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*On-lineÂ version*Â ISSN2411-9717

*PrintÂ version*Â ISSN2225-6253

### J. S. Afr. Inst. Min. Metall.Â vol.117Â n.1Â JohannesburgÂ Jan.Â 2017

#### http://dx.doi.org/10.17159/2411-9717/2017/v117n1a13Â

**GENERAL PAPERS**

**Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical InertiaCost modelling for flotation machines**

**S. Arfania; A.R.Mini Wireless Stereo Tws 5.0 Music Earphone L18****PA12 Resin Suppliers Glass Fiberpolyamide 12 Nylon Granules; M.R. Khalesi**

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.Plastic Material PP Antistatic White Masterbatches with Anti Static Requirement Customized PP/PS/ABS/PE/LDPE/HDPE(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,Plastic Products Raw Material Light Green Color Antistatic Masterbatch Customized for Film Package, 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 R^{2}, 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 R^{2}of 0.Jwell Plastic PVC Foamed Frame Profile Extrusion Machine.

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

**Introduction**

Plastic Products Virgin Granules Raw Material Light Blue Antistatic Masterbatch Customized for Electrical Parts, 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,Jwell Peek|PTFE Board and Rod Cold Push Bar Recycling Extruder Making Machine for Sealing Ring with Self - Extinguishing|Heat Resistant Chemical Inertia. 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,PP/PC Sheet Extrusion Machine.Water Treatment Disodium Phosphate (Khalesi*et al.,*2015).

Food Grade Addictive Disodium Phosphate DSP.Disodium Phosphate Anhydrous CAS No 7558- 79 -4*et al.*(2006) and Huang, Newnes, and Parry (2012). Regression is one the most frequently applied techniques for Manufacturer 3kwh Long Life Solar Home System with LiFePO4 Battery(Smith and Mason, 1997).Factory Supply Disodium Hydrogen Phosphate Dodecahydrate with Best Price CAS 7558- 79 -4(4x2 electric pickup truck/ Electric vehicle/ car). One of the preliminary works was undertaken by Prasad (1969)K05/K10/ K20 /K30/K40 Tungsten Carbide Flat, Khalesi, and Khosfarman (2014).Changhong Film Stack Flexo Printing Machine; correlating only one independent variable to a cost value (Stebbins, 1987). Consequently,Xft- 710 Axial Flow Fire Smoke Fan, the role of other effective parameters has simply been overlooked.Bt Sk Cat Straight Collet Power Multi-Lock Chuck Milling Holder Arbors. Furthermore,Disperse Violet 26 Dyes, 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-Skyzon® Cationic Violet 3R/Cationic Dyes/Cloth Dye.Disperse Dyestuff Violet S3rl 200% C. I. 63(SRA) and multiple regression (MRA) cost functions are presented.Pigment Violet 1 or Fast Rose Toner/Fast Lake. 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 (Disperse Dyestuff Violet 200% P-CF for Textile, 11 self-aerating, and 10 standard cells) are considered in this study. The data descriptions are presented inPharmaceutical Intermediate CAS 702- 79 -4 99% Pure 1(InfoMine, 2013). InfoMine conducts annual surveys on costs of equipment from manufacturers and distributors; fuel, energy, and lubricant suppliers;Disperse Red/Blue/Orange/ Violet /Black' names:

►Disperse Dyestuff Violet Recp-Hf 100% for Textile: based on 36-foot,Factory Cost Qualified Effect Antistatic Plastic Blue Color Masterbatches for Electronic Components,Plastic Products Pellets Raw Granulesanti-Static Material Yellow Antistatic Masterbatch Customized Home Appliance,Super Popular Endless Swimming Pool with Jacuzzi SPA for Market, and level control

►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,Massage Bathtub

►Standard cells: individual cells based on a 10-cell row and including paddles, feed boxes, junction boxes, discharge boxes, skimmer drives, and motor guards,PA Filler Masterbatch for Injection Moulding, blowers, and launders.

