วารสารมหาวิทยาลัยศิลปากร by SURIC

ISSN 1905-9159

Silpakorn University

Science and Technology Journal Special issue from OR-Net 2011 Conference Volume 5 Number 2 (July-December) 2011 Flexible Printed Circuit Process Improvement via Interchangeable Linear Constrained Response Surface Optimisation Models Pichpimon Kanchanasuttisang and Pongchanun Luangpaiboon Parameter Setting for Rod Push Production Process on Multiple Responses : A Case Study in Motorcycle Parts Factory Erawin Thavorn and Prapaisri Sudasna-na-Ayudthya The Study of Suitable Factors for Welding on Canned Food by Design of Experiment Method Prachuab Klomjit and Paisan Chantasoponno

A Study of Proper Conditions in Face Milling Palmyra Palm Wood by Computer Numerical Controlled Milling Machine Surasit Rawangwong, Jaknarin Chatthong, Julaluk Rodjananugoon and Worapong Boonchouytan

Optimisation Using a Central Composite Rotatable Design for Lacquer Production Process Chanpen Anurattananon, Suchavadee Pattanavatcharakul and Manit Soypetch

The Development of Mathematical Model for a University Course Timetabling Problem Ronnakit Wattanamano, Kanjana Thongsanit and Patipat Hongsuwan

SILPAKORN UNIVERSITY Science and Technology Journal SUSTJ

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SILPAKORN UNIVERSITY Science and Technology Journal Editorial Office Silpakorn University Research and Development Institute (SURDI), Silpakorn University, Sanamchandra Palace Campus, Nakhon Pathom, Thailand

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Editor Assoc. Prof. Onoomar (Poobrasert) Toyama, Ph.D Faculty of Pharmacy, Silpakorn University

SILPAKORN UNIVERSITY Science and Technology Journal Editorial Board Assist. Prof. Bussarin Ksapabutr, Ph.D Faculty of Engineering and Industrial Technology, Silpakorn University Prof. Chawewan Ratanaprasert, Ph.D Faculty of Science, Silpakorn University Assist. Prof. Chockpisit Thepsithar, Ph.D Faculty of Science, Silpakorn University Assoc. Prof. Mana Kanjanamaneesathian, M.Appl.Sc. Faculty of Animal Sciences and Agricultural Technology, Silpakorn University Assist. Prof. Pramote Khuwijitjaru, Ph.D Faculty of Engineering and Industrial Technology, Silpakorn University Agnes Rimando, Ph.D U.S. Department of Agriculture, Agricultural Research Service, USA Prof. Juan Boo Liang, Ph.D Institute of Bioscience, Universiti Putra Malaysia, Malaysia Prof. Shuji Adachi, Ph.D Graduate School of Agriculture, Kyoto University, Japan Vincenzo Esposito, Ph.D Department of Chemical Science and Technology, University of Rome, Italy

Managing Editor Pranee Vichansvakul

Periodicity Twice yearly

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Chapter in a book Langer, T. and Neupert, W. (1994) Chaperoning mitochondrial biogenesis. In The Biology of Heat Shock Proteins and Molecular Chaperones (Morimoto, R. I., Tissieres, A. and Georgopoulos, C., eds.), pp. 53-83. Cold Spring Harbor Laboratory Press, Plainview, New York. Article in a journal Hammerschlag, F. A., Bauchan, G., and Scorza, R. (1985) Regeneration of peach plants from callus derived from immature embryos. Journal of Natural Products 70(3): 248-251. Hammerschlag, F. A., Bauchan, G., and Scorza, R. Regeneration of peach plants from callus derived from immature embryos. Journal of Natural Products (in press). Article on the web Lee, K. (1999) Appraising adaptaive management. Conservation Ecology 3(2). [Online URL:www. consecolo.org/Journal/vol3/iss2/index.html] accessed on April 13, 2001. Proceedings MacKinnon, R. (2003) Modelling water uptake and soluble solids losses by puffed breakfast cereal immersed in water or milk. In Proceedings of the Seventh International Congress on Engineering and Food, Brighton, UK. Patent Yoshikawa, T. and Kawai, M. (2006) Security robot. U.S. Patent No. 2006079998. Tables and Figures Each Table and Figure must be on a separate page of the manuscript. Tables: Number the tables according to their sequence in the text. The text should include references to all tables. Vertical lines should not be used to separate columns. Leave some extra space instead. Figures: Figures should be of high quality (not less than 300 dpi JPEG or TIFF format), in black and white only, with the same size as the author would like them to appear in press. Choose the size of symbols and lettering so that the figures can be reduced to fit on a page or in a column. Submission of Manuscripts Authors should verify, on the submission form, that the submitted manuscript has not been published or is being considered for publication elsewhere. All information contained in an article is full responsibility of the authors, including the accuracy of the data and resulting conclusion. Authors are requested to send the manuscript on a CD labeled with the authors’ names and file names. The files should be prepared using MS Word only. Three copies of manuscript must be supplied. The editorial office will acknowledge receipt of the manuscript within 2 weeks of submission. The ‘accepted date’ that appears in the published article will be the date when the managing editor receives the fully revised version of the manuscript. The manuscript may be returned to authors for revision. Authors will be given 2 weeks after receipt of the reviewers’ comments to revise the article.

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Silpakorn University Science and Technology Journal

Contents

Volume 5 Number 2 (July - December) 2011

Special issue from OR-Net 2011 Conference Research Articles

Flexible Printed Circuit Process Improvement via Interchangeable Linear Constrained

Response Surface Optimisation Models..........................................................................................................................................................................................

Pichpimon Kanchanasuttisang and Pongchanun Luangpaiboon

Parameter Setting for Rod Push Production Process on Multiple Responses :

A Case Study in Motorcycle Parts Factory................................................................................................................................................................................

A Study of Proper Conditions in Face Milling Palmyra Palm Wood by

Computer Numerical Controlled Milling Machine......................................................................................................................................................

