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ScienceDirect Materials Today: Proceedings 4 (2017) 3173–3181

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5th International Conference on Materials Processing and Characterization, ICMPC- 2016

Performance of Box-Behnken and prediction model are compared with Al-Nano MMC to maximize the MRR Dinesh Kumar Kasdekara*,Vishal Parasharb a

Department of Mechanical Engineering, Madhav Institute of Technology & Science, Gwalior- 474005, India (M.P) Department of Mechanical Engineering,Maulana Azad National Institute of Technology, Bhopal-462051, India (M.P)

b

Abstract Electrochemical machining (ECM) is one of the finest method to machine hard materials of complex geometry. In this paper, box behnken (CCRD) is employed to find out the optimal combinations of process parameters of ANMMC for maximum material removal rate (MRR). Four process parameters viz.voltage, feed rate, electrolyte concentration and Sic% are considered in this study. Experiments are carried out to establish an empirical relationship between process parameters and responses. This composite is widely used in automotive industries due to high wear resistance, high strength to low weight ratio, elevated temperature toughness and high stiffness. In this regard, a versatile prediction model is required to determine the maximum MRR of the composite considering the effect of machining parameters. The box behnken (CCRD) and Artificial neural network (ANN) based prediction model is developed to determine the MRR of AA6061/cu/Sic+Grp and the performance of the Box-behnken and ANN models are compared with experimental results for their effectiveness. © 2017 Published by Elsevier Ltd. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).

Keywords: Electrochemical machining (ECM); Box behnken design; ANOVA;Regression model; ANN; Desirability function.

*Corresponding author. Tel.: +09752201523 . E-mail address: [email protected]

© 2017 Published by Elsevier Ltd. Selection and peer-review under responsibility of Conference Committee Members of 5th International Conference of Materials Processing and Characterization (ICMPC 2016).

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Nomenclature ECM BBD V ID (A) ANOVA MAE RMSE PEP BPNN ANN DF

Electro Chemical Machining Box-behnken design Voltage Discharge current Analysis of variance Mean absolute error Root mean square error Prediction error percent Back propagation neural network Artificial Neural Network Desirability Function

1. Introduction Metal matrix composites (MMCs) are materials that are prominent for a large range of engineering applications. These materials are known as the tough-to-machine materials, because of the hardness and abrasive nature of reinforcement element like silicon carbide (Sic) particles [1]. Recent advanced materials having the properties of high specific strength and a low thermal expansion coefficient. These complex materials are extensively used in aerospace, defense and automotive industries. These materials have deliberated being use in automobile brake rotors, piston and various components in internal combustion (I.C.) engines as the materials used for such applications generally require lightweight and good wear resistance than those of conventional materials. MMC composed by Al6061 as metallic base material called matrix which is reinforced with Sic. Due to possession of higher hardness and reinforcement strength, composite materials are problematic to be machined by traditional methods. Therefore, Electrochemical machining (ECM) process becomes a more viable method for machining with required MRR. ECM has been carried out based on the Box-behnken (CCRD) by utilizing the significant experimental data to predict the optimal parameters. Rana et al. [2], Presented AA 5083 alloy-Sic composites have been fabricated by Ultrasonic assisted Stir casting. Different weight % of Sic (3, 5, 8 and 10 wt %) were used for synthesis of composites. SEM micrographs show uniform distribution of Sic particles with agglomeration at some places. The application of ultrasonic vibration on the composite during melting not only refined the grain structure of the matrix, but also improved the distribution of Nano-sized reinforcement. Tiwari et al. [3], to develop a mathematical model for responses i.e., MRR and SR through regression analysis for ECM on EN-19 and ANOVA test is perform to check the aptness of the developed mathematical models. Goswami et al. [4], presented a comparative study of optimization performance between DSA, genetic algorithm (G.A.) and desirability function approach proves the wide acceptability of DSA as a global optimization tool. Giribabu et al. [5], Presented multiple linear regression models are developed for MRR, SR and ROC. Optimum machinating constraints to maximize MRR, minimize SR and minimize ROC are found available using genetic algorithms. Rao et al. [6], an attempt is made to machine the LM6 Al/B4Cp compounds using electrochemical machining process. Signal-to-noise (S/N), the analysis of variance (ANOVA) and regression analyses are engaged to find the optimal levels and to analyze the influence of electrochemical machining constraints on MRR, SR and ROC. Shankar et al. [7], attempts have been made to model and optimize process parameters in Abrasive supported Electro- Chemical Machining (AECM) of Aluminium-5-15% boron carbide- 5-10% graphite compound by means of pre-shaped cylindrical copper tool electrodes. Das et al. [8] described the artificial bee colony (ABC) algorithm. To find out the optimal arrangements of process parameters in ECM of EN 31 steel for maximum material removal rate (MRR) and least surface roughness (Ra). Ghosh et al. [9] to optimize the wear behaviour of Al-7.5%SiC metal matrix composite using

