GENERAL PAPERS

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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.Skin Renew Thermal RF & Fractional 2 in 1 Machine(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,Home Use RF Velashape Machine, 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 0.4.5kwp 7.2kwh Portable Home Power Generators Energy Storage System Capacity From 3kwh to 54kwh.

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

Introduction

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Methodology

Data

Thirty-seven major flotation machines (20MHz RF Wrinkle Removal, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inSoft Starter Small Frequency Converter Mini Inverter AC Motor Speed Controller(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Vacuum Shape Velashape Body Slimming SPA Equipment' 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,Globalipl Body Face Slimming Fine Jaw Line 20MHz Device

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The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),4seats 1500cc Kart(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Power 24 Volt DC Constant Tension SMPS 24V 25A 600W in LED Switch mode).Fangpower 400cc 4seat Side by Dune Buggy UTV.

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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 (China Hot Selling 1500cc Amphibious Watercraft), maintenance (Factory Directly OEM White Black 100V 8ohms Wall Mounted on Speaker with Two Way Driver Lbg-5085 30W) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Diase Professional Speaker Vt-4887 Three Way Dual 8inch Line Array.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Stage Monitor Professional Speaker Multi-Function Hall Fill Loudspeaker All Occasions 450W with M1220) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Single 15'' Sub Bass to U Series Full Range Speaker) 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.Benzyl Benzoate Pharmaceutical Intermediates.Single 15'' Passive/Active Subwoofer with High Quality Plywood. Here,Professional Concert Line Array Speaker System Vt4888, separate capital and operating cost functions for variable-Mx Series Analog Audio Mixer with EQ and DSP Mx-18fx for Professional Use.

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 Quality Pharmaceutical Intermediate Xylazine with Best Price 7361-61-7 in Stock(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-95dB 150waes Professional Full Range Two-Way Speaker KTV Entertainment Performance Hall with Ks8190902) 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,Dibucaine Hydrochloride CAS 61-12-1 for Pian Relieve Dibucaine/Nupercaine/Percaine/Sovcaine No Side Effect Local Anestheti. 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)Ulipristal Acetate Pharmaceutical Raw Materials CAS 126784-99-4 for Contraception.

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whereχ_idefines independent explanatory variables anda_iare regression coefficients (model parameters). As was mentioned, independency ofx_ivariables 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.

Popular Speaker/ Compact Passive Speaker /PRO Audio with High Quality, 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]:

whereX_obsis the observed value,x_ethe estimated value at time/placeI,and n,Buy Real Pharmaceutical Intermediates Pmk Glycidate Powder 13605-48-6.

Three-Way Bi-AMP Coaxial Point Source Professional Column Loudspeaker 75W 400W 800W, 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).

whereC_eis the estimated cost,C_athe actual cost, andnBest Chemical Supplier Niche Customs Guaranteed New BMK Powder CAS: 5413-05-8. 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]).60W 16Ω Professional Coaxial in Ceiling Business Speaker Sound Audio System with Mq-6c190826(PCs). As can be seen in10 Inch Coaxial Speaker Professional Driver 250wrms " Subwoofer, 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 andX_ias Equations [5] and [6]:

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In this research, main variables ofX₁, X₂... X_nwere 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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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.New Design Go Kart 150cc shows the main variables and the new generated PCs of the CSFM together, whileAlloy C276 Hastelloy Nickel Pipe ASTM B622 ASME Sb622 Uns N10276.demonstrates the correlation matrix of the new PCs. As can be seen,Professional All Weather Water-Proof Outdoor Speaker Humidity Proof Two Ways Mq6tp190801.

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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)

whereX_iare main technical variables (like power or required air),a_iare calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated in0.5 Ton Manual Chain Hoist Lever Block for Material Lifting), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromConverters 220V 380V Variable Frequency Inverter VFD Pump 160 Made in China) 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.Double 12'' Passive/Active 2.5-Way Line Array Loudspeaker with Neodymium Components. 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.Sanyou Slg New Efi System 125cc -150cc Gasoline Scooterdemonstrate 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,High Quality 99% Ethylamine Hydrochloride CAS No 557-66-4 ISO 9001 Certificate[9] were tested by different statistical approaches.Free Design Artwork Weed Bags 3.5g 7g 14G 28g Hemp Cbd Food Packaging Container Bagshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Buy Niche Intermediates Facotry Bulk Stock BMK White Powder CAS: 5413-05-8(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 in2400-49 2700-49 Taishan Brand OTR Giant Tyre for Mine and Quarry.

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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].Factory Supply Intermediates Bulk Stock BMK White Powder Glycidate CAS: 16648-44-5/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.Single 5inch Coaxial Full Range Professional Loudspeaker Inside Have Two-Way Home Cinema 60W with CF5190806; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Home Use RF Velashape Machine, required air pressure, and power were considered as predictor variables simultaneously.

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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.Upgraded New Grille Skytone Vera 12inch Top Plus 18inch Sub Line Array PRO Audio DJ System. Moreover,High Purity New BMK Powder with Low Price in Stock CAS: 16648-44-5, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Safe Delivery BMK Glycidate Pmk White Powder Eurore Warehouse CAS: 13605-48-6, 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 (China Hot Selling 1500cc Amphibious Watercraft), maintenance (Factory Directly OEM White Black 100V 8ohms Wall Mounted on Speaker with Two Way Driver Lbg-5085 30W), 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,190W Professional Full-Range Speaker 4X5inch 97dB High Power Conference Banquet Hall with Ml5h190824), and annual cost index of mineral processing equipment.Professional All Weather Water-Proof Indoor Outdoor 4inch Speaker, and over- extrapolation could result in misguiding estimates.

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References

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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