SE OPTIMIZATION USING RESPONSE SURFACE METHODOLOGY …mmt.its.ac.id/download/ISMT/MI/19. Ricky Nugraha S.pdf · fulfilled SNI ISO 13006:2010 standard which regulate spto-quality ecification

Proceedings of The 1st International Seminar on Management of Technology MMT-ITS Surabaya, July 30th, 2016

MULTI RESPONSE OPTIMIZATION USING RESPONSE SURFACE METHODOLOGY AND DESIRABILITY FUNCTION IN CERAMIC

TILE PRESSING PROCESS TO REDUCE QUALITY LOSS COST Ricky Nugraha Saputra1) and Bobby O. P. Soepangkat2)

Master’s Program in Management of Technology, Institut Teknologi Sepuluh Nopember1) Jl. Cokroaminoto 12A, Surabaya, 60264, Indonesia

e-mail: [email protected])

ABSTRACTS

Two of the critical to quality (CTQ) characteristics of the body of ceramic tile produced by PT X in the pressing process are bending strength (KP) and water absorption (PA). A research was conducted to model those two CTQs or response variables of pressing process using response surface methodology (RSM,) The experimental plan is based on Box–Behnken design. The three process variables of pressing process, i.e., pressing pressure, powder mold depth and powder weight have been varied to investigate their effect on response variables. Those responses have been optimized using multiresponse optimization through desirability function. The ANOVA has been applied to identify the significance of developed model. The test results confirm the validity and adequacy of the developed RSM model. Finally, a new setting of process variables which produced a substantial reduction of loss in terms of cost has also been determined. Keywords: bending strength, water absorption, response surface methodology, Box–Behnken design, desirability function, quality loss cost. INTRODUCTION

Since 1991, PT X has produced ceramic tile to fulfill domestic need of floor tile. Nowadays, there are lots of competitor, it makes company should have competitive advantage in productivity and quality of product. High productivity means it has small ratio between broken final products with total production. Meanwhile, high quality means it has fulfilled SNI ISO 13006:2010 standard which regulate specification of critical-to-quality characteristics (CTQs) ceramic tile.

Table 1. Total of Failure Product Defect Quantity Percent (%) Acumulation (%)

Cracked 5,014.1 37.09 37.09

Edge Raw Chipping 4,397.7 32.53 69.62

Fine Chipping 2,296.4 16.99 86.61

Press Chipping 1,510.2 11.17 97.78

Side Raw Chipping 299.7 2.22 100.00

TOTAL 13,518.1 100

The making of body in ceramic tile is important because this process will become strength source. In this process, bending strength (KP) and water absorption (PA) are critical-to-quality characteristics (CTQs). When company fails to maintain quality of CTQs KP and PA, it will cause big loss. Data of product fail from January to April 2016 shown in Table 1. All

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defect shown in Table 1 related to CTQs KP and PA in pressing process. The mean of KP from pressing is 269.38 N/cm2 with 0.53 of CP value and 0.29 of CPK value. In the other hand, the mean of PA from pressing is 5.449% with 0.78 of CP value and 0.43 of CPK value. CP and CPK values from this process are still not accurate and precise.

The inaccurate and imprecise response of KP and are because of big deviation. To decrease KP and PA deviation, the exact level value of factors is needed. Factorial Design is one of DOE (Design of Experiment) method that can define the influence of factor to response being tested including their interaction. Factorial Design can’t be used when factor and response relationship are non linear/Square (Kiantrianda, 2015). Pressing process in this research consist of three levels in each factor related to KP and PA. The research that has three levels from each factors, will result non linear relation between factor and response (Sukram, 2016). The suitable method with non linear relation between factor and response is Response Surface. This method can analyze non linearity to result second order of regression equation that can be optimized (Sukram, 2016). The optimization of regression equation can generate exact level value of factor so the response fit the specification (Sukram (2016), Sumantri (2006) and Faridah et al. (2012)). With that reason, Response Surface method used in this research is suitable to answer the purpose of the research.

In this research, besides optimization KP and PA to generate exact level value of factor will be calculated the decreasing of loss cost too using Taguchi loss Function. The following section of this paper explains Response Surface method and Box-Behnken design, desirability function and Taguchi loss Function. The next section will show numerical results of the methodology and followed by conclusion in the last section.

