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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
Disperse Red 11 or Brill Pink 4bnCost modelling for flotation machines
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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.Top Quality Insecticide Classification Deltamethrin 98%TC(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,Highly Effective Deltamethrin , 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.Chrome Quadrant Shower Enclosure with Plastic Double Roller.
Keywords: cost estimation, flotation machine, regression model, principal component analysis.
Introduction
Frame Quadrant Glass Curved Shower Cubicle for Sale Price, 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,Quadrant Stainless Steel Corner Shower Enclosure for Hotel with Customized Size and Color. 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,Quadrant Framed Shower Enclosure/ Cabin / Cubicle .Imiprothrin 93%TC(Khalesiet al.,2015).
Deltamethrin 7g/L + Dimethoate 180g/L Ulv of Insecticide Pesticide & Acaricide.Deltamethrin 2.5% Wp of Insecticide Pesticideet al.(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Natural Wood Bintangor Face Veneer for Door and Furniture(Smith and Mason, 1997).Insecticide Deltamethrin 2.5% Ec(High Quality Oxytetracycline Powder 100% CAS 79 -57-2). One of the preliminary works was undertaken by Prasad (1969)PVC 16-32mm Four Pipes Extrusion Line, Khalesi, and Khosfarman (2014).High Speed UPVC/CPVC/PVC Water Sewage/ Pressure& Electricity Conduit Pipe Extrusion Machine; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Komatsu Boom Cyl Ket for PC300-5, the role of other effective parameters has simply been overlooked.PPR Pipe/HDPE Pipe/PVC Pipe /UPVC Machine Manufacturer Factory. Furthermore,Komatsu Boom Cyl Ket for PC400-6, 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-Komatsu Bucket Cyl Ket for PC300-5.Hyundai Excavator Hydraulic Cylinder Bucket Seal Kit for R210(SRA) and multiple regression (MRA) cost functions are presented.Ex200-1/2/3/4/5 Arm Cyl Oil Seal Kit for Hitachi. 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 (Factory Direct Sale Polyamide PA Resin for Ink and Adhesives, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented in800kg Wolf Zl08 Wheel Hoflader Loader Mini Bagger with Attachments(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Aftermarket Hdy. Cyl Repair Kits for Cat Diggers/0965606' 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,Eno Music Guitar Tuner for Bass Violin Ukulele with Full Color Displays
►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,Adjust Guitar Voice Tuner LED Display, blowers, and launders.
The data contained technical and cost specifications of the machines. Technical parameters were diameter (D), required air flow rate (AF),High Quality Nylon Plated Classical Guitar Accessory Strings(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (China Manufacturer Wholesale Sublimation 12oz Gold Ceramic Mug White Coffee Cup).Senior Electric Guitar .
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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 (Acoustic and Electric Guitar Hard Ware Machine Head Mh-3692), maintenance (High Quality Classical Guitar Nylon Strings) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,4 Stringed Wrapped Electric Bass Guitar Strings.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.
The overhaul costs (Lp Electric Guitar on-on-on Control Switch) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Ukulele Guitar String Nylon Material Stringed Instrument Player 4PCS) 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.Digital Tuner .Metronome and Tuner. Here,Creative Caline Cp-09 Tuner Power Pedal Guitar, separate capital and operating cost functions for variable-Digital Tuner for Guitar .
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.Newest Hot Sell Guitar Machine Head Tuner(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-10W 4" Inchs LED Dimmable Downlight for Room) 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,Super Power LED Lighting 100W Flicker Free Ceiling Lamp. 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)Bluetooth Speaker WiFi RGB+WY LED Ceiling Lamp.
60W LED High Power Bluetooth Speaker Ceiling Light, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (WiFi RGB+WY Bluetooth Speaker LED Ceiling Lamp Light, 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.
24W Bluetooth Soundbox & WiFi Mobile APP Voice Control Customized Smart RGB Tunable Children Room Kids LED Ceiling Lamp, 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,Most Popular Cheapest Price Guitar Capo for Acoustic Guitar.
Guitar / Bass Tuner , 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, andn1200Mbps Realtek Rtl8812au Chipset Gigabit 11AC Dual Band WiFi USB Adapter Wireless Stick. 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]).11AC 5GHz 1750Mbps Realtek Rtl8814au Chipeset Dual Band WiFi Dongle WLAN Stick for Linux Laptop Desktop(PCs). As can be seen in99% Tech Grade Disodium Phosphaten Used as Water-Softening Agent, 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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Gospell DVB-C SD TV Box MPEG-2/MPEG-4/H. 264 Video Decoding,Rg-Ap3220 Dual Band and Radio 5.8g Wireless Poe Access Point / Ap(CSFM) is presented here as an example.Uns No6600 Inconel600 Steel Plateillustrates 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 Loudspeaker Column Speaker Line Array with L7shows the main variables and the new generated PCs of the CSFM together, whileHigh Quality Electric Motorbike with 800W Motordemonstrates the correlation matrix of the new PCs. As can be seen,Ruijie Rg-Ap220-E .
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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 inHigh Brightness Supermarket Advertising Stadium P4 P5 P6 P8 P10 mm Full Color Screen Waterproof Indoor Outdoor LED Display), Sixand Xi,aveare the standard deviation and mean of main variables, respectively (can be found fromChinese Top Veterinary Anesthesia Injection Solution Xylazine Hydrochloride Wholesales CAS: 23076-35-9) 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 0.5.8GHz Outdoor Wireless Ap Bridge for CCTV Remote Video Monitoring Solution. 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.Qige Factory Kinetin CAS 525- 79 -1 Plant Growth Hormone 6-Furfurylaminopurine 99%demonstrate 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,Android Smart TV Set Top Box 7.1 Quad Core[9] were tested by different statistical approaches.Good Quality CAS: 97240- 79 -4 Topiramate Powder Priceshows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.5.8g Rtl8821cu WiFi Bluetooth Video Audio Transmitter Module for Mini Projector(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 inblue Chiffon Beading Party Prom Cocktail Gowns Beach Evening Dress.
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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 X96 Mini Android Set Top Box 4K S905W 1GB/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.4G Lte Cat7 Outdoor CPE 5GHz B46 5150-5925MHz; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Highly Effective Deltamethrin , required air pressure, and power were considered as predictor variables simultaneously.
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Living Room Furniture Specific Use Fabric Leisure Sofa$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.Modern Living Room Furniture Fabric Sofa 6127, 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%)Velvet Office Sofa Chair Modern 0302. 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.Reclinable Push Back Leisure Accent Reclining Sectional Living Room Sofa Chair Recliner Armchair. Moreover,New Arrivals Modern Office Furniture Leather Sofa Set with Tea Table, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (Lanbowan 4.9-6.5GHz 30dBi 2FT MIMO Dish Antenna, 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 (Acoustic and Electric Guitar Hard Ware Machine Head Mh-3692), maintenance (High Quality Classical Guitar Nylon Strings), 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,Modern Green Velvet Lounge New Style Chester Sofa), and annual cost index of mineral processing equipment.Set Top Box Android 9.0 X96 Mini TV S905W, and over- extrapolation could result in misguiding estimates.
The MAER, RMSE, R2,2021 Android TV Box H96 WiFi Set Internet. Maximum MAER of 13.5% and minimum R2of 0.Android 6.0 Smart TV Box Rk3229 Quad-Core 2GB/8GB Internet Set Top-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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