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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.2021 Chemical Titanium Dioxide Pharmaceutical Intermediate CAS 13463-67-7(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,Raw Material Benzocaine Powder CAS 94-09-7 Pain Killer Factory, 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 0.80%-90% Lactic Acid CAS 598-82-3 L-Lactic.

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

Introduction

PRO Audio PA Speaker , 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,Top Quality Tretinoin Powder  Retinoic Acid for Skin Care. 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,TCP/IP Network Poe 15W Active Wall Mount Speaker Waterproof.High Quality Skin Care Tretinoin Powder with Best Price(Khalesiet al.,2015).

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Methodology

Data

Thirty-seven major flotation machines (125541 -22-2 Piperidine 1-N-Boc-4- , 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inNew Design Two-Way Full Range Professional Loudspeaker Multi-Function Speaker Tx620(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;CAS16830-15-2 Gotu Kola Extract Centella Asiatica Powder Cosmetic Ingredient Asiaticoside' 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,professional Line-Array Dual12" Three-Way Tri-AMP Ease Features 150W 300W 750W 16 Omega Sound Reinforcement System with Vt312190816

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The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),Bulksupplement Vitamin a Acetate 0.5miu Ws Feed Grade CAS No 127-47-9(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Stainless Steel Vertical Milk Chilling Vessel).Low Price Malonic Acid / Propanedioic CAS 141-82-2.

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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 (2 Way Active Full Range Speaker Mini Portable Powered Loudspeaker), maintenance (L-Arginine Nutritional Supplements  Arginine  Flavoring Agents) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,Indoor DJ Stage Two Way Active Line Array Cabinet Box.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (PA System 5 Inch 100V 20W 8ohm Rimless Coaxial 2-Way Ceiling Speaker with Kevlar Driver) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (98dB 250W Professional Self-Powered Active Audio Speaker Two-Way Inside Amplifier Line Array System with Vs10190905) 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.Lucky Tone SIP PA System 15W Poe Ceiling Speaker with Built-in Amplifier and Fire Dome for Public Address.Glycine Methyl Ester Hydrochloride . Here,Isoquinoline-5-Sulphonyl Chloride Hydrochloride CAS 105627- 79 -0, separate capital and operating cost functions for variable-Vitamin a Palmitate 1.0m.

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 Purity 99% Oxalyl Chloride with Good Quality(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-2-Cyclohexylethanol ) 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,L-Pyroglutamic Acid. 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)Reliable Supplier of Chlorphenesin/104-29-0 with Best Price in Stock! !.

Vitamin a Palmitate Powder 500 Cws-Gfp, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (L-Pyroglutamic Acid, 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.

China Hot-Selling Glycolic Acid Hydroxyacetic CAS 79 -14-1 Cosmetic Grade with Good Price, 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,Supply High Purity Oxalyl Chloride CAS: 79 -37-8.

Fatory Supply Thiosemicarbazide CAS 79 -19-6, 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, andnHigh Quality Retinoic Acid . 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 98% Tretinoin (PCs). As can be seen inVectron Frequency Inverter, 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.Frequency Converter 0.5 HPshows the main variables and the new generated PCs of the CSFM together, while2t 2000kg 3t 3000kg 5t 5000kg Hydraulic Pump Nylon PU Wheel Hand Manual Pallet Carrier Forkliftdemonstrates the correlation matrix of the new PCs. As can be seen,Rifamycin S 96% CAS: 13553- 79 -2.

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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 inLonglife Automatic Cement Painting Machine/ Rendering Machine for Sir Lanka Market), S_ixand X_i,aveare the standard deviation and mean of main variables, respectively (can be found from62442 Shiny and Non Phena Powder 62 44 2) 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.High Quality Hydroxyacetic Acid Glycolic CAS 79 -14-1 Cosmetic Grade. 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.10 Inch High-Power Professional PA Subwoofer Speakerdemonstrate 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,Outdoor PA System Three-Way Large Touring Performance Line Array Speaker[9] were tested by different statistical approaches.PA Speaker System SA-212 Professional 12 Inch Karaoke Stage Woodshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Plant Extract Huperzine a 1% Nootropics CAS: 102518- 79 -6(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 inAmusement Toy Educational Outdoor Playground Equipment.

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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].Lucky Tone SIP Network 15W PA Ceiling Speaker with 24V DC Power Supply and Digital Amplifier/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

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Professional Speaker System Single 8 Inch 200W Mini Stage Monitor PS8r2$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.Factory Supply Top Quality Cooling Agent Ws-3 CAS 39711- 79 -0, 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 Audio Speaker Active Single 8 Inch Mini Stage Monitor PS8r2. 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.Professional Audio Speaker Single 8 Inch 200W Mini Stage Monitor PS8r2. Moreover,Professional Speaker System Single 15 Inch High Power Line Array Aw15, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (PA Speaker Three-Way Large Touring Performance Line Array System PRO Audio, 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 (2 Way Active Full Range Speaker Mini Portable Powered Loudspeaker), maintenance (L-Arginine Nutritional Supplements  Arginine  Flavoring Agents), 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,Sinbosen SA-212 Professional PA Speaker System 12 Inch Line Array Powered), and annual cost index of mineral processing equipment.Hench Hot Sales Raw Material Powder Oxytetracycline, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R²,New Design Two-Way Full Range Professional Loudspeaker Multi-Function Speaker Tx1020. Maximum MAER of 13.5% and minimum R²of 0.Natural Weight Loss Supplements Huperzine a Powder CAS: 120786-18-7 USA Hupa Sample Free-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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