Chanpen Anurattananon, Suchavadee Pattanavatcharakul and Manit Soypetch

The Development of Mathematical Model for a University Course Timetabling Problem ...................

Surasit Rawangwong, Jaknarin Chatthong, Julaluk Rodjananugoon and Worapong Boonchouytan

Optimisation Using a Central Composite Rotatable Design for Lacquer Production Process.........

Prachuab Klomjit and Paisan Chantasoponno

Erawin Thavorn and Prapaisri Sudasna-na-Ayudthya

The Study of Suitable Factors for Welding on Canned Food by Design of Experiment Method.....

Ronnakit Wattanamano, Kanjana Thongsanit and Patipat Hongsuwan

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Foreword

In the special issue of Silpakorn University Science and Technology Journal (SUSTJ), six invited papers were selected from the 8th National Operations Research Conference 2011 (OR-Net 2011) held in Bangkok in September 2011. These papers were extended and had been reviewed according to SUSTJ process. This conference was very successful with over sixty papers submitted and presented during the period of September 8-9, 2011. Papers presented at the conference came from all parts of Thailand and encompassed many areas of operations research, logistics and manufacturing management, as well as applied statistics. The first paper is a co-authored article by Pichpimon Kanchanasuttisang and Pongchanun Luangpaiboon with the title “Flexible Printed Circuit Process Improvement via Interchangeable Linear Constrained Response Surface Optimisation Models”. The authors present a collection of experimental design and mathematical programming techniques for quality improvement in automotive electronic parts. Their paper improved the quality and performance of FPC by measurement via the relationship of the etched rate of acid solution and circuit width, one of the key failure and break down to LED of lighting vehicles. Article number two entitled “Parameter Setting for Rod Push Production Process on Multiple Responses: A Case Study in Motorcycle Parts Factory” by Erawin Thavorn and Prapaisri Sudasnana-Ayudthya presents the appropriate setting of parameters in the production process of Rod Push which have impacts on quality characteristics such as diameter and surface roughness. Central composite design was used to examine Rod Push produced by CNC with 5 controllable process factors including three factors from rough-cutting process (spindle speed, feed rate, and depth of cut) and two factors from finish-cutting process (spindle speed and feed rate). The third paper is authored by Prachuab Klomjit and Paisan Chantasoponno. Their paper is entitled “The Study of Suitable Factors for Welding on Canned Food by Design of Experiment Method”. In their co-authored article, the authors aim to use the proper conditions for high quality by experimental design method. The main factors included the electric current, a spring pressure, and a size of copper wire and overlap. The response variable included welding strength, welding flexibility, and welding thickness. The fourth article is by Surasit Rawangwong, Jaknarin Chatthong, Julaluk Rodjananugoon, and Worapong Boonchouytan and is entitled “A Study of Proper Conditions in Face Milling Palmyra Palm Wood by Computer Numerical Controlled Milling Machine”. The purpose of this article is to investigate the effect of main factors on the surface roughness (Ra) in Palmyra Palm wood face milling process by computer numerical controlled (CNC) milling machine and using shell end mill cutting tools 6 edges. It was found from the experiment that the factors affecting surface roughness were feed and speed, with tendency for reduction of roughness value at lower feed rate and greater cutting speed. Therefore, in the facing Palmyra Palm wood, it was possible to determine a face milling condition by means of the equation Ra=0.954+20.4 feed+0.00126 speed.

In the fifth article entitled “Optimisation Using a Central Composite Rotatable Design for Lacquer Production Process” , is co-authored by Chanpen Anurattananon, Suchavadee Pattanavatcharakul, and Manit Soypetch. The objective of this research is to study the controllable factors affecting the Lacquer quality and to find out the optimal conditions of the controllable factors by Central Composite Rotatable Design. The sixth article is co-authored by Kanjana Thongsanit, Ronnakit Wattanamano, and Patipat Hongsuwan, and is entitled “The Development of Mathematical Model for a University Course Timetabling Problem”. Their paper aims to arrange the course timetable properly according to the limited resources, i.e. number of classrooms, loading capacity of classroom, periods, and number of teachers. The main objectives are 1) the lowest expenses generating; and 2) the least extra-period spending. This special issue of SUSTJ provides responses and discussions that expand our knowledge in the field of operations research, logistics and manufacturing management, as well as applied statistics. Finally, we would like to thank cooperation from all committee and participants for successfully organising the OR-Net 2011 conference. Prachuab Klomjit, D.Eng., Asst.Prof. OR-Net 2011 Paper Review and Publication Chair Patcharaporn Neammanee, Ph.D., Assoc. Prof. OR-Net 2011 Secretary

Research Article Flexible Printed Circuit Process Improvement via Interchangeable Linear Constrained Response Surface Optimisation Models Pichpimon Kanchanasuttisang * and Pongchanun Luangpaiboon Industrial Statistics and Operational Research Unit (ISO-RU), Department of Industrial Engineering, Faculty of Engineering, Thammasat University, Pathumthani, Thailand * Corresponding author. E-mail address: pichpimon@hotmail.com Received October 21, 2011; Accepted December 25, 2011 Abstract This paper presents a collection of experimental design and mathematical programming techniques for quality improvement in automotive electronic parts. The quality performance of interest is measured via the relationship of the etched rate of acid solution and circuit width, one of the key failure and break down to LED of lighting vehicles. With lower levels from monitoring the product quality the manufacturer has spent a lot of cost and time for product verification procedures. This brings the production with higher levels of waste and lead time. To validate on processing and to sustain finished goods with the permanent prevention, the precisely etched condition should be optimised. The proper factorial experiments, multiple regression and mathematical programming approaches are applied to investigate the preferable levels of significant process variables in order to improve the quality of etched rate. The interchangeable constrained response surface optimisation models provide the new operating conditions. The experimental results in each part with less than twenty five lines showed that the first model decreases the bottom circuit width deviation from 0.0026 to 0.0024 and the latter model decreases the etching rate from 2.033 to 1.124. Keywords : Flexible Printed Circuit Process; Circuit Width; Etched Rate; Response Surface Methodology; Multiple Regression; Steepest Descent Introduction In the field of an electronic circuitry, the flexible printed circuits (FPC) have been developed for lighting automotive vehicles by assembling with the LED. The emission light and optical properties are mainly relied on the width of an FPC circuit line. An existing process to confirm the correct width of a lead line in an electronic field is a damaged part investigation. The process obviously