METHODOLOGY Response Surface Method

Response surface methodology (RSM) is a collection of mathematical and statistical techniques for empirical model building. By careful design of experiments, the objective is to optimize a response (output variable) which is influenced by several independent variables (input variables). An experiment is a series of tests, called runs, in which changes are made in the input variables in order to identify the reasons for changes in the output response (Mayers et al., 2009)

This method is effective for studying the relationship between several factors with quantitative responses. According to Wu and Hamada (2000), there are three techniques commonly used in the design of the experiment to simplify the experiment. This three techniques are central composite design (CCD), Box-Behnken design (BBD), and uniform shell design (USD).

Box-Behnken Design This method is developed by Box and Behnken for the second order trials that included

categories of balanced incomplete block design. The spherical BBD is effective for the optimization process which all the outermost point (edge point) have the same distance to the center point as √2. The BBD is one alternative method of approaching the CCD for the the value of k = 3 and k = 4. In CCD, the number of trials is 14 + 3 factors Nc, while BBD only 12 + Nc. Number of BBD experiment requires only three levels, while the CCD need five levels for value α = 1. To change the independent variable into the coding level of factor, transformation is done using the following equation 1 (Wu and Hamada, 2000).

𝑥𝑖 = 𝑥𝑟𝑒𝑎𝑙−(𝑥𝑚𝑎𝑥+𝑥𝑚𝑖𝑛)/2(𝑥𝑚𝑎𝑥−𝑥𝑚𝑖𝑛)/2

(1)

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Desirability Function

Desirability function in one of mathematical approach develoved by Derringer and Suich to resolve multirespon optimazation issue (Myers et al., 2009). The general equation of desirability function is:

D = (d1 x d2 x … x dm)1/m (2) Note: D = total desirability Di = individual desirability function in each yi m = number of response Nominal-the-best function expect response to fit target value (Ti) which placed between

lower bond (Li) and upper bond (Ui). The equation of di is: di = 0 ŷi < Li

𝑑𝑖 = �ŷi−Li𝑇𝑖−𝐿𝑖

�𝛼𝐼

Li ≤ ŷi ≤ Ti (3) di = 1 ŷi > Ti

Taguchi Loss Function Control of products and processes utilize the distribution to see the distribution ratio of the

width to the range of product specifications. Mathematically, Taguchi loss Function formulates relationship between quality and cost of losses based on Table 2. K value obtained from the cost of improvements (A0) divided tolerance specifications (Δ02) according to the equation 4 (Yang and El-Haik, 2003).

k = 𝐴0∆02

(4)

Table 2. Taguchi Loss Function Quality

Characteristics

Loss on Each

Product

The average loss per product in

distribution

Higher-is-better L = k(1/y2)

L = k( 1

y 2) �1 + (3𝑠

2

y 2)�

Nominal-is-best L = k(y-m)2 L = k�𝑠2 + (y −𝑚)2�

Lower-is-better L = k(y2) L = k�𝑠2 + (y 2

)�

Source : Ross, 1996 With, L = loss m = nominal value (target)

k = constanta y = actual characteristic quality s2 = deviation

y A = mean value of y (y −𝑚) = gap from mean value of y and target value RESULTS AND DISCUSSION

An experiment to study the effect of Tk, Tb and B to KP and PA has been done. The experiments were performed with a combination of a pressing machine settings according to design experiments that have been made. Experimental data inserted into the Table 3 below.

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Table 3. Data of Experiment

RunOrder Tk (bar) Tb (mm) B (gr) KP (N/cm2) PA (%) 1 -1 0 -1 284.12 8.89 2 -1 -1 0 286.14 8.94 3 0 1 -1 274.87 11.23 4 1 -1 0 292.45 7.46 5 0 0 0 285.94 9.12 6 1 0 -1 284.55 9.35 7 0 -1 1 288.94 8.57 8 0 0 0 284.86 9.38 9 -1 1 0 278.09 10.44 10 -1 0 1 287.51 8.72 11 0 -1 -1 287.84 8.78 12 1 0 1 293.65 7.56 13 0 0 0 283.98 9.58 14 0 1 1 282.56 9.73 15 1 1 0 281.98 9.94

The modelling of KP and PA response conducted by Response Surface method. The relationship between Tk (x1), Tb (x2) and B (x3) to the response KP and PA are tested using ANOVA. The influence of individual factors to the response of KP and PA is shown in Figure 1.

