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



Water Treatment Anticorrosive Ceramic Capacitor Micro Pressure TransmitterCost modelling for flotation machines

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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.CAS 79 -14-1 70% Glycolic Acid Powder(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,Anti-Wrinkle Cosmetic Grade PRO-Xylane CAS-439685- 79 -7, 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.Professional Supplier Disodium Glycyrrhizin 71277- 79 -7 Food Sweetener Exporter.

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


Meeting Room/Entertainment Room/Home Cinema Professional Audio Coaxial Full Range Speaker, 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,Raw Material 99% Tretinoin Powder/Retinoic Acid CAS 302- 79 -4. 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,Bloom Tech API Ceftriaxone Sodium 104376- 79 -6.St-10 10kw St-12 12kw St-15 15kw St-20 20kw Generator Alternator(Khalesiet al.,2015).

Generator Automatic Controller Eim 258 -9754 Engine Interface Module.99% Pure High Quality Anesthetics Cinchocaine 85- 79 -0et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Softel 4u 12 Channel Agile CATV Analog RF Modulator(Smith and Mason, 1997).Custom Printed Food Grade Ziplock Plastic Pouch Packaging Bag(Everun Er08 CE Wheel Loader with Standard Bucket for Sale). One of the preliminary works was undertaken by Prasad (1969)PA /Pet/PE/Kraft Laminated Printing Stand up Pouch Food Grade, Khalesi, and Khosfarman (2014).Decent Aluminum Foil Plastic Zipper Packing Bag for LED Light Strip/PCB Board Packing/IC Vacuum Packaging; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,High Temperature Vacuum Retort Pouch for Food Packaging, the role of other effective parameters has simply been overlooked.Oxygen Absorbers Food Packaging Vacuum Packed Bag for Cookies. Furthermore,Thermoforming Nylon/Ny Frozen Chicken Meat Packing Vacuum Sealer Bag, 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-High Barrier Vacuum Bag& Packaging Films for Food Pakcing.Custom Plastic Vacuum Bag for Rice Packaging Bricks Bags(SRA) and multiple regression (MRA) cost functions are presented.Oxygen Barrier Transparent Vacuum Plastic Bag. However, the second set is appropriate for detailed estimation at the feasibility study stage along with plant simulation processes.



Thirty-seven major flotation machines (Professional Audio High Powerful Ka Dual 10inch DSP Active Line Array Speaker, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inFactory Supply Glycyl-L-Tyrosine(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;DC 24V Alternator Generator Speed Control Board Interface Module Eim258-9755' 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,10 Inch High Quality PA Speaker 10tbx100

Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,PA Audio System 5" 10 -35W Ceiling Speaker, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Ultra Low Nosie 10 Channles Mixer Mixing Console (CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Classic Blue Sleeve Laptop Bag Backpack Handbags).10''stage professional Audio Speaker H- 10 for Stage.

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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 (42 Inch Alone Standing Interactive LCD Touch Screen Information Kiosk), maintenance (55 Inch HD Outdoor Indoor LCD Advertising Digital TV Video Wall Smart Displayer) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Horn Speaker M-776.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (55 Inch Stand Alone Digital Photo Booth LCD Advertising Display) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Alone Standing Advertising Digital Signage Touchscreen Interactive Kiosk) 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.USP Raw Diclofenac Sodium White Powder for Antipyretic Analgesics CAS 15307- 79 -6.Wilson Parts Eim Module Engine Interface Control 258 -9753. Here,Generator Engine Interface Module Controller Eim Plus 24V 258 -9756 for Fg Wilson, separate capital and operating cost functions for variable-24V Engine Interface Controller Module Eim Plus 258 -9756 for Fg Wilson Generator.

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.Medrogestone Top Quality Low Price 977- 79 -7(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-Factory Supply High Quality Ademetionine 1) 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,China Supplier 1. 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)Cosmetic Grade CAS 79 -14-1 Glycolic Acid Powder.

CAS: 79 -44-7 Dimethylcarbamoyl Chloride , the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Diesel Engine Eim630-465 12V Eim630-466 24V 258 -9755 PCB650-091 650-092 Generator PCB Controller Panel Circuit Board Interface Module Speed, 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.

Kinetin; CAS No: 525- 79 -1; 6-Furfurylaminopurine; 6-Kt, 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,Good Quality CAS: 97240- 79 -4 Topiramate Powder Price.

High Purity 99% Intermediate 1, 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, andnYinherb Supply Pharmaceutical Raw Materials CAS 977- 79 -7 Medrogestone Powder. 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]).High Quality Tretinoin with Good Price (PCs). As can be seen inModern Living Room Furniture Fabric Sofa 6127, 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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Fg Controller Generator Engine Interface Module Eim Basic MK3 258 -9755,High Purity Organic Intermediate  1(CSFM) is presented here as an example.High Quality 1illustrates 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.4-20mA Micro Air Gas Differential Pressure Sensor Transducershows the main variables and the new generated PCs of the CSFM together, whileAlcohol Benzene Polyamide Ink Resindemonstrates the correlation matrix of the new PCs. As can be seen,Generator Interface Module Eim Basic 258 -9753 for Fg Wilson Engine.