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Taguchi Method.The L27 orthogonal array is constructed using three levels of each tribological testing parameter Load (L), Sliding Speed (S) and Time (T). ANOVA analysis is carried out to find out the significant test parameters and their interactions affecting the wear behaviour of the composite. Bahre et al. [10], described the Smooth surface finishes, even goes down to a roughness average Ra value 0.05μm with Precision ECM are investigated. Paul et al. [11], presented the effect of process parameters of ECDM on Material Removal Rate (MRR) is studied on borosilicate glass. Response Surface Modeling (RSM) is used for optimization of process parameters. Durairaj et al. [12], presented the Grey relational theory and Taguchi optimization method were used to optimize the cutting parameters in wire EDM for SS304. Durairaj et al.[13], presented Multi-Objective optimization technique based on genetic algorithm used to optimize the cutting parameters in turning process such as cutting speed, feed and depth of cut. Ford et al. [14], presented experimental investigation by simulation and optimization of WEDM process using gaseous dielectric also carried out. Biswesh et al. [15], presented Non-dominated sorted genetic algorithm (NSGAII) to produce set of parts optimum solution. All the solution in the parts front is optimal solutions. Sahu et al. [16], discussed about the best trade-off among the two contradicting objectives of ECM process SA was successfully integrated with regression model equation. Bahe et al. [17], presented a comprehensive mathematical model is developed for correlating the interactive and higher order effects on the various machining parameters. Acharya et al. [18], have developed a MRR and surface roughness prediction model in electro chemical machining (ECM) of super alloys using response surface methodology (RSM). Bhattacharyya et al.[19], described the investigations into the influence of parameters have been conceded out by developing mathematical models based on the Response Surface Methodology approach (RSM). Senthilkumar et al.[20], To described a multiple regression model to signify relationship between input and output variables and a multi-objective optimization method based on a nondominated sorting genetic algorithm-II (NSGA-II) was used to optimize ECM process. In this paper, attempts have been made to predictive models based on BBD and ANN during Electro Chemical Machining (ECM) of Aluminium-96.5, 94.5, 92.5%, copper-1.5%, silicon carbide-1-3%, and graphite-1-3% composite using square baseshaped copper tool electrodes. Optimization of process parameters is established on the statistical techniques with four independent input parameters such as Voltage (v), Feed rate (mm/min), Electrolyte Concentration (gm. /l), wt%. of Sic were used to assess the ECM process performance in terms of Maximum material removal rate. The obtained results are compared with box- behnken (CCRD) and artificial neural network (ANN) assisted ECM machining of AA6061/Cu-Sic/Graphite composite. The input-output data essential to develop both RSM and ANN models have been attained through Box-Behnken design (BBD) of experiments. 2. Experimental dataset 2.1. Experimental setup The experiments were accompanied on the specimens using METATECH (EC MAC-I) electrochemical machining equipment. The ECM setup consists of control panel, machining chamber, electrolyte circulation system. The workpiece is fixed inside the machining chamber and the cathode (tool) is attached to the main screw which is driven by a stepper motor. For avoiding short-circuits, a current sensing circuit is interfaced between the tool and the stepper motor controller circuit. If the current exceeds an adequate limit, a signal is sent to the stepper motor controller circuit which immediately reverses the downward motion of the tool. The electrolyte is pumped from a tank, lined by corrosion resistant coating with the help of corrosion resistant pump & fed to the job. Spent electrolyte will return to the tank. The hydroxide sludge rising will settle at the bottom of the tank & can be easily drained out. Electrolyte supply shall be governed by flow control valve. Additional electrolyte flow is by- passed to the tank. Reservoir provides separate settling and draw off compartments. All fittings are of corrosion resistant material.The Pictorial view of the experimental setup is presented in Fig. 1(a). In this way, even hardest possible material can be given a complicated profile in a single machining operation.