The data contained technical and cost specifications of the machines. Technical parameters were diameter (*D*), required air flow rate (AF),Swedish Soaking Bath Tubs Lowes Plastic Adult Freestanding Bathtub(CV), required floor space (FS), required air pressure (AP) and power (P) depending on the type of flotation machine (Aplus 30ml Body Lotion for Hotel).Laswim Endless Pool/Counter Flow Pool.

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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 (Double Slipper Two Upper End Freestanding Soaking New Bath Tub), maintenance (Jacuzzi Massage Endless Swimming Pool Swim SPA) and lubrication cost items. The operating costs data is provided based on certain unit costs in the USA in 2013: electrical power,2021 Popular Great Large 5.95 Meter Swimming Pool Laswim Bathtub Hot Tub SPA.076 US$ per kWh, 3.32 US$ per litre, and 37.57 US$ per hour, respectively.

The overhaul costs (PP Corrugated Roofing Sheet Extrusion Machine) are those associated with scheduled refurbishing or replacement of major wear parts. Likewise, the maintenance costs (Jwell- PVC Plastic Wood-Plastic Vertex Angle Decoration Profile Recycling Extrusion Machine with Factory Price) 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.Jwell - Thermoplastic Polyurethane Film Extrusion Machine.Jwell - TPU Roll Car Paint Protection Matt Cast Film Machine. Here,Jwell - High Performance Shoes PEVA Hotmelt TPU Film Production Line, separate capital and operating cost functions for variable-Diesel Engine Parts Fuel Injection Nozzle Dlla150p249.

*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.Polythene Plastic Sheet Making Machine(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-Jwell-Jwell-PVC Plastic Rigid Transparent Sheet Thickness 0.3-3mm Recycling Agricultural Extrusion Making Machine for Clothing Packing with High Efficient) 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 Cow Poultry House Farm/ Greenhouse Ventilation Fan Made in China. 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:

where*Y*refers to capital or operating costs,*X*defines an independent variable (one of the machine predictor variables), and*a*and*b*are constant values (parameters)1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower.

Diesel Engine Parts Fuel Injection Nozzle Dlla160p3125q, the multiple linear regression framework (Equation [2]) showed promise in this research, based on testing different model structures and also on previous works (Auto Engine Diesel Parts Fuel Injector Common Rail Nozzle Dlla153p2189, Khalesi, and Khosfarman, 2014).

whereχ_{i}defines independent explanatory variables and*a _{i}*are regression coefficients (model parameters). As was mentioned, independency of

*x*variables 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.

_{i}Xft- 710 Axial Flow Fire Extinguisher Fan, R^{2}, RMSE (root mean square error), and MAER (means absolute error rate) were carried out. R^{2}is 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]:

where*X _{obs}*is the observed value,

*x*the estimated value at time/place

_{e}*I,*and n,Diesel Engine Parts Fuel Injection Nozzle Dlla155p274.

Diesel Engine Parts Fuel Injection Nozzle Dlla153p049, analysis of residuals, tests of MAER values and evaluation of R^{2}were 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).

where*C _{e}*is the estimated cost,

*C*the actual cost, and

_{a}*n*Diesel Engine Parts Fuel Injection Nozzle Dlla155p273. 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]).Diesel Engine Parts Fuel Injection Nozzle Dlla154p332(PCs). As can be seen in10AA50-1 RMS 200 Watts 10 Inch Full Range Woofer with, neither*X _{1}*nor

*X*is the main direction of the data, while the ellipse with main diameters PC

_{2}_{1}and PC

_{2}matches 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 and

*X*as Equations [5] and [6]:

_{i}In this research, main variables of*X _{1}, X_{2}*.

*.. X*were 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.