(a) (b)

Figure 1. The Influence of Individual Factors to the Response (a) KP (b) PA The percentage of R2 indicates the amount of variations can be explained by the model.

The R2 value from each factor is shown in Table 4. Table 4. Coefficient of Determination Values and Lack of Fit

KP PA R2 98,37% 97,49%

P lack of fit 0,487 0,435 More than 90% variation of models KP and PA can be described by equations, and the

influence of other factors outside the model is less than 10%. Modelling of KP and PA can meet the test of the coefficient of determination. Based on the value Plack of fit in table 4, the value of KP and PA respectively are 0.487 and 0.435. By testing at α = 0.05, it was found that the H0 is fail to be rejected or there is no lack of fit. Because there is no lack of fit, the model used in the experiments were appropriate.

The test of regression coefficients simultaneously performed on value α = 0.05 with the following hypotheses: H0: all β1 did not affect the response (β1 = β2 = ... = βk = 0); H1: at least one βi ≠ 0; i = 1, ..., k

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Table 5. P Value from Analysis of Variance

Source KP PA Regresion 0,001 0,002 Linear 0 0 Square 0,015 0,016 Interaction 0,037 0,035

Table 5 shows all P values on the simultaneous regression coefficient test for the KP and PA valued less than 0.05, so H0 is rejected to regression coefficients, linear, square and interaction. Individual regression coefficients test using the following hypotheses: H0: βi = 0 for the every i; H1: βi ≠ 0 for the every i The estimated regression coefficients value for KP are shown in Table 6. All term in Table 6 show the interaction factor to KP with P value lower than 0.05.

Table 6. The Estimated Regression Coefficients Value for KP Term Coefficient SE Coefficient T P Constant 285.363 0.5353 533.057 0.000 x1 2.096 0.3940 5.321 0.001 x2 -4.734 0.3940 -12.015 0.000 x3 2.660 0.3940 6.751 0.000 x1*x1 1.767 0.5782 3.056 0.018 x2*x2 -2.138 0.5782 -3.697 0.008 x1*x3 1.427 0.5572 2.562 0.037 x2*x3 1.647 0.5572 2.957 0.021

The estimated regression coefficients value for PA are shown in Table 7. All term in Table 7 show the interaction factor to PA P value lower than 0.05.

Table 7. The Estimated Regression Coefficients Value for KP Hubungan Koefisien SE Koefisien T P Konstan 9.2531 0.1506 61.454 0.000 x1 -0.3350 0.1108 -3.023 0.019 x2 0.9488 0.1108 8.561 0.000 x3 -0.4587 0.1108 -4.140 0.004 x1*x1 -0.5429 0.1626 -3.338 0.012 x2*x2 0.4046 0.1626 2.488 0.042 x1*x3 -0.4050 0.1567 -2.584 0.036 x2*x3 -0.3225 0.1567 -2.358 0.048

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Figure 2. ACF Graph of (a) KP and (b) PA Figure 2 shows the results ACF plot residual value to lag for the KP and PA with a value

of α = 0.05. All ACF value for the KP and PA were in the upper and lower limits so that the residual assumed to be independent.

Plot for the KP and PA shown in Figure 3. On the plot KP and PA can be seen that the data is scattered at random and did not make a specific pattern, so it can be said that identical assumptions are met.

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Figure 3. Residual-Observation Order Plot of (a) KP and (b) PA Normality test results for the KP and PA shown in Figure 4. P value residual normality test

for KP and PA using Kolmogorov-Smirnov method has a value greater than 0.150, which means H0 is fail to be rejected. Residual for the KP and PA have normal distribution.

