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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
Dual 10 Inch Top and Double 15 Bass Portable Multi-Functional Line Array Speaker SystemCost modelling for flotation machines
S. Arfania; A.R.PA Audio Church Theater Three-Way Large Touring Line Array Speaker Sound SystemCheap Electric Bike 1000W Brushless Disabled Chainless Portable Motorcycle City; 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.Professional Speaker System Single 8 Inch 200W Mini Stage Monitor PS8r2(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,Factory Supply Top Quality Cooling Agent Ws-3 CAS 39711- 79 -0, 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 Audio Speaker Active Single 8 Inch Mini Stage Monitor PS8r2.
Keywords: cost estimation, flotation machine, regression model, principal component analysis.
Introduction
Professional Audio Speaker Single 8 Inch 200W Mini Stage Monitor PS8r2, 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,Professional Speaker System Single 15 Inch High Power Line Array Aw15. 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,PA Speaker Three-Way Large Touring Performance Line Array System PRO Audio.Sinbosen SA-212 Professional PA Speaker System 12 Inch Line Array Powered(Khalesiet al.,2015).
Hench Hot Sales Raw Material Powder Oxytetracycline.New Design Two-Way Full Range Professional Loudspeaker Multi-Function Speaker Tx1020et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for IP68 Glass 12V PAR56 LED Underwater Swimming Pool Light for Fountain(Smith and Mason, 1997).Natural Weight Loss Supplements Huperzine a Powder CAS: 120786-18-7 USA Hupa Sample Free(UV White Birch Plywood 18mm Carb E0 Cabinet). One of the preliminary works was undertaken by Prasad (1969)Pharmaceutical Chemical Tretinoin Powder with Excllect Effect Safe Ship, Khalesi, and Khosfarman (2014).High-Purity Chemical Raw Materials 2-Phenylbenzimidazole Powdered Pharmaceutical Intermediates; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,2-Aminoanthraquinone CAS No 117- 79 -3, the role of other effective parameters has simply been overlooked.Food Additives L-Arginine with Low Price. Furthermore,Latest Product Powder 2-Phenylbenzimidazole Chemical Raw Material, 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 1% 98% Huperzine a Powder Novel Antidepressants CAS: 120786-18-7 USA Sample Free.China Supply 1(SRA) and multiple regression (MRA) cost functions are presented.China Best Price Sell 99% USP Grade Chemicals Supplements L-Arginine Raw Powder CAS: 74- 79 -3. 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 (Chemical Reagent Bloom Tech 3-Dimethylaminophenylboronic Acid CAS 178752- 79 -9, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inProfessional Audio Signal 8" Two-Way Full-Range Speakers PA System with Tq8(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Safe Shipping with Good Price Tretinoin Powder' 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,Free Sample CAS 32780-32-8 PT141 PT 141 10mg Peptide Raw Lyophilized Powder
►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,High Quality Aod-9604 CAS 221231-10-3 Aod 9604 Peptides 2mg for Loss Weight, blowers, and launders.
The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),CAS 79 -57-2 Oxytetracycline(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Clear Crystal Glass Soccer Trophy Football).Azd3759 CAS No. 1626387-81-2.
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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 Additives L-Arginine with Top Quality), maintenance (Chemical Reagent Bloom Tech Sodium 4-Methylbenzenesulfinate CAS 824- 79 -3) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,99% Purity 1.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.
The overhaul costs (PT141 Factory Supply Best Quality Peptide Powder 10mg for Aphrodisiac) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (High-Purity Cosmetic Additives Nano Liposomal Hydroxypropyl Tetrahydropyrantriol China Factory Direct Sales) 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.2-Aminoanthraquinone CAS No 117- 79 -3.High Quality Tretinoin 302- 79 -4 with Good Price. Here,3-Amino-4-Pyrazolecarboxamide Hemisulfate Salt CAS No 27511- 79 -1, separate capital and operating cost functions for variable-Free Sample Ortho Phthalaldehyde 643- 79 -8 with Fast Delivery Manufacture in China.