Silpakorn U Science & Tech J 5 (2): 9-18, 2011

causes the high quality cost in FPC manufacturers. Currently, the circuit width of the FPC is with lower process capability (Cpk) at -3.03 on the top circuit width and 0.85 on the bottom circuit width that comparing to the minimal target at 1.33 as shown in Figure 1. In this case, the deep details of an etching process should be investigated so that the optimal working condition would be determined as a standard process.

Silpakorn U Science & Tech J Vol.5(2), 2011

Flexible Printed Circuit Process

Methodology Multiple Regression Analysis An aim of the simple regression analysis is to adjust the values of slope and intercept to find the expected line that best predicts the dependent variable or response of Y from the independent variable or factor of X. More precisely, the goal of regression is to minimise the sum of the squares of the vertical distances of the design points from the expected line. The slope quantifies the steepness of the expected line. It equals the change in Y for each unit change in X. It is expressed in the units of the Y-axis divided by the units of the X-axis. If the slope is positive, Y increases as X increases. In contrast, if the slope is negative, Y decreases as X increases (Luangpaiboon and Peeraprawit, 2009). In statistics, the most commonly used mathematical formulas for expressing linear relationships among more than two variables are equations of the following form (Luangpaiboon et al., 2010),

Process Capability of Top circuit width LSL P rocess LS L T arget USL S ample M ean S ample N S tD ev (Within) S tD ev (O v erall)

Target

USL

D ata 0.09 0.1 0.11 0.0740333 60 0.00175612 0.00173661

W ithin O v erall P otential (Within) C apability Cp 1.90 C PL -3.03 C PU 6.83 C pk -3.03 O v erall C apability Pp PPL PPU P pk C pm

1.92 -3.06 6.90 -3.06 0.13

0.072 0.078 0.084 0.090 0.096 0.102 0.108 O bserv ed P erformance P P M < LS L 1000000.00 PPM > USL 0.00 P P M T otal 1000000.00

E xp. Within P erformance P P M < LS L 1000000.00 PPM > USL 0.00 P P M T otal 1000000.00

E xp. PPM PPM PPM

O v erall P erformance < LS L 1000000.00 > USL 0.00 T otal 1000000.00

Process Capability of Bottom circuit width LSL P rocess LS L T arget USL S ample M ean S ample N S tD ev (Within) S tD ev (O v erall)

Target

USL W ithin O v erall

D ata 0.09 0.1 0.11 0.09655 60 0.00257149 0.00256062

P otential (Within) C apability Cp 1.30 C PL 0.85 C PU 1.74 C pk 0.85 O v erall C apability Pp PPL PPU P pk C pm

1.30 0.85 1.75 0.85 0.77

0.0900 0.0936 0.0972 0.1008 0.1044 0.1080 O bserv ed P erformance P P M < LS L 0.00 P P M > U S L 0.00 P P M T otal 0.00

E xp. Within P erformance P P M < LS L 5430.21 PPM > USL 0.08 P P M T otal 5430.30

E xp. O v erall P erformance P P M < LS L 5264.21 PPM > USL 0.07 P P M T otal 5264.28

Figure 1 Current performance on top and bottom circuit widths

Process Review Characteristics of the FPC circuit width based on a crossed section image view as shown in Figure 2 have composed with the top (T) and bottom (B) circuit lines. These are the varieties on the horizontal etching. The principles of the upward acid spray and the use of additives to reduce the etching ability are necessary for successful implementations (Coombs, 1988).

(1) In the multivariate case, when there are more than one independent variable, the regression line cannot be visualised in the two dimensional space, but can be computed just as easily. Multiple regression models for k independent variables are usually fitted by using the method of least squares. The least-squares method, published by Legendre and Gauss, minimises the variance of the unbiased estimators of the coefficients. Multiple regression analysis played an important role in the development of regression analysis, with a greater emphasis on issues of design and inference. An aim of multiple regression analysis is again to formulate a model of influential variables (or vector of influential variables) of xâ&#x20AC;&#x2122;s. In the multiple linear regression line, the following model is used,

Top circuit

Bottom Circuit

Figure 2 Crossed section view of the circuit width

. 10

(2)

P. Kanchanasuttisang and P. Luangpaiboon

Silpakorn U Science & Tech J Vol.5(2), 2011

x2, …, xk. Estimation of such surfaces, and hence identification of near optimal setting for process variables is an important practical issue with interesting theoretical aspects.

An unobserved random error of ε is with the mean of zero on scalar influential variables of x’s. In this model, for each unit increase in the value of x, the conditional expectation of y increases by βi units of xi. Conveniently, these models are all linear from the point of view of estimation, since the regression model is linear in terms of the unknown parameters of β0, β1, ..., βk. Therefore, for least squares analysis, the computational and inferential problems of multiple regressions can be completely addressed using the multiple regression techniques. This is done by treating x1, x2, ... , xk as being distinct independent variables in a multiple regression model. More details are referred to in many statistical textbooks. Response Surface Methodology (RSM) The objective of the RSM is to describe how the response of a process varies with change in k process variable as shown in Figure 3. The process variable determined will depend on the specific problem of the applications (Luangpaiboon, 2010). The RSM is the combination of mathematical and statistical aspects to improve the response. One of the most widely used in the area of Response Surface Methodology (RSM) is the steepest descent (descent) method that an aim is to minimise (minimise) the system of interest. However, various iterative procedures in the field of RSM are proposed to find the appropriate choices of process variables such as the modified simplex (MSM), super modified simplex (SMS), weighted centroid modified simplex (WCMSM), modified complex (MCM) and linear constrained response surface optimisation (LCRSOM) methods (Luangpaiboon, 2011). On the theory and practice of RSM, it is assumed that the mean response (h) is related to values of the process variables (x1, x2, …, xk) by an fitted unknown mathematical function f. The functional relationship between the mean response and k process variables can be written as h = f(x), if x denotes a column vector with elements x1,