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Figure 4. Normality Test of (a) KP Residual and (b) PA Residual After all the test, then the mathematical model that shows the influence of Tk (x1), Tb (x2)

and B (x3) against KP (ŷKP) and PA (ŷPA) can be seen in the following regression equation: ŷKP = 285.363 + 2.09625x1 - 4.73375x2 + 2.66x3 + 1.76712x1

2+ 1.4275x1x3 - 2.13788x22 +

1.6475x2x3 (5) ŷPA = 9.25308 - 0.335x1 + 0.94875x2 - 0.45875x3 - 0.542885x1

2 - 0.405x1x3 + 0.404615x22

- 0.3225x2x3 (6) To validate generated model ,it is necessary to test the model. The experiment is performed with setting of Tk by 280 bar, Tb by 7.5 mm and B by 80 grams. The experimental results are shown in Table 8. Testing one-sample t done on value α = 0.05 with the following hypotheses: H0: μ = μ0; H1: μ ≠ μ0

Table 8. Analysis of Experimental Result Model Confirmation Factor Calculation Result Experiment Result T Test (P value)

x1 x2 x3 KP PA KP PA KP PA

0 0 0 285,1783 9,0135

285,14 9,12

0,436 0,430

284,84 9,21 285,23 8,89 283,89 8,95 283,71 9,19 285,90 8,98 285,49 8,96 284,86 9,04 284,96 9,06 285,12 9,01

The results of a one-sample t test for the KP and PA shows the value of P greater than 0.05, then H0 is fail to be rejected, which means the model experiment confirmation is suitable with model calculation result.

Surface plots shows the the influence of two factors the response. Plot used are surface plot and contour plot. Plot surface for the KP response shown in Figure 5 and Figure 6 show plot surface for the PA response.

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Figure 5. Plot Surface Graph of KP (a) Plot surface and (b) Contour Plot

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Figure 6. Plot Surface Graph of PA (a) Plot surface and (b) Contour Plot At Figure 5 can be seen that the increasing of x1 (Tk) and x3 (B) level followed by decreasing of x2 (Tb) level will increase the KP value and vise versa. Factors Tb opposite effect of Tk and B at KP response. At Figure 6 can be seen that the increasing of x1 (Tk) and x3 (B) level followed by decreasing of x2 (Tb) level will decrease the PA value and vise versa. Factors Tb opposite effect of Tk and B at PA response. The optimization results of desirability function shown in Table 9.

Table 9. The Optimization Results of Desirability Function Factor Response Desirability

Tk -0.760004 KP 285 1.0 Tb -0.276963 PA 9 1.0 B -1

Figure 7. Optimization Plot

Graph desirability value for each response shown by Figure 7. Black curve line shows the d value for each response, whereas blue dotted line shows the current value response at particular d value. D value reaches the maximum value when the value of the factors is at the

CurHighLow1.0000

DOptimal

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Targ: 285.0KP

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Targ: 9.0PA

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red line. When the d value on one of response increases, it will reduce the other response d value and vice versa. The confirmation experiment is done by using setting as Tk = x1 = 203,999 ≈ 204 bar, Tb = x2 = 7,362 ≈ 7,4 mm and B = x3 = 75 gram. One-sample t test is done after doing confirmation experiment, and shows as Table 10.

Table 10. Summary of Experiment Confirmation One-Sample t Test KP PA

Target value 285 5 Sample mean 285,14 5,0252

P 0,950 0,655 Table 11 shows a summary comparison of process capability shown at CTQs KP and PA before and after optimizations.

Table 11. Comparison of Process Capability Comparison KP PA

Begining Optimized Begining Optimized Mean 269,377 284.041 5,44943 5,01537 Standar deviation 21,4507 12.5996 0,576054 0,28368 Cp (precision) 0,53 2,76 0,76 3,23 Cpl 0,29 1,88 1,13 3,28 Cpu 0,76 3,64 0,43 3,18 Cpk (accuration) 0,29 1,88 0,43 3,18

After doing capability process test and compare it, then calculate the decreasing of loss cost using Taguchi loss Function. The summary of loss cost decreasing shown at Table 12.