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Fig. 1. Pictorial view of: (a) Experimental setup of the ECM, (b) Muffle electric furnace

2.2. Workpiece and tool materials The work material used for the current investigation is AA6061/Cu –Sic/Graphite T6 composites. The composites were manufactured by a stir casting method. The workpiece material used has a dimension of 50 x 50x 17mm size. This material is appropriate for a wide variety of automotive-type applications ,Aircraft , aerospace component, Bicycle frames, Drive shafts, Brake components, Valve, Couplings, etc. The experiments were planned using CCD for the design of experiments (DOE), which helps to reduce the number of experiments. The tool was made up of copper with a square cross section. The electrolyte used for experimentation is fresh sodium chloride (NaCl) solution with varying electrolyte concentration due to its less throwing power. Machining experiments is carried out for a fixed time interval. Experiments is conducted by fluctuating predominant process parameters such as voltage, feed rate, Electrolyte Concentration and % Wt. of Sic. MRR is measured from the weight loss technique. EDX (energy dispersion X-ray spectroscopy) helps to find out the type of element present in samples. 2.3. Heat treatment of the Al based metal matrix composite The alloy and composites is heat treated in a muffle electric furnace. Following three stages were involved during heat treatment of the materials Fig. 1(b).Figure of Muffle electric furnace. (i) Solution treatment: the composite are heated for 8 h at a temperature of 4900C until the alloying solute elements are completely dissolved in Al solid solution. (ii) Quenching: the solution treated material is cooled rapidly in the quenching oil to prevent the precipitation of the solute elements and to obtain a supersaturated solid solution. (iii) Artificial aging: hardening can be done by reheating the quenched alloy to a temperature of 180 0C for 8h in order to get improved properties. 2.4. Design of experiment (DOE) The response surface methodology (RSM) is a procedure able to determine a relationship between independent input process parameters and output data [21]. The data required to develop the computation is collected by designing the trials based on Box–Behnken Designs (BBDs) and by varying each numeric factor over three levels coded as -1; 0; and +1. The BBDs are existing for 3–10 factors, which are formed by combining two-level factorial designs with incomplete block designs. The design of experiment is generated using MINITAB 17.0 statistical package. Each time the trial is performed, an optimized set of input parameters is selected. This procedure creates designs with desired statistical properties and, more importantly, only a fraction of the number of experiments is required compared with three level factorial design. The levels of the four factors or machining parameters are reported in Table 1.

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Table 1. Experimental Parameters and their levels S.No

Process Parameter

1

Notations

Codes -1

0

1

Voltage(v)

A

6

8

10

2

Feed rate(mm/min)

B

0.16

0.19

0.23

3

Electrolyte Concentration(gm./l)

C

200

300

400

4

%Wt. of Sic

D

1

2

3

3. Results and discussion 3.1. Response surface analysis Response surface methodology is an experimental method used for predicting and modeling complicated relation between independent factors and one or more responses [22]. In this study, response surface methodology is applied to optimize the MRR by ECM. Experiments is performed using Box– Behnken design (BBD). Table 2. Box–Behnken design for optimization Trail. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

Voltage(v)

Feed rate (mm/min)

Electrolyte Concentration(gm./l)

%Wt. of Sic

MRR (gm./min)

6 6 6 6 6 6 6 6 6 8 8 8 8 8 8 8 8 8 10 10 10 10 10 10 10 10 10

0.16 0.16 0.16 0.19 0.19 0.19 0.23 0.23 0.23 0.16 0.16 0.16 0.19 0.19 0.19 0.23 0.23 0.23 0.16 0.16 0.16 0.19 0.19 0.19 0.23 0.23 0.23

200 300 400 200 300 400 200 300 400 200 300 400 200 300 400 200 300 400 200 300 400 200 300 400 200 300 400

1 2 3 2 3 1 3 1 2 2 3 1 3 1 2 1 2 3 3 1 2 1 2 3 2 3 1

0.126 0.083 0.208 0.272 0.081 0.135 0.238 0.116 0.378 0.191 0.202 0.090 0.011 0.212 0.252 0.002 0.010 0.373 0.276 0.261 0.125 0.153 0.342 0.212 0.306 0.433 0.181

For instance, Box–Behnken design is created to evaluate the second-order model, however there may be situations in which non- random portion of this model provides an insufficient representation of the true mean response, an indication of lack-of-fit of the second- order model [23]. Thus, in this study some third order model terms is added to the second order polynomial equation. Accuracy of model fitting is evaluated by means of ANOVA.