Figure 3 Response surface and its contour plot The procedure begins with any types of designed experiments around the prevailing operating condition. A sequence of first order model and line searches are conventionally justified on the basis that such a plane would be fitted well as a local approximation to the true response. The estimated coefficients for the first order model are determined using the principle of least square. An algorithm for finding the nearest local minimum of a function which presupposes that the gradient of the function can be generated. The method of steepest descent, also called the gradient descent and, as many times as method, starts at a point to by minimising needed, moves from along the line extending from Pi in the direction or the local downhill gradient. of When applied to a 1-dimensional function of , the method takes the form of iterating from a starting point x0 for some small e > 0 until a fixed point is reached. In contrast to this other algorithmic processes search the system approximation via the systematic searches or the measurement of the response in the design points. When curvature is detected, another factorial experiment is conducted. This is used either to estimate the position of the optimum or 11

Silpakorn U Science & Tech J Vol.5(2), 2011

Flexible Printed Circuit Process

Experimental Results and Analyses The responses of the system are measured as the top and bottom circuit widths. The lower and upper specifications of both circuit widths are shown in Table 1. There are three steps of experimental analyses which consist of a base line analysis, an etched rate analysis and a circuit width analysis.

the systematic searches to specify a new direction of steepest descent or the new design point with the better yields (Luangpaiboon, 2010). In this study, the interchangeable linear constrained response surface optimisation model (IC-LCRSOM) is deployed to set up a relationship of the linear constrained responses and influential process variables. Originally, linear programs are problems that can be expressed in canonical form:

Minimise CTX Subject to And X ≥ 0

Table 1 Responses and their feasible specifications AX ≥ B

Response

where X represents the vector of process variables (to be determined), C and B are vectors of (known) coefficients and A is a (known) matrix of coefficients of problem constraints. The expression to be maximised or minimised is called the objective function (CTX in this case). The constraints Ax ≥ B specify a convex polytope over which the objective function is to be optimised. In this problem, some of the expected regression equations of process responses are interchangeable. The problem is then called an interchangeable (IC) problem. Sequential procedures of IC-LCRSOM are able to switch upon the circumstances of interest. A factorial experiment design is use to investigate the optimal responses of process of interest. When the model is formulated, analysis of variance (ANOVA) is applied to find statistically significant process variables and determine the most effective levels. Regression analysis is used to fit a relationship equation of the response and its process responses. Interchangeable functions of process variables and various responses are considered as the objective and also the constraint of the LCRSOM. Those possible models are the representatives of the system. The optimal levels in each process variable from a mathematical programming model are determined via a generalised reduced gradient algorithm.

Specification Lower

Upper

Top Circuit Width

0.09

0.110

Bottom Circuit Width

0.09

0.110

Base Line Analysis In this first step, the experiments aim to analyse the current data of the circuit width (Rcw) by using a completely randomised design or one-way analysis of variance (ANOVA). The experimental designs were performed to determine the statistically significant process conditions or the capability of measurement system which consist of the pattern and sheet positions. The process positions and feasible ranges are provided in Table 2. Table 2 Process positions and their feasible ranges Position

Level

Pattern

MT, Cen1, Cen2, OP

Sheet

S1 – S15

In this study, at 95% confidence interval sources of variance and P-value were shown in Table 3. On the numerical results, the significant factor on both circuit widths is the pattern position. The pattern position is then applied as the design factor for the next two steps throughout.

P. Kanchanasuttisang and P. Luangpaiboon

Silpakorn U Science & Tech J Vol.5(2), 2011

Table 4 Process variables and their feasible and tested levels for etched rate analysis

Table 3 ANOVA for base line analysis Source or P-Value Position Top Circuit Width Bottom Circuit Width

Process Variable

Feasible Level

Tested Levels Low

High

Pattern

0.00

30 â&#x20AC;&#x201C; 60

Sheet

0.881

0.954

2.0 â&#x20AC;&#x201C; 4.0

2.9

3.1

Attribute

-1

Etched Rate Analysis According to the results from the base line analysis the circuit width is unbalanced so the response in the second step is the etched rate (RER). Currently the etched rate is with the deviation of 0.033 and the three sigma level of 6.1 as shown in Figure 4. A two level experimental design with additional two centre design points was performed to determine the statistically significant process variables of A, B and C (an attribute factor). The levels of process variables (A, B, C) on the centre design points are (45, 3.0, -1) and (45, 3.0, 1). Low and high levels including centre points are selected cover values of feasible ranges in a production line (Table 4). The objective at this step is to analyse main and interaction effects via 20 experimental data. The analysis of variance revealed that the main effects of A and B are significant, but there was no statistically significant on the interaction effect at 95% confidence interval.

Table 5 ANOVA with all main effects and interactions P-Value for the Etched Rate 0.001 0.029 0.371 0.791 0.675 0.169 0.201 0.162

Sources A B C A*B A*C B*C A*B*C Centre Point

In order to determine the appropriate setting of the process variables, the main effects were plotted in Figure 5. The appropriate levels of process variables A and B are set at 60 and 3.1, respectively. After an implementation of the new operating condition, the response of the etched rate is improved with the deviation of 1.365 and the three sigma level of 4.1 (Figure 6).