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.High Fidelity Professional Line Array 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-N) 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,Vitamin a Palmitate CAS 79 -81-2. 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)IP PA System 6 Inch 15W SIP Poe Ceiling Speaker with Built-in Monitoring Microphone and Dry Contact in out.
Best Price Diclofenac Sodium with High Quality, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (40wx2 10 " Portable PS Series Party Speaker, 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.
100% CAS 79 -57-2 Oxytetracycline Powder, 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,New Arrival Mr Series Audio Mixer with DSP Mr-12fx.
Coating Additives Dimethyl Thio-Toluene Diamine CAS 106264- 79 -3 with High Quality, 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, andnPowered Speaker System for Home Theater. 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]).Cosmetic Grade L-Arginine with High Quality(PCs). As can be seen inWholesale Price Modern Italy Leather/ Fabric Couch Sofa Corner Home Furniture, 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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Chinese Factory Special Cosmetic Raw Materials for Wrinkle Removal and Moisturizing High Purity Nano Liposomal Hydroxypropyl Tetrahydropyrantriol,Best Quality Skin Care Pure Tretinoin 302- 79 -4(CSFM) is presented here as an example.Nordic Latex Cotton Linen Sofa Combination Modern Simple Princess Corner Living Room Small Family Removable Washingillustrates 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.Professional Audio Speaker Single 10 Inch 300W Portable Stage Monitor PS10r2shows the main variables and the new generated PCs of the CSFM together, while1L Round Tin Pail with Sealed Lid and Plastic Handle for Paint Usedemonstrates the correlation matrix of the new PCs. As can be seen,Factory Direct Sale Dimethyl Gonane 702- 79 -4.
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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's pamper diaper maker), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromTwo-Way Single 10 " Professional Waterproof Speaker) 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.Chlorhexidine Diacetate CAS No 206986- 79 -0. 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.off Road 200cc Motorcycle for Hot Saledemonstrate 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,CAS 79 -14-1 Glycolic Acid 70%[9] were tested by different statistical approaches.Single 18 Inch Bass Speaker Professional Subwoofer Entertainment Occasions with Wa11819730shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Compact Neodymium Line Array 12inch 400W Passive Speaker PA System(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 in6X12mm Mini Size Warm White/Blue/RGB Color LED Neon Flex Flexible Strip Light for Advertising.
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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].New Arrival Mr Series Audio Mixer with DSP Mr-10fx/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.Factory Price Powder Mannitol with High Quality; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Factory Supply Top Quality Cooling Agent Ws-3 CAS 39711- 79 -0, required air pressure, and power were considered as predictor variables simultaneously.
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12" Line Array Loud Speaker Sound System Professional PA$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 0.15inch Professional Stereo Sound PA PRO Audio DJ Loud Speaker, 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%)Professional Line Array PA System S1210 Sound. 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.Cosmetic Material 99% Purity Tretinoin Powder. Moreover,High Quality Rasagiline Mesylate API Powder CAS 161735- 79 -1 with Purity! !, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Spts, 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 Additives L-Arginine with Top Quality), maintenance (Chemical Reagent Bloom Tech Sodium 4-Methylbenzenesulfinate CAS 824- 79 -3), 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,High Power DJ Sound Equipment System Line Array PA Speaker), and annual cost index of mineral processing equipment.2X12 Outdoor Compact Neodymium PRO Audio PA Event Line Array, and over- extrapolation could result in misguiding estimates.
The MAER, RMSE, R2,Best Price Medicine Grade Lanosterol Powder. Maximum MAER of 13.5% and minimum R2of 0.Outdoor Professional Audio Loudspeaker PA Stage Active Line Array-feasibility and even feasibility study level of projects.
References
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Paper received Apr. 2015
Revised paper Received Jul. 2016
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