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3.1.1. Box–Behnken design The Box–Behnken design consists of 27 experimental points. The experimental conditions, and the MRR obtained for each point set by the Box– Behnken design are shown in Table 2. The relationship between responses and processed variables is examined for the response approximation function using Eq. (1), following by the statistical analysis of the model obtained. 3.2 Models and ANOVA analysis The quadratic models of MRR are established through nonlinear regression analysis of the statistical analysis software. Some terms in the fitted models can be regarded as irrelevant terms due to their “Prob. >F” value being much more than 0.05. On the contrary, the significant terms have their “Prob. >F” value being less than 0.05. These insignificant model terms can be removed while the significant terms are retained. Then, the final quadratic models of response equation in terms of coded factors are presented as follows: MRR = 1.93 - 0.185 A - 8.9 B - 0.00118 C - 0.202 D + 0.0172 A*A + 8.8 B*B + 0.000000 C*C - 0.0338 D*D 0.109 A*B - 0.000188 A*C + 0.0026 A*D + 0.01271 B*C + 1.647 B*D + 0.000135 C*D ……………eq. (1) The significances of the fitted quadratic models for the MRR are evaluated by ANOVA analysis, as shown in Table 3. When the value of Prob.>F for the term of models are less than 0.05 (i.e., 95 % confidence), this indicates that the models are deliberated to be statistically significant. In addition, the determination coefficient R2, is defined as the ratio of the described variation to the total variation and is a measure of the degree of fit. The closer R2 approaches to unity, the better the response models fit the actual data. The values of the determination coefficients R2 for MRR are 0.94, respectively. Consequently, it suggests that the models of MRR have high goodness of fit and can provide satisfied prediction for the experimental results. Table 3. The ANOVA for the fitted models Source Model Residual Error Total

Model Summary R-sq. R-sq. (adj) 94.52% 88.45%

DF 14 12 26

Adj SS 0.186372 0.155488 0.341859

Adj MS 0.013312 0.012957

F-Value 1.03

P-Value 0.0487

3.3. Comparison of artificial neural network and response surface methodology Response surface methodology (RSM) and artificial neural network (ANN) has become the most preferred methods for machining. Both models have been employed for building response/output surface plots in order to reveal the effect of input variables on extraction effectiveness as well as to figure out the interaction effects between variables. RSM and ANN are modelling tools able to answer linear and nonlinear multivariate regression problems. At this stage, comparison criteria are required to enumerate the difference between values produced by the models and the actual values. The RSM and ANN models created out of the experimental data associated fairly well and having Rvalue 0.945 and 0.999. These results indicate that the RSM prediction has a larger deviation than the ANN prediction. Advantage of RSM is its capability to exhibit the feature contributions from the coefficients in the regression model. This ability is powerful in identifying the irrelevant main influences and interaction factors or insignificant cubic terms in the model and thereby can reduce the complexity of the problem. Instead, this technique requires good definition of ranges for each factor to ensure that the response under deliberation changes in a regular manner within this range [24]. The chosen optimal process parameters are Levenberg-Marquardt training algorithm and 10 numbers of hidden neuron. ANN modelling of MRR, with the optimal process parameters setting has been shown. Variation of MSE of data set w.r.t. the epoch has been shown in Fig. 2(b). Validation data set is used to stop

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the training process in early stopping criteria for providing improved generalization. So the training is not moving at this point and the weights and biases were used to model MRR. Correlation coefficient(R) among desired target and actual output of training, validation and testing is shown in Fig. 2(a). The comparison of the trial, predicted value of RSM and ANN value are illustrated in Table. 4. The results of comparison were proved to predict values of the MRR close to those readings recorded experimentally with a 95% assured interval. If there is some variation in experimental RSM and ANN model. The ANN showed a clear benefit over the RSM for the data fitting as well as for the estimation capabilities.