Histogram of Etched rate (Current) Normal Mean StDev N

Main Effects Plot for Range

46.57 2.033 198

Data Means

15.6

14.4 13.2

Mean

Frequency

16.8

12.0 -1

0 C

16.8

-1

15.6 14.4

13.2

Figure 4 Current measure

48 Etched rate

etched

12.0

rate

Figure 5 Main effect plots of the etched rate analysis

performance

Silpakorn U Science & Tech J Vol.5(2), 2011

Flexible Printed Circuit Process

etched rate is improved with the deviation of 1.124 and the three sigma level of 3.4 (Figure 7).

Histogram of Etched rate (Main effect) Normal Mean StDev N

46.84 1.365 216

Histogram of Etched rate (Multiple regression) Normal 30

39.50 1.124 216

20 15 10

43.5

45.0

46.5

48.0 49.5 Etched rate

51.0

52.5 5

Figure 6 Etched rate performance measure at new process condition from the factorial design

Coef SE Coef

(3)

P-Value

Constant

63.14

17.31

3.65

0.002

-0.1708 0.0382

-4.47

0.000

-13.875 5.738

-2.42

0.027

Source

Regression

135.86 67.932 12.90 0.000

Residual

89.557 5.268

Total

225.42

40 41 Etched rate

Setting

Deviation

Current

2.033

6.1

Factorial Design

1.365

4.1

Steepest Descent

1.124

3.4

Circuit Width Analysis From the previous section, the pattern position brings the lower etched rate deviation when compared to the current operating condition. From the etched rate analysis, the process variable of A is then fixed at the suitable level of 60 and the remaining variable of B returns to be a process variable when focused on the response of the circuit width. The low and high levels of the process variables of B and D including centre points are selected cover values of feasible ranges in a production line to investigate the response of the circuit width (Rrw) (Table 8).

Table 6 Regression model including its significant coefficients and ANOVA table Predictor

Table 7 A comparison of the etched rate among various settings

Expected Response of RER = 63.1-0.171A-13.9B.

Figure 7 Etched rate performance measure at new process condition from the steepest descent

The method of multiple regression analysis at 95% confidence interval is then applied for statistically significant process variables to determine the most preferable fitted equation of associated process variables of A and B to the response of the etched rate (Table 6). The relationship of the process variables and the response (RER) in terms of the path of steepest descent is

Mean StDev N

Frequency

P-Value

Table 8 Process variables and their feasible and tested levels for circuit width analysis

The preferable levels of process variables A and B from the path of steepest descent are 60 and 3.8, respectively (Table 5). When the new levels of process variables have been applied, the new

Tested Level

Process Variable

Feasible Level

Low

Center

High

2.0 â&#x20AC;&#x201C; 4.0

2.9

3.1

3.3

3.0 â&#x20AC;&#x201C; 4.0

3.4

3.5

3.6

P. Kanchanasuttisang and P. Luangpaiboon

Silpakorn U Science & Tech J Vol.5(2), 2011

The method of steepest descent is then applied for statistically significant process variables to determine the most preferable fitted equation of associated process variables to the response of Rrw at both top and bottom circuits. The actual step size is determined by the experimenter with a consideration of other practicals or the process knowledge. These experiments will be terminated when there is an increase in responses from the last step. Eventually the experiments arrived to the vicinity of the optimum. The mathematical programming model is then formulated to minimise the desired response of the circuit width difference from the target. From the current operating condition, the relationship of the process variables and the responses are categorised by the top (Figure 8) and bottom (Figure 9) circuit widths. The new levels of process variables via the model are then solved via a generalised reduced gradient algorithm. The former shows that the preferable levels of process variables B and D are at 4 and 3.4, respectively. However, their preferred levels are 3.3 and 3.5 for process variables B and D, respectively. Both new operating conditions from the IC-LCRSOM are different, but a higher level of the circuit width affects the short circuit defect more seriously for FPC processes. So the most proper operating condition could follow the operating condition from the bottom circuit analysis. The preferable levels of all process variables from the IC-LCRSOM are also given in Table 11. The performance measures on top and bottom circuit widths from the new operating condition seem to be better (Figure 10 and Table 12).

The method of multiple regression analysis at 95% confidence interval is then applied for statistically significant process variables to determine the most preferable fitted equation of associated process variables of B and D to the response of the top and bottom circuit widths (Tables 9 and 10). The relationships of the process variables and the responses (RCW) in terms of the paths of steepest descent are then determined. Table 9 Regression model including its significant coefficients and ANOVA table for top circuit width. Predictor

Coef

SE Coef

P-Value

Constant

0.05392

0.007415

7.27

0.018

-0.0162

0.000968

-16.78

0.004

0.00750

0.001936

3.87

0.061

Source

P-Value

Regression

0.000045 22x10-6 148.33 0.007

Residual

0.0000003 15x10-7

Total

0.000045

Table 10 Regression model including its significant coefficients and ANOVA table for bottom circuit width Predictor

Coef

SE Coef

P-Value

Constant

0.1279

0.04287

2.98

0.096

-0.0342

0.005598

-6.12

0.026

-0.0035

0.01120

-0.31

0.784

Source

Regression

0.000188 94x10-6 18.77

Residual

0.000010 5x10-6

Total

0.000198

P-Value 0.05

Silpakorn U Science & Tech J Vol.5(2), 2011

Flexible Printed Circuit Process

Contour Plot of Top circuit width vs B, D 3.7 3.6 3.5 3.4

Surface Plot of Top circuit width vs B, D Top < 0.0200 – 0.0225 – 0.0250 – 0.0275 – 0.0300 – >

0.0200 0.0225 0.0250 0.0275 0.0300 0.0325 0.0325 0.035

3.3

0.030

3.2

Top

3.4

0.025

3.1

3.5

0.020

3.0 3.0

2.9 3.40

3.45

3.50 D

3.55

3.2

3.4

3.6

3.60

(a)

3.6

(b)

