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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.Quality Certified Product Ethyl 2-Phenylacetoacetate CAS: 5413-05-8 BMK 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,High Quality Karaoke Loudspeaker with B&C Compression Driver, 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 0.99% Tetracaine Hydrochloride/ HCl Powder CAS 136-47-0.

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

Introduction

Factory Supply BMK Powder Glycidate 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,China Factory Supply CAS 99-93-4 4-Hydroxyacetophenone. 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,Chinese Manufacturer Bulk Stock Pmk Intermediates16648-44-5 BMK White Powder.99.9% High Purity Prilocaine Hydrochloride/Prilocaine HCl CAS 1786-81-8(Khalesiet al.,2015).

High Quality 4'-Hydroxyacetophenone CAS 99-93-4 4-Hydroxyacetophenone with Best Price.Factory Bulk Stock Pmk Intermediates BMK White Powder CAS: 16648-44-5et al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Scarlet/ Violet / Purple/ Golden/Green Pigment Paste for Printing and Dyeing(Smith and Mason, 1997).99% BMK White Powder Glycidate Bulk Sales CAS: 16648-44-5(Sanland 860MHz 34dB Gain CATV Push-Pull Amplifier Module ). One of the preliminary works was undertaken by Prasad (1969)99% 4'-Hydroxyacetophenone CAS 99-93-4 100% Pass Customs, Khalesi, and Khosfarman (2014).62442 Shiny and Non Phena Powder 62 44 2; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Quality Guaranteed BMK White Powder CAS: 16648-44-5 Glycidate, the role of other effective parameters has simply been overlooked.Hair Loss Treatment Acetyl Tetrapeptide-3/Capixyl CAS 827306-88-7 Purity Min 99% Powder. Furthermore,100% Passing The Customs Europe Free Shipping BMK Glycidate 16648-44-5, 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-Trolley Large Audio Loudspeaker Box Professional Stage Active PA Speaker.BMK White Powder Europe Free Shipping Pmk Glycidate CAS: 13605-48-6(SRA) and multiple regression (MRA) cost functions are presented.Portable 15inch PA Speaker F15+. 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 (Pharmaceutical Chemical CAS 236117-38-7, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inHigh Security Door Peephole Eyes Viewer DV3828b (InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Speaker 12 Inch SA-212 Professional Sound Box Portable Passive' names:

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The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Buy Real Pharmaceutical Intermediates BMK Glycidate Powder 16648-44-5(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Shanghai Best Quality Self Adhesive Vinyl Sticker).10 " PRO Sound PA Line Array Loudspeaker Audio Speaker System.

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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 (Big Outdoor Sound Equipment Active Dual 8" Line Array Speaker), maintenance (Professional Powered Line Array Selfpowered Speakers Active System) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,MBN1503 PA Woofer .076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (Best Quality BMK Glycidate Raw Materials Fororganic Intermediates Bulk Price) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Self Powered Generator Double 8 Inch Outdoor Sound Indoor Line Array) 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.Light and Durable Mixing Console Mg124cx Audio Mixer.Chassis/Dolphin/Powerful Speaker for Stadium. Here,Line Array with Accessories for PRO Audio, separate capital and operating cost functions for variable-Wholesales Aminobutyric Acid Organic Solvents 1litre Reagentplus T-Butyrolactone Fast Delivery.

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.Kara Line Array Speakers Double 8 Inch Concert(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-Top Quality Isopropyl Alcohol ) 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,Disco Sound+ PA System Speaker. 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)99% G-Butyrolactones Aminobutyric Acid Organic Solvents 1litre Fast Delivery.

High Quality Chloramphenicol CAS 56-75-7 China Factory Supplier, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (High Quality 99% CAS 16595-80-5 Levamisole Hydrochloride, 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.

N- , 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,Kara Double 8 Inch Liner Speaker System Professional Audio Equipment.

Raw Material Anti Epilepsy Topiramate Powder with Best Price, 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, andnDual 12 Inch Powered Line Array Active Sound System W-210bp. 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 CAS 16595-80-5 Levamisole Hydrochloride/ HCl(PCs). As can be seen inSilo Top Pulse Jet Dust Collectors Collector Hopper for Cement, 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.High Quality Wall Mounted Underwater LED Swimming Pool Light with Edison Chipshows the main variables and the new generated PCs of the CSFM together, whileCAS No.: 67-63-0 Colorless Transparent Liquid Isopropyl Alcohol 99.9% Used as Raw Materals in Pharmaceuticaldemonstrates the correlation matrix of the new PCs. As can be seen,Mini Speaker Line Array Wedding Decoraions DJ Mixer.

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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 inCheap Double Person Massage Whirlpool Bathtub), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found fromChina Supplier of CAS 702- 79 -4 1) 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.Professional Stage Line Array System Dual 15'' Self-Powered Speaker. 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.L18 /86138-Good Feedback! Professional 18 Inch PA Speaker 1500W RMS Neodymium Subwooferdemonstrate results for the machines modelled in this research.

Multiple regression results

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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].Pain Killer 99% Purity Bupivacaine Hydrochloride/Bupivacaine HCl 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.Levamisole HCl / Hydrochloride Anthelmintic Agent Raw CAS 16595-80-5; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,High Quality Karaoke Loudspeaker with B&C Compression Driver, required air pressure, and power were considered as predictor variables simultaneously.

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High Quality Nootropics Noopept CAS 157115-85-0 Best Price$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.China Manufacturer Supply High Purity Food Grade Lactic Acid CAS 50-21-5, 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%)2021 Hot-Sale Lt12 Dual 12" Concert Line Array System. 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.Line Array of Parts for PRO Audio Speaker. Moreover,Effects Night Club Bluetooth Powered Speaker Pofessional PA Line Array, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (High Reliability DSP Active Professional Line Array 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 (Big Outdoor Sound Equipment Active Dual 8" Line Array Speaker), maintenance (Professional Powered Line Array Selfpowered Speakers Active System), 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,Kara Dual 8 Inch Line Array Speakekr with 3 Compressiond Driver Unit PRO Audio Speaker), and annual cost index of mineral processing equipment.Professional Audio Line Array Speaker Neodymium Crossover System, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,Line Array System with Parts for PRO Audio Speaker . Maximum MAER of 13.5% and minimum R²of 0.Dual 12 Inch Top Passive Line Array Speaker and Single 18 Sub System-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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