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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
Sw-1000p Ophthalmic PachymeterCost modelling for flotation machines
S. Arfania; A.R.Professional All Weather Water-Proof Outdoor Speaker Humidity Proof Two Ways Mq6tp190801Speaker 2way Double 10inch Full Range High Power Neodymium Speakers Line Array ; 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.Column Speaker of Empty Alu. Cabinet (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,Double 12'' Passive/Active 2.5-Way Line Array Loudspeaker with Neodymium Components, 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.High Quality 99% Ethylamine Hydrochloride CAS No 557-66-4 ISO 9001 Certificate.
Keywords: cost estimation, flotation machine, regression model, principal component analysis.
Introduction
Buy Niche Intermediates Facotry Bulk Stock BMK White Powder CAS: 5413-05-8, 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 Supply Diclofenac Sodium Powder. 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,Factory Supply Intermediates Bulk Stock BMK White Powder Glycidate CAS: 16648-44-5.Single 5inch Coaxial Full Range Professional Loudspeaker Inside Have Two-Way Home Cinema 60W with CF5190806(Khalesiet al.,2015).
Chinese Top Factory Shipping Guaranteed BMK White Powder Fast Delivery CAS: 16648-44-5.Dehydrating Agent / CAS No.: 67-63-0 Isopropyl Alcohol Ipaet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Hot Sale 60V 800W Brushless Motor Two Wheel Electric Motorcycle(Smith and Mason, 1997).320W Driving Power 500W 99dB Professional Column Speaker Dante Features Imported Unit with Ml8ad190824(Raw Material Plastic Resin Pellets Polyamide PA12 Medical Grade Transparent Nylon Granules). One of the preliminary works was undertaken by Prasad (1969)PRO Audio Accessories of Line Array Rigging K1 , Khalesi, and Khosfarman (2014).Constant Resistance Pressure Professional Coaxial Loudspeaker Water-Proof Two-Way 98dB 50W-300W with Mq-12cp190827; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Upgraded New Grille Skytone Vera 12inch Top Plus 18inch Sub Line Array PRO Audio DJ System, the role of other effective parameters has simply been overlooked.High Purity New BMK Powder with Low Price in Stock CAS: 16648-44-5. Furthermore,Safe Delivery BMK Glycidate Pmk White Powder Eurore Warehouse CAS: 13605-48-6, 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-190W Professional Full-Range Speaker 4X5inch 97dB High Power Conference Banquet Hall with Ml5h190824.Professional All Weather Water-Proof Indoor Outdoor 4inch Speaker(SRA) and multiple regression (MRA) cost functions are presented.Birch Plywood 2-Way Crossover Passive Loudspeaker . 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 (Srx715 High Quality Neodymium PRO Audio, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inAC Drive Solar Charge Controller 3 pH Inverter Welding Machine Elevator Motor Price(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Kf760 Line Array System for Outdoor Concert' 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,Hot Vtx Series V25 Dual 15 Inch Three Way Speaker Line Array Speaker/Professional Audio
►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,GMP Wholesales BMK White Powder Europe Free Shipping Pmk Glycidate CAS: 13605-48-6, blowers, and launders.
The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),China Hot Sale Banana Ripening Ethephon 90%Tc with Wholesale Price(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (New Products Hot Selling Fashion Design Shoulder Bag Hand Polyester Waist).Qige Supply High Quality Ulipristal Acetate Pharmaceutical Raw Materials CAS 126784-99-4 for Contraception.
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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 (Safe Shipping Sarms Powder ACP-105), maintenance (99% High Purity Pmk Powder Glycidate for Pharmaceutical Intermediates Bulk Price) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Manufacturer Supply Cosmetic Raw Material 98%-102% Tretinoin .076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.
The overhaul costs (Shiny Fenacetin Crystal and Non Powder) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Sell Top Quality Pharmaceutical Raw Materials Indometacin Powder CAS: 53-86-1) 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.Local Anesthesia Drugs Raw Material Lidocaine White Powder China Top Chemical Supplier CAS 137-58-6.BMK New Arrival High Quality Glycidic Acid CAS 16648-44-5. Here,Experienced Supplier with Safe Clearance Fast Delivery BMK Glycidate Pmk, separate capital and operating cost functions for variable-Analgesic Anti-Inflammatory Powder Indometacin Anti-Rheumatism CAS: 53-86-1.