Figure 8 Contour (a) and surface (b) plots of top circuit width

Surface Plot of Bottom circuit width vs B, D

Contour Plot of Bottom circuit width vs B, D 3.7

Bottom < 0.003 0.003 – 0.006 0.006 – 0.009 0.009 – 0.012 0.012 – 0.015 > 0.015

3.6 3.5

3.4 3.3

0.015

3.2

Bottom

0.010

3.4

0.005

3.1

3.5

0.000

3.0

2.9 3.40

3.2

3.6

3.4

3.6

3.45

3.50 D

3.55

3.60

(a)

(b)

Figure 9 Contour (a) and surface (b) plots of bottom circuit width

Table 11 Process variables and their levels on two scenarios Process Variable

Process Capability of Top width LSL

New

3.1

3.3

3.5

Process Capability of Bottom width

USL

LSL

Within Overall

Process Data LSL 0.09 Target 0.1 USL 0.11 Sample Mean 0.0752143 Sample N 28 StDev(Within) 0.00137904 StDev(O verall) 0.00119744

Scenario Current

Target

Potential (Within) C apability C p 2.42 C PL -3.57 C PU 8.41 C pk -3.57 O verall C apability Pp PPL PPU Ppk C pm

Exp. Within Performance PPM < LSL 1000000.00 PPM > USL 0.00 PPM Total 1000000.00

Exp. O verall Performance PPM < LSL 1000000.00 PPM > USL 0.00 PPM Total 1000000.00

(a)

USL Within Overall Potential (Within) Capability Cp 1.25 CPL 1.19 CPU 1.32 Cpk 1.19 O verall Capability

2.78 -4.12 9.68 -4.12 0.13

Pp PPL PPU Ppk Cpm

1.37 1.29 1.44 1.29 1.33

0.090 0.093 0.096 0.099 0.102 0.105 0.108

0.075 0.080 0.085 0.090 0.095 0.100 0.105 0.110 O bserved Performance PPM < LSL 1000000.00 PPM > USL 0.00 PPM Total 1000000.00

Target

Process Data LSL 0.09 Target 0.1 USL 0.11 Sample Mean 0.0994643 Sample N 28 StDev(Within) 0.00265957 StDev(O verall) 0.00244165

O bserved Performance PPM < LSL 0.00 PPM > USL 0.00 PPM Total 0.00

Exp. Within Performance PPM < LSL 186.44 PPM > USL 37.25 PPM Total 223.69

Exp. O verall Performance PPM < LSL 53.05 PPM > USL 7.98 PPM Total 61.03

(b)

Figure 10 Performance of top (a) and bottom (b) circuit width from new scenario

P. Kanchanasuttisang and P. Luangpaiboon

Silpakorn U Science & Tech J Vol.5(2), 2011

Table 12 Comparison on circuit width Item

Top Circuit Width

in the Box-Whisker plots (Figure 11 and 12). This research was scoped only on one the product and product layout. Consequently conclusions may not be globally optimal. However, the sequential procedures can be applied to the FPC manufactures with many circuit width designs and limited machine capabilities.

Bottom Circuit Width

Before

After

Before

After

Mean

0.074

0.075

0.097

0.099

0.0017

0.0012

0.0026

0.0024

0.005

0.004

0.008

0.007

Cpk

-3.03

-3.57

0.85

1.19

Boxplot of Top width (before), Top width (After) 0.077 0.076

Conclusions and Recommendations In this paper the proper factorial experiments, multiple regression and mathematical programming approaches are applied to investigate the preferable levels of significant process variables in order to improve the quality of etched rate. Firstly, the 2k factorial design was applied to preliminarily study the effects of those three factors. The responses which consist of circuit widths (RCW) and etching rate (RER) from the preset experimental designs are measured by Hand-Held Instruments of the Eddy current method. The multiple regression models of those responses were then developed from only significant factors affecting each response. Finally, the regression model of RCW in forms of the path of steepest descent was placed as the objective function of the linear constrained response surface optimisation model to minimise the circuit width subject to the remaining response and the limitation from feasible ranges of two main factors. However, in this study the RCW could be interchangeable to be only the model constraint and the RER is formulated as the response instead. After an implementation, the experimental results on top and bottom circuit widths were analysed via t-tests (Table 13). The new condition statistically affects both top and bottom widths at 95% confidence interval. There is a decrease in the deviation from a customer requirement as appeared

Data

0.075 0.074 0.073 0.072 0.071 Pattern position

C1 C2 OP Top width (before)

C1 C2 OP Top width (After)

Figure 11 Box-whisker plot of top circuit width

Boxplot of Bottom width (before), Bottom width (After) 0.104 0.102

Data

0.100 0.098 0.096 0.094 0.092 0.090 Pattern position

MT C1 C2 OP Bottom width (before)

C1 C2 OP Bottom width (After)

Figure 12 Box-whisker plot of bottom circuit width Table 13 Comparison via two sample T-tests Circuit Width

T-Stat

P-Value

Top

-2.76

0.008

Bottom

-4.03

0.000

Acknowledgment The authors wish to thank the Faculty of Engineering, Thammasat University, Thailand for the financial support.

Silpakorn U Science & Tech J Vol.5(2), 2011

Flexible Printed Circuit Process

References Clyde, C. F. (1988) Printed Circuits Handbook. Third Edition. Luangpaiboon, P. and Peeraprawit, N. (2009) Nonlinear Constrained Steepest Ascent Method for a Laser Welding Process. The Journal of Industrial Technology 5(1): 18-25. Luangpaiboon, P., Suwankham, Y., and Homrossukon S. (2010) Constrained Response Surface Optimisation for Precisely Atomising Spraying Process. IAENG

Transactions on Engineering Technologies 5: 286-300. DOI: 10.1063/1.3510555 Luangpaiboon, P. (2010) Improving an Electrostatic Powder Coating Process via Signal to Noise Response Surface. American Journal of Applied Sciences 7(11): 1521-1527. DOI: 10.3844/ajassp.2010.1521.1527. Luangpaiboon, P. (2011) Constrained Response Surface Optimisation for a Laser Beam Welding Process. Journal of Mathematics and Statistics 7(1): 5-11. DOI: 10.3844/ jmssp.2011.5.11.