(a)

(b)

Fig. 2.Graph of :( a) Correlation Coefficients (b) Variation of MSE w.r.t. epoch Table 4. Comparison of the experimental and predicted value of RSM and ANN value Trail. No 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27

MRR (gm./min) 0.126 0.083 0.208 0.272 0.081 0.135 0.238 0.116 0.378 0.191 0.202 0.090 0.011 0.212 0.252 0.002 0.010 0.373 0.276 0.261 0.125 0.153 0.342 0.212 0.306 0.433 0.181

Predicted RSM

%Error

0.1512 0.1535 0.1152 0.1348 0.1705 0.1311 0.1843 0.091 0.3110 0.1659 0.0817 0.0549 0.1299 0.0695 0.1404 0.0074 0.1815 0.3151 0.2609 0.2131 0.1641 0.2206 0.2457 0.2301 0.2649 0.3525 0.1361

-0.2 -0.8493 0.4461 0.5044 -1.1049 0.0288 0.2256 0.2155 0.1772 0.1314 0.5955 0.39 -10.809 0.6721 0.4428 -2.7 -17.15 0.1552 0.0547 0.1835 -0.3128 -0.4418 0.2815 -0.0853 0.13431 0.1859 0.2480

3.4. Desirability Function (DF) based optimization

ANN Prediction 0.1262 0.0830 -0.0225 0.1873 0.0815 0.1349 -0.0614 0.1385 0.3783 0.1908 0.2020 0.1303 0.0122 0.0058 0.2518 0.0020 0.0100 0.2797 0.2755 0.2595 0.1242 0.2075 0.3423 0.2114 0.3063 0.4340 0.1809

%Error -0.0015 0 1.1081 0.3113 -0.006 0.0007 1.2579 -0.1939 -0.0007 0.00104 0 -0.4477 -0.1090 0.9726 0.0007 0 0 0.2501 0.0018 0.0057 0.0064 -0.3562 -0.0008 0.0028 -0.0009 -0.0023 0.0005

One valuable approach to optimization of multiple responses is to use the simultaneous optimization technique popularized by Derringer and Suich [25]. The ranges and goals of input parameters viz. Voltage (v), Feed rate

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(mm/min), Electrolyte Concentration (gm./l),%Wt. of Sic vs. output parameters viz. MRR of the ANMMC composite is given in Table 5. The goal of optimization is to find a set of situations that will meet all the goals. It is not necessary that the desirability value is 1.0 as the value is fully dependent on how closely the lower and upper limits are set relative to the actual optimum [26]. A set 27 optimal solution is derived for the specific design space constraints for MRR of ANMMC using MINITAB.17 statistical software. The set of conditions possessing highest desirability value is selected as optimum condition for the desired responses. Desirability varies from 0 to 1 depending upon the closeness of the response toward target. The optimized value of the parameter is shown in Table 6. Table 5. Goals and parameter ranges for optimization of cutting conditions Condition Voltage(v) Feed rate(mm/min) Electrolyte Concentration(gm./l) %Wt. of Sic MRR

Goal Is in range Is in range Is in range

Lower limit 6 0.16 200

Upper limit 10 0.23 400

Importance 1 1 1

Is in range Maximize

1 0.002

3 0.433

1 1

Table 6. Input parameters and optimum values of ANMM composite Parameters Voltage(v) Feed rate(mm/min) Electrolyte Concentration(gm./l) %Wt. of Sic MRR Desirability

Goal Is in range Is in range Is in range

Optimum value 6.0 0.23 400

Is in range Maximize

3 0.4268 0.9857

Usually, a reduced gradient algorithm with multiple starting points is employed that maximizes the complex desirability to determine the optimal input variable settings. Most of the standard statistical software packages (Minitab, design expert) employ this popular technique for response optimization. In the present case, Minitab was used to optimize the response parameters. Optimization plot for the response is shown Fig. 3. The objective is to maximize the response considered at a time. As the composite desirability is close to 1, it can be concluded that the parameters are within their operational range. The optimized values of process parameters are Voltage (v) 6.0, Feed rate (mm/min) 0.23, Electrolyte Concentration (gm. /l) 400, %Wt. of Sic- 3.0.

