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.Factory Supply BMK Powder Glycidate CAS: 5413-05-8(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,China Factory Supply CAS 99-93-4 4-Hydroxyacetophenone, 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.Chinese Manufacturer Bulk Stock Pmk Intermediates16648-44-5 BMK White Powder.

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

Introduction

99.9% High Purity Prilocaine Hydrochloride/Prilocaine HCl CAS 1786-81-8, 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,High Quality 4'-Hydroxyacetophenone CAS 99-93-4 4-Hydroxyacetophenone with Best Price. 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 Bulk Stock Pmk Intermediates BMK White Powder CAS: 16648-44-5.99% BMK White Powder Glycidate Bulk Sales CAS: 16648-44-5(Khalesiet al.,2015).

99% 4'-Hydroxyacetophenone CAS 99-93-4 100% Pass Customs.62442 Shiny and Non Phena Powder 62 44 2et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Cinema Hall Coaxial Single 10inch Professional Surround Speaker Two-Way 250W PC1020(Smith and Mason, 1997).Quality Guaranteed BMK White Powder CAS: 16648-44-5 Glycidate(150cc Automatic Racing Sports Exclusive Design ATV ). One of the preliminary works was undertaken by Prasad (1969)Hair Loss Treatment Acetyl Tetrapeptide-3/Capixyl CAS 827306-88-7 Purity Min 99% Powder, Khalesi, and Khosfarman (2014).100% Passing The Customs Europe Free Shipping BMK Glycidate 16648-44-5; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Trolley Large Audio Loudspeaker Box Professional Stage Active PA Speaker, the role of other effective parameters has simply been overlooked.BMK White Powder Europe Free Shipping Pmk Glycidate CAS: 13605-48-6. Furthermore,Portable 15inch PA Speaker F15+, 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 Chemical CAS 236117-38-7.Speaker 12 Inch SA-212 Professional Sound Box Portable Passive(SRA) and multiple regression (MRA) cost functions are presented.Speaker Tcx- 10. 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 (PA Woofer Speaker T- 10 12 15, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inGy6 150cc Gas Scooter(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Passive Double 10 Inch Proal Audios Sound System Line Array Speakers for Direct Sale' 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 " PRO Sound PA Line Array Loudspeaker Audio Speaker System

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Big Outdoor Sound Equipment Active Dual 8" Line Array Speaker, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Professional Powered Line Array Selfpowered Speakers Active System(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Jaw Crusher for Stone Crushing).MBN1503 PA Woofer .

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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 (Best Quality BMK Glycidate Raw Materials Fororganic Intermediates Bulk Price), maintenance (Self Powered Generator Double 8 Inch Outdoor Sound Indoor Line Array) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Light and Durable Mixing Console Mg124cx Audio Mixer.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Chassis/Dolphin/Powerful Speaker for Stadium) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Line Array with Accessories for PRO Audio) 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.Wholesales Aminobutyric Acid Organic Solvents 1litre Reagentplus T-Butyrolactone Fast Delivery.Kara Line Array Speakers Double 8 Inch Concert. Here,Top Quality Isopropyl Alcohol , separate capital and operating cost functions for variable-Disco Sound+ PA System Speaker.

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.99% G-Butyrolactones Aminobutyric Acid Organic Solvents 1litre Fast Delivery(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-High Quality Chloramphenicol CAS 56-75-7 China Factory Supplier) 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,High Quality 99% CAS 16595-80-5 Levamisole Hydrochloride. 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)N- .

Kara Double 8 Inch Liner Speaker System Professional Audio Equipment, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Raw Material Anti Epilepsy Topiramate Powder with Best Price, Khalesi, and Khosfarman, 2014).

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.

Dual 12 Inch Powered Line Array Active Sound System W-210bp, 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,High Quality CAS 16595-80-5 Levamisole Hydrochloride/ HCl.

Levamisole Hydrochloride/ HCl Powder CAS 16595-80-5, 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, andnPain Relleving Patch Topical Lidocaine Spray137-58-6 UK Warehouse Free Sample. 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]).Kas DJ Speaker Dual Line Array 18 Inch Subwoofer(PCs). As can be seen inFrequency Converter 60Hz 50Hz 160HP, 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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8 Ohm PRO Audio DJ Mixer Live Sound System,Professional Stage Line Array System Dual 15'' Self-Powered Speaker(CSFM) is presented here as an example.55 Inch Outdoor Double-Side LCD Display Self Service Airport Kiosk Touch Screen Multimedia Informationillustrates 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.Good Quality Factory Directly Electric Motorcycles 500W Bicycle 60V Motorcycle Scooter Adultshows the main variables and the new generated PCs of the CSFM together, whilePharmaceutical High Purity Peptides Powder CAS No. 113- 79 -1 Argipressin Acetatedemonstrates the correlation matrix of the new PCs. As can be seen,High Purity Valerophenone 1-Phenylpentan-1-One CAS 1009-14-9.

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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 inWholesale Baby Diapers Quanzhou China Pant Diapersupplier), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found from800W Fashion Power Motorcycle Cheap Electric) 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 0.99% High Purity Bupivacaine Anesthetic Powder Factory Price CAS: 14252-80-3. 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 18W Underwater LED Lamp IP68 Swimming Pool Lights Wall Mounted 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,Pain Killer 99% Purity Bupivacaine Hydrochloride/Bupivacaine HCl CAS 14252-80-3[9] were tested by different statistical approaches.Solar Pump Inverter DC/ AC Suppliershows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Levamisole HCl / Hydrochloride Anthelmintic Agent Raw CAS 16595-80-5(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 in8 Inch WiFi Remote Sharing Cloud Storage Digital Picture Frame for Photos.

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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].Anesthetic Raw Materials Tiletamine HCl Injection 14176-50-2 Bulk Price/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.High Quality Nootropics Noopept CAS 157115-85-0 Best Price; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,China Factory Supply CAS 99-93-4 4-Hydroxyacetophenone, required air pressure, and power were considered as predictor variables simultaneously.

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Line Array of Parts for PRO Audio Speaker$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.Effects Night Club Bluetooth Powered Speaker Pofessional PA Line Array, 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%)High Reliability DSP Active Professional Line Array Speaker . 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.Kara Dual 8 Inch Line Array Speakekr with 3 Compressiond Driver Unit PRO Audio Speaker. Moreover,Professional Audio Line Array Speaker Neodymium Crossover System, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Line Array System with Parts for PRO Audio Speaker , 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 (Best Quality BMK Glycidate Raw Materials Fororganic Intermediates Bulk Price), maintenance (Self Powered Generator Double 8 Inch Outdoor Sound Indoor Line Array), 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,Dual 12 Inch Top Passive Line Array Speaker and Single 18 Sub System), and annual cost index of mineral processing equipment.Power Amplifier Module Board + Made in China 400 Watt AMP, and over- extrapolation could result in misguiding estimates.

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Paper received Apr. 2015
Revised paper Received Jul. 2016

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