Research Article Parameter Setting for Rod Push Production Process on Multiple Responses : A Case Study in Motorcycle Parts Factory Erawin Thavorn * and Prapaisri Sudasna-na-Ayudthya Department of Industrial Engineering, Faculty of Engineering Kasetsart University, Bangkok, Thailand * Corresponding author. E-mail address: nana_erawin@hotmail.com Received October 21, 2011; Accepted December 25, 2011 Abstract The aim of this research is to study appropriate setting of parameters in the production process of Rod Push which affect quality characteristics such as diameter and surface roughness. Cycle time is also considered. The problem was done at a study plant and it was found that the actual process capability index (Cpk) of two quality characteristics was less than the manufacturer’s standard of 1.33. Central composite design was used to examine Rod Push produced by CNC with 5 controllable process factors including three factors from rough-cutting process (spindle speed, feed rate, and depth of cut) and two factors from finish-cutting process (spindle speed and feed rate). The nuisance factor of CNC was cutting tool wear. After collecting all data, the appropriate setting was investigated. The new results indicated that the new condition yielded the better process performance index and shorter cycle time. Keywords: DOE; Central Composite Design; Rod Push Process; CNC Turning Machine Introduction Rod Push is the pin in the clutch-gear of the motorcycle (as shown in Figure 1) fabricated by Computer Numerical Control (CNC) turning machine. CNC turning process are many factors; i.e. insert, spindle speed, feed rate, and depth of cut which affect quality characteristics (diameter and surface roughness) and cycle time. This research aims at setting appropriate value of the factors’ parameters. Design of experiment was applied to improve quality characteristics of Rod Push directly and secondary cycle time.

Silpakorn U Science & Tech J 5 (2): 19-25, 2011

Figure 1 Rod push

Silpakorn U Science & Tech J Vol.5(2), 2011

Parameter Setting for Rod Push Production Process

Methodology Response Surface Methodology Response surface methodology (RSM) is a collection of mathematical and statistical techniques that are useful for the modeling and analysis of problems in which a response of interest is influenced by several variables and the objective is to optimize this response (Montgomery, 2008). This research applied RSM to find optimal condition of Rod Push production process. Central composite design (CCD) was used to approximate second order response surface model to analyse the optimal condition. Five factors were investigated including spindle speed of rough-cutting (A), feed rate of rough-cutting (B), depth of cut of roughcutting (C), spindle speed of finish-cutting (D), and feed rate of finish-cutting (E), and the nuisance factor of CNC was cutting tools wear. The research was studied whether five factors affected diameter, surface roughness, and cycle time (95% confident intervals). According to limitation of the amount of Rod Push, central composite design wherein the factorial portion of a 25-1 fractional factorial design and blocking was used to reduce variance generated by nuisance factors. The experimental plan in this study study was to divide the control factors into three levels as low (-1), medium (0), and high (+1) and increase outside range of the control factors up to Âą2. This makes 33 samples to be used as summarized in Table 1.

After analysis of variance (ANOVA), it was necessary to verify the assumptions about the residual which included (i) a normal distribution, (ii) the average equal to zero, (iii) variance stability, and (iv) independence. Assumptions in regression were tested by graphical difference. (Sudasna-naAyudthya and Luangpaiboon, 2008) Normal probability plot and histogram were used to test (i) that if the graph was a straight line and histogram was symmetric, then the normality assumption was satisfied Residuals versus fits plot was used to test (ii), (iii) if the residuals randomly balance around the axis and scatter randomly on the display, suggesting that the average of residual equal to zero and variance of the original observations were stability Residuals versus order plot was used to test (iv) if the residuals were random patterns, then residual are independence. Result and Discussion The commercial software, Minitab was used to determine second order response surface model and then the model was used to test the assumptions in regression model and ANOVA analysis. This step employed coefficient of determination (R2adj.) and lack of fit to test the fit of regression model.

Table 1 Factors and their levels for central composite design Factor

Level of factors -2

-1

2,250

3,000

3,750

4,500

5,250

Feed rate of rough-cutting; B (mm./minute)

0.1

0.4

0.7

1.3

Depth of cut of rough-cutting; C (mm.)

0.1

0.4

0.7

1.3

Spindle speed of finish-cutting; D (rpm.)

2,250

3,000

3,750

4,500

5,250

Feed rate of finish-cutting; E (mm./minute)

0.02

0.08

0.14

0.2

0.26

Spindle speed of rough-cutting; A (rpm.)

E. Thavorn and P. Sudasna-na-Ayudthya

Silpakorn U Science & Tech J Vol.5(2), 2011

Residual Plots for Diameter

Residual Plots for Cycle Time

Normal Probability Plot

Versus Fits

Normal Probability Plot

10 -0.01

0.00 Residual

0.01

-0.01 -0.02

0.02

0.00

4.850

4.875 Fitted Value

6 2 8 4 0 4 .01 0.01 0.00 0. 00 0.00 0.00 -0 Residual

8 00 0.

0.00 -0.01 -0.02

2 01 0.

10 15 20 25 Observation Order

Residual

Percent

90 50 10

1 0 -1 -2

-2

-1

0 Residual

Histogram

Versus Order 2

10.0

Residual

7.5 5.0

60 Fitted Value

0 -10

-20 -20

-10

0 Residual

10 15 20 25 Observation Order

1 0

-2 -2

-1

0 Residual

10 15 20 25 Observation Order

Figure 3 Assumptions in regression model testing (Surface roughness) Table 2 ANOVA Table for diameter Source

df.