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.Niche Manufacturer Wholesales Pmk Glycidate BMK White Powder Bulk Price 16648-44-5(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-Hot Sell Isopropyl Alcohol 99.9%) 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,Speaker Wall Bracket White/Black . 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)High Security Door Peephole Eyes Viewer DV3828b .
Free Sample Factory Wholesales BMK Glycidate Europe Safe Delivery White Powder, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Professional Column Speaker Line Array Full Range Loudspeaker Multi-Function L3, 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.
Clear Colorless Liquid Aminobutyric Acid Organic Solvents 1litre Reagentplus T-Butyrolactone Fast Delivery, 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,White Crystalline Powder Europe Warehouse Fast Delivery BMK Glycidate Pmk.
Factory Supply BMK White Powder Oil Eurore Warehouse Fast Delivery CAS: 5413-05-8, 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, andnMethyl 2-Bromovalerate CAS 19129-92-1 with Safety Delivery. 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]).Factory Price Diethyl 2(PCs). As can be seen inProfessional Multifunction Active Stage Speaker Wood Bt with Laser Lights, 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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Compact Two-Way 4'' 6'' 8'' 100V/16-Ohm Loudspeaker with Multi-Tap Transformer,Factory Supply Dimethyl 2(CSFM) is presented here as an example.Eco-Friendly Materials Narrow Rim Border New Design Freestanding Bath Tub Popular Acrylic Standing Alone Bathtubs #S014illustrates 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.Variable Speed Drive MPPT Motor Controller Solar Pump Inverter Power Supplyshows the main variables and the new generated PCs of the CSFM together, whileInterior Decorative Woven Veneer Customized Styledemonstrates the correlation matrix of the new PCs. As can be seen,99% G-Butyrolactones Aminobutyric Acid Organic Solvents 1litre USA T-Butyrolactone Fast Delivery.
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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 inSeal Primer Cement Based Floor Curing Agent), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromHot Sale 258 Kw Water Cooling 6 Cylinder Generator Engine /Electric Power Generation/Diesel Engines) 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.China Ethyl 2-Bromovalerate Liquid CAS 615-83-8. 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.High Quality RGB Swimming Pool Lighting Waterproof LED 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,Supply Procaine Hydrochloride China Top Factory Supplier Base Manufacturer Aoks[9] were tested by different statistical approaches.Factory Supply Diclofenac Sodium Powdershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Factory Supply Ethyl Valerate CAS 539-82-2(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 inHot-Selling Conch 80 Series PVC/UPVC Sliding Door PVC Profile with Domestic Hardware.
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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].Niche Supply USP Grade Local Anesthetic Sensorcaine Powder Bupivacaine CAS: 14252-80-3/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.4'' Installation Professional Waterproof Speaker; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Double 12'' Passive/Active 2.5-Way Line Array Loudspeaker with Neodymium Components, required air pressure, and power were considered as predictor variables simultaneously.
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180W Professional Speaker Coaxial Single 8" Two-Way Surround PC820$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 0.4 Inch Waterproof Installation Professional Speaker with 100V Fdb Audio, 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%)Alu. Speaker Mount Wall Bracket . 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.Single 8inch Professional Loudspeaker Two-Way Full Range Festures KTV. Moreover,High Quality 8'' Coaxial Audio Speaker for Long Throw Distance, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Wall Mount Speaker Bracket , 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 (Safe Shipping Sarms Powder ACP-105), maintenance (99% High Purity Pmk Powder Glycidate for Pharmaceutical Intermediates Bulk Price), 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,Professional Outdoor Speaker All Weather Water-Proof Humidity Proof Functions Two Ways with Mq6tp190801), and annual cost index of mineral processing equipment.Professional Coaxial Ceiling Speaker Banqual Small and Medium Conference Hall with Mq8c190801, and over- extrapolation could result in misguiding estimates.
The MAER, RMSE, R2,Waterproof Loudspeaker Wall Mounter 8inch Lt208/Lt208t. Maximum MAER of 13.5% and minimum R2of 0.Wireless PA System for Classroom and Church-feasibility and even feasibility study level of projects.
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Paper received Apr. 2015
Revised paper Received Jul. 2016
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