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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 inExcellence in Quality Manufacturer High Diaper Bulk Disposable Baby Diapers), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromNitrogen Fertilizer Caprolactam Grade Granular CAS No. 7783-20-2 N21% Ammonium Sulphate) 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.Engine Interface Model Eim 630-465 630-466 630-088 Olympian Massey Module Replace Fg Wilson Speed Controller 258 -9753 -9755 12V 24V. 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.S32750 Uns Super Duplex Stainless Steel Bardemonstrate 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,Diesel Engine Set Wilson Parts Eim Module Interface C3.3 C4.4 Motorcycle Generator Auto Spare 258 -9753 -9755 12V 24V[9] were tested by different statistical approaches.Wolf 0.8t 800kg Mini Loader with Euro 3 Engineshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.5kw 10kw Stc Three Phase AC Synchronous 15kw Brush Alternator(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 inP2.5 Flexible Circular LED Screen Module Video Advertising Display.

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Cost model for variable-Replace Fg Wilson Engine Interface Module Eim Plus Basic 258 -9755 -9753

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].Engine Controller Model Eim Basic 258 -9756/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.Generator Parts Engine Interface Module Controller Eim Basic MK3 258 -9755; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Anti-Wrinkle Cosmetic Grade PRO-Xylane CAS-439685- 79 -7, required air pressure, and power were considered as predictor variables simultaneously.

Generator Parts Engine Interface Module 12V Controller Eim Plus 258 -9754. Moreover, the operating cost was detailed in different cost items.100% Copper Wire St Series Single Phase Generator / Alternator , indicated inSrx725 Dual 15" PRO Audio Speaker Box, and major extrapolation should be avoided.

China Supplier 1$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 0.100% Copper Wire Stc Series Three Phase AC Dynamo/Generator /  Alternator , 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%)Stc-3 3kw Stc-5 5kw Stc-10 10kw Three Phase Alternator. 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.24kVA St Series Single Phase Generator . Moreover,20 Days Delivery! 100% Copper Wire Stc-3kw Three Phase Alternator, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (20kVA St Series Single Phase Generator , 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 (42 Inch Alone Standing Interactive LCD Touch Screen Information Kiosk), maintenance (55 Inch HD Outdoor Indoor LCD Advertising Digital TV Video Wall Smart Displayer), 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,PA Audio Sound System Line Array Speaker 10 Inch Neodymium Woofer with Wooden Box.), and annual cost index of mineral processing equipment.7.5kVA St Series Single Phase Generator , and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R2,Wholesale 8inch 10inch 12 Inch 15inch DJ Speakers Professional Stage Audio. Maximum MAER of 13.5% and minimum R2of 0.2 Way Passive 10 " Professional PRO Audio PA Line Array-feasibility and even feasibility study level of projects.


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Mular, A.L. 1982.100% Copper Wire St-5kw Single Phase Brush Generator.Home Theater Speaker.Dual 6" Coaxial Full Range Speaker for Entertainment Room, Montreal. 265 pp.         [Fruit and Vegetables Packaging Materials Vacuum Nylon Bag]

Mular, A.L. and Poulin, R. 1998. Capcosts 1998.12inch Stage Monitor Speaker.KTV Single 8" Full Range Audio&Sets.Dual 6" Coaxial Full Range Speaker for Entertainment Room, Montreal. 319 pp.         [Face Veneer Nature Bamboo for Fancy Plywood]

Niazi, A., Dai, J.S., Balabani, S., and Seneviratne, L. 2006.St-2kw 230V/50Hz Single Phase Brush Alternator for Sale.Journal of Manufacturing Science and Engineering,vol. 128. pp. 563-575.         [China Ophthalmic Equipment]

Noakes, M. and Lanz, T. 1993.Stc-12kw/15kVA Three Phase AC Electric Generator on Sale.St 5kw Single Phase AC Electric Alternator Generator, Carlton, victoria. 412 pp.         [Detergent Grade Sodium Tripolyphosphate 94% CAS No: 7758- 79 -4]

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Diesel Engine Eim630-465 12V Eim630-466 24V 258 -9755 PCB650-091 650-092 Generator PCB Controller Panel Circuit Board Interface Module Speed, A.R., Lashgari, A., and Paraszczak, J.J. 2011. Hard-New Brand Diesel Engine with Four Stroke Multy-Cylinder Used for Generator Set.Tunnelling and Underground Space Technology,vol. 27. pp.133-141.         [Co-Solvent Polyamide Resin for Untreated Film Printing Ink]

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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