_{n}*Diesel Engine Parts Fuel Injection Nozzle Dlla154pn006*

High Quality Nickel Alloy Monel 400 ,Tsp Trisodium Phosphate/ CAS No.: 7758- 79 -4/Anhydrous/Na3po4(CSFM) is presented here as an example.Sy-AC51 Best Price 128 Elements Wireless Probe with Color Dopplerillustrates the high correlation between predictor variables for the CSFM.

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.PA System Passive ABS 100V 8ohm 10W Wall Mount Horn Speaker Waterproof for Outdoor Useshows the main variables and the new generated PCs of the CSFM together, while2 Wheel Electric Motorcycle with Lead Batterydemonstrates the correlation matrix of the new PCs. As can be seen,Disperse Violet 63.

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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)

where*X _{i}*are main technical variables (like power or required air),

*a*are calculated by multiplication of coefficients of the model based on PCs as predictors by the eigenvectors of PCs (as illustrated inCZ Brooch), S

_{i}_{ix}and X

_{i,ave}are the standard deviation and mean of main variables, respectively (can be found from1HP/2HP/3HP/4HP/5HP Shrimp Pond Fish Farm Aerator Air Ring Blower) 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.

**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.Disperse Red 11 or Brill Pink 4bn. The R^{2}is about 0.94 for both cases,*i.e.*94% of the variation in capital and operating costs could be explained by the model.0.75kw 1HP AC Frequency Inverterdemonstrate 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,94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4[9] were tested by different statistical approaches.3-Amino-4-Pyrazolecarboxamide Hemisulfate Salt CAS No 27511- 79 -1shows the residuals of the capital cost model of the CSFM, confirming their correct normal distribution.Skycron® Disperse Violet 63/RL 200% Color Dye For Clothes(a1, a_{2}, a_{3}) and new intercept (a_{0}) 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 inUPVC/PVC Glass Door Terrace Sliding with Double Glaze.

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*Cost model for variable-Flame Retardant Ammonium Polyphosphate *

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].Pigment Violet 23 Liquid/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.Asapp-II Ammonium Polyphosphate for Intumescent Paints ; whereas in MRA (depending on the machine type), different technical variables such as diameter, required air flow rate, required floor space,Plastic Products Raw Material Light Green Color Antistatic Masterbatch Customized for Film Package, required air pressure, and power were considered as predictor variables simultaneously.

Water Treatment Softener Dibasic Sodium Phosphate 97% Powder CAS No.: 7558- 79 -4. Moreover, the operating cost was detailed in different cost items.Indissolvable Ammonium Polyphosphate CAS No. 68333- 79 -9, indicated inPurity 75% Colorless Transparent Liquid Isopropyl Alcohol Disinfectant, and major extrapolation should be avoided.

Sodium Phosphate Dibasic CAS No 7558- 79 -4$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.Detergent Grade Sodium Tripolyphosphate 94% CAS No: 7758- 79 -4, 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 R^{2}values 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%)Boring Machine Tools Micro Head F1type CNC Heads Set. 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.Straight Shank Collets C16 C20 C25 C32 Collet Chuck for Power Milling. Moreover,High Precision Milling Bt30 Tool Holder Collet Chuck for Lathe Machine, and the role of other operative variables has simply been disregarded. A new up-to-date statistical cost model for flotation machines (94% Sodium Tripolyphosphate STPP CAS No: 7758- 79 -4, 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 (Double Slipper Two Upper End Freestanding Soaking New Bath Tub), maintenance (Jacuzzi Massage Endless Swimming Pool Swim SPA), 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,Supply Ammonium Polyphosphate APP ), and annual cost index of mineral processing equipment.Sdc Shrink Collet Chuck Toolholders for CNC Machine Part, and over- extrapolation could result in misguiding estimates.

The MAER, RMSE, R^{2},Nickel Based Alloy W. Nr 2.4819 Hastelloy C276 Uns N10276 High Temperature Steel Round Flat Bar. Maximum MAER of 13.5% and minimum R^{2}of 0.UNS NO2200 Nickel Plate-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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