Fig. 3. Optimum results of Maximum MRR

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4. Conclusion The leading conclusions which can be drawn are as follows: (i) ANOVA of second order model found to be significant as its p-value is less than 0.05 (ii) Comparison of experimental and predicted values of the MRR show that a good agreement has been achieved between them. (iii) Presence of Cu/Graphite/Sic particle into Al 6061 MMCs improves the MRR. Hybrid composite reinforced with graphite is easier to machine and delivered smooth surface. (iv) ANN and RSM modelling, ANN model produced less percentage error as compare to the RSM modelling. (v) The ANN model and RSM so developed can be used to analyse the effects of the selected process parameters on MMR. The RSM and ANN models constructed out of the experimental data correlated fairly well value 0.945 and 0.999 respectively. It shows that RSM model is better than ANN. (vi) Box-Behnken (RSM) shows that the optimal combination for process parameter is Voltage (v) at 6.0, Feed rate (mm/min) at 0.23, Electrolyte Concentration (gm. /l) at 400, and %Wt. of Sic- 3.0. Based on these combination, the value of MRR is 0.426 whose desirability is 0.985. (vii)The research findings along with RSM, ANN models and multi response optimization will offer effective strategies and the results would be a good technical database for the aerospace, automotive applications in fabrication and machining aspects. References [1] O. Kılıckap, M. Cakır, A. Inan, J. Mater. Process. Technology. 15 (2005) 862–867. [2] R.S. Rana, Rajesh Purohit, V.K. Soni, S. Das,4th International Conference on Materials Processing and Characterization ,Materials Today: Proceedings. 2 (2015) 1149-1156 [3] A.Tiwari, A.Mandal, K.Kumar, Materials Today: Proceedings. 2 (2015) 2569-2575. [4] D. Goswami and S. Chakraborty, International Journal of Industrial Engineering Computations. 5 (2014) 41–54. [5] A Giribabu1, S. R. Rao and G Padmanbhan, Int. J. Mech. Eng. & Rob. Res. 3 (2014) 32-38. [6] S. R. Rao and G. Padmanabhan, International Journal of Applied Science and Engineering. 12 (2014 ) 87-97. [7] M.Sankar, A.Gnanavelbabu, K.Rajkumar, 12th Global Congress On Manufacturing And Management, GCMM 2014, Procedia Engineering. 97 ( 2014 ) 381 – 389. [8] M.K.Das, K. Kumar, T. K. Barman, P. Sahoo, 12th Global Congress on Manufacturing and Management, GCMM 2014, Procedia Engineering. 97 (2014) 1587-1596. [9]S. Ghosh, P. Sahoo, G. Sutradhar, Advanced Materials Manufacturing & Characterization.4 (2014) 93-99. [10] D. Bahre, A. Rebschalager, O. Webr, P. Steuer, procedia CIRP. 6 (2013) 384-389. [11] L. Paul and S. S. Hiremath, International Conference on Design and Manufacturing, IConDM, Procedia Engineering. 64 (2013) 1395-1404. [12] M. Durairaj, D. Sudhersun, N. Swamynathan, Procedia Engineering. 64 (2013) 868-877. [13] M. Durairaj, S. Gowri, Procedia Engineering. 64 (2013) 878-887. [14] R. K. Ford, R. A, Afza, R. Teimouri, journal of manufacturing processes. 15 (2013) 483-494. [15] R. Biswesh, A. Chinmaya, P. Mohanty, S. S. Mahapatra, Procedia Engineering. 51 (2013) 554-560. [16] S. N. Sahu, D. Nayak, H.K. Rana, International Journal of Advanced Trends in Computer Science and Engineering. 2 (2013) 18-21. [17] D. Bahe, O. Weber, A. Rebchlager, Procedia CIRP. 2 (2012) 98-101. [18] B. R. Acharya, C. P. Mohanty, S. S. Mohapatra, Procedia Engineering. 51 (2012) 554-560. [19] B. Bhattacharyya, S. K. Sorkhel, J. Mater. Process. Technology. 86 (2011) 200-207. [20] C. Senthilkumar, G. Ganesan, R. karthikeyan, Trans. nonferrous Met.Soc.China. 21 (2011) 2294-2300. [21] V.N. Gaitonde, S. R. Karnik, M. Faustino, J. P. Davim, Int. J. Refract. Metals Hard Mater. 27 (2009) 754-763. [22] Box, G.E.P., K. B. Wilson, J. R. Stat. Soc. Ser. B. 13 (1951) 1-45. [23] H. M. Arshad, M. Akhtar, S. G. Commun. Stat. Theory. Methods. 41 (2012) 4225-4239. [24] R. Kumar, S. Chauhan, Measurement. 65 (2015) 166-180. [25] G. Derringer, R Suich. J Qual Technology. 12 (1980) 214-219. [26] N. Kiaee, M. Aghaie-Khafri, Mater. Des. 54 (2014) 25-31.