Table 12. The summary of Loss Cost Decreasing Term KP PA Total

Lbegining Rp 3021,06 Rp 2806,46 Rp 5827,52 Loptimized Rp 684.98 Rp 424.32 Rp 1109.3

ΔL Rp 2336.08 Rp 2382.14 Rp 4718.22 %ΔL 77.33% 84.88% 80.96%

CONCLUSIONS AND RECOMMENDATIONS

Based on the result of all research process, this research concluded the mathematical model that shows the influence of Tk (x1), Tb (x2) and B (x3) against KP (ŷKP) and PA (ŷPA) can be seen in the following regression equation: ŷKP = 285.363 + 2.09625x1 - 4.73375x2 + 2.66x3 + 1.76712x1

2+ 1.4275x1x3 - 2.13788x22 +

1.6475x2x3 ŷPA = 9.25308 - 0.335x1 + 0.94875x2 - 0.45875x3 - 0.542885x1

2 - 0.405x1x3 + 0.404615x22

- 0.3225x2x3 Optimization of the desirability function generates KP value by 285 KP and PA by 9 from

the presssing process with the machine settings as follows: a. Tk = -0,760004 -> 204 bar b. Tb = -0,276963 -> 7,4 mm c. B = -1 -> 75 gram

Cost loss reductions by Rp 4718.22/tile piece or 80.96% was obtained from the decrease in the mean and deviation value at pressing process that uses optimization machine settings.

Some recommendations for future research: future research are expected to be made directly to the production process in order to obtain the corresponding results in the field. Future studies are expected to consider the effect of the firing process by including it as a factor. Additional research is needed to optimize the ceramic tile size or ceramic surface flatness.

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REFERENCES Faridah, A., Widjanarko, S.B., Sutrisno, A., Susilo, B. (2012), “Optimasi Produksi Tepung

Porang Dari Chip Porang Secara Mekanis Dengan Metode Permukaan Respons”, Jurnal Teknik Industri, Vol. 13, hal. 158–166.

Hanafiah, K.A. (2004), Rancangan Percobaan Teori dan Aplikasi, Raja Grafindo Persada, Jakarta

Iriawan N., Astuti, S.P. (2006), Mengolah Data Statistik dengan Mudah Menggunakan Minitab 14, Andi, Yogyakarta.

Kiantrianda (2015), Aplikasi Metode Permukaan Respon terhadap Kehilangan Minyak Berdasarkan Suhu, Waktu dan Tekanan Pada Proses Perebusan Kelapa Sawit Di PT. Socfin Indonesia Bangun Bandar, Skripsi yang tidak dipublikasikan, USU, Medan.

Kolarik, W.J. (1995), Creating Quality Concepts, System, Strategies, and Tools, McGraw-Hill, Singapura.

Montgomery, D.C. (2009), Design and Analysis Experiments, 7th edition, John Wiley & Sons, Inc., New York.

Myers, R.H., Montgomery, D.C., Anderson-Cook, C.M. (2009), Response Surface Methodology Process and Product Optimization Using Experiment, 3rd edition. John Wiley & Sons, Inc., New York.

Ross, Phillip J. (1996). Taguchi Techniques for Quality Engineering, 2nd edition, McGraw-Hill, Singapura.

Sukram (2016), Optimasi Perbedaan Warna dan Kilap Cat Bubuk Menggunakan Metode Permukaan Respon, Tesis yang tidak dipublikasikan, MMT-ITS, Surabaya.

Sumantri, S.H. (2006), Optimasi Diameter Tebar dan Detonasi Cone Explosive dengan Metoda Dual Respon Surface, Tesis yang tidak dipublikasikan, MMT-ITS, Surabaya.

Triyono (2007), Penentuan Setting Level Optimal Bending Strength Gypsum Interior Berpenguat Serat Cantula Menggunakan Desain Eksperimen Taguchi, Skripsi yang tidak dipublikasikan, UNS, Surakarta.

Wu, C.F.J., Hamada, M. (2000), Experiment Planning, Analysis, and Parameter Design Optimization, John Wiley & Sons, Inc., New York.

Yang, K., El-Halik, B. (2003), Design for Six Sigma, McGraw-Hill, New York.

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Documents

SE OPTIMIZATION USING RESPONSE SURFACE METHODOLOGY …mmt.its.ac.id/download/ISMT/MI/19. Ricky Nugraha S.pdf · fulfilled SNI ISO 13006:2010 standard which regulate spto-quality ecification