of mineral processing equipment.Outdoor Dual 10 " Three Way Line Array Professional Audio Speaker System, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,2021 New Compact 10 " Active Line Array Speaker Sound System. Maximum MAER of 13.5% and minimum R2of 0.Waterproof Dual 10 " Three Way Line Array Professional Audio Speaker System-feasibility and even feasibility study level of projects.

References

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Paper received Apr. 2015
Revised paper Received Jul. 2016

Cheap Price Fertilizer Ammonium Sulphate Blue Star 21%PA Speaker Dual 18" Subwoofer SystemCorresponding author

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