P-Value

Block

0.000003

0.03

0.876

Regression

0.004521

0.000226

1.68

0.189

Linear

0.002839

0.000568

4.22

0.022

Square

0.000331

0.000066

0.49

0.776

Interaction

0.001480

0.000135

1.00

0.493

Residual Error

0.001069

0.000135

Lack of Fit

0.000411

0.000178

2.17

0.207

0.000411

0.000082

0.006004

Pure Error Total R2 = 75.36%

Versus Order 20

-1

2.5 0.0

6 Fitted Value

The assumptions tested by graphical difference in regression showed that all of three regression models were correct. The models had normal distribution with average equal to zero, variance stability, and independence (as shown in Figure 2-4).

Versus Fits

Figure 4 Assumptions in regression model testing (Cycle Time)

Residual Plots for Roughness Normal Probability Plot

0 Residual

Figure 2 Assumptions in regression model testing (Diameter)

-10

Histogram

Frequency

Residual

-20 -20

Versus Order 0.01

Frequency

4.900

-10

Histogram 8

Residual

1 -0.02

Residual

Percent

Residual

Percent

Frequency

Versus Fits

99 0.01

R2(adj.) = 28.31%

Silpakorn U Science & Tech J Vol.5(2), 2011

Parameter Setting for Rod Push Production Process

Table 3 ANOVA Table for surface roughness Source

df.

P-Value

Block

11.070

11.0700

7.99

0.016

Regression

56.416

4.3208

3.12

0.028

Linear

70.762

14.1524

10.21

0.001

Square

12.480

2.4960

1.80

0.193

Interaction

3.174

0.3174

0.23

0.986

Residual Error

15.241

1.3855

Lack of Fit

13.118

2.1863

5.15

0.046

2.123

0.4245

112.727

Pure Error Total

R2 = 86.48% R2(adj.) = 60.07%

Table 4 ANOVA Table for cycle time Source

df.

P-Value

Block

276.14

276.136

1.47

0.251

Regression

6629.42

331.471

1.76

0.167

Linear

4133.88

826.775

4.40

0.019

Square

2138.92

427.78

2.27

0.119

Interaction

356.63

35.63

0.19

0.993

Residual Error

2068.98

188.090

Lack of Fit

2068.98

344.831

0.00

0.000

8974.55

Pure Error Total

R2 = 76.95% R2(adj.) = 32.93%

Diameter = 4.87899 + 0.00092A - 0.00175B + 0.00067C - 0.00233D + 0.01042E -0.00011A2 - 0.00086B2 - 0.00211C2 - 0.00024D2 + 0.00226E2 - 0.00438AB + 0.00400AC - 0.00162AD + 0.00350AE - 0.00325BC - 0.00162BD + 0.00100BE + 0.00350CD + 0.00062CE - 0.00275DE (1)

The results from ANOVA Table (Table 2-4) showed that either linear or square term in the regression models were significant which implied that all three models exist. All R2(adj.) were high which demonstrated the appropriation of the three models showed in equation (1), (2), and (3). However, for RSM the significances of the coefficients will not be considered in order to get the complete second order response surface models as follows:

Surface Roughness = 3.8130 – 0.0865A – 0.2235B – 0.0823C + 0.1442D + 1.6922E + 0.0022A2 – 0.3239B2 – 0.1625C2 + 0.2931D2 +

E. Thavorn and P. Sudasna-na-Ayudthya

Silpakorn U Science & Tech J Vol.5(2), 2011

0.4185E2 + 0.1802AB – 0.1494AC + 0.0125AD – 0.1481AE + 0.0720BC – 0.0218BD + 0.1195BE + 0.3110CD – 0.0391CE – 0.0570DE (2) Cycle Time = 33.28 – 1.96A – 6.12B – 5.87C – 1.46D – 9.71E – 1.24A2 + 3.64B2 + 3.39C2 – 0.99D2 + 6.76E2 – 0.31AB + 0.31AC – 0.94AD – 0.56AE + 3.69BC + 1.19BD + 2.06BE – 0.19CD – 1.06CE + 0.69DE (3)

B 2.0 [0.0606] -2.0

C 2.0 [1.8383] -2.0

D 2.0 [-0.4950] -2.0

x D = ( D * 750 ) + 3,750

(7)

x E = ( E * 0.06 ) + 0.14

(8)

The actual value used in the production were

mm, x D = 3,379 rpm, and x E = 0.11 mm/minute. Confirmation Test The validation was to use the analysed parameters in actual production. The sample was randomly collected up to 20 replicates and the three response variable was recorded. Before and after improvement were investigated as summarized in Table 5. After implement the new setting, the average of the diameter and surface roughness were closer to the target and standard deviation is reduced. The Cpk of diameter and the surface roughness was equal to 4.06 and 2.37, respectively (as shown in Figure 6 and 7), while the cycle time is decreased to 37 seconds (17.78% reduction).

The Appropriate Setting This Research used equation (1) (2) and (3) to determine the appropriate parameters with response optimiser function in Minitab program, the appropriate parameters were A, B, C, D and E equal to 1.11, 0.60, 1.84, -0.49, and -0.46 respectively. The diameter was 4.8725 mm, the surface roughness of 2.44 micrometers (µm) and cycle time of 42.36 seconds, the composite desirability of 0.97 (as shown in Figure 5). A 2.0 [1.1111] -2.0

(6)

x A = 4,583 rpm, x B = 0.72 mm/minute, xC = 1.25

-2≤ A, B, C, D, E≤2

New High D Cur 0.96932 Low

xC = ( C * 0.3) + 0.7

E 2.0 [-0.4654] -2.0

Table 5 Comparative analysis of the before and after improvement

Composite Desirability 0.96932 Diameter Targ: 4.8725 y = 4.8725 d = 0.99868

Responses Variable

Before

After

Target (mm)

4.8725

Average (mm)

4.8821

4.8782

Standard Deviation (mm)

0.0038

0.0021

0.64

4.06

Target (µm)

2.50

Average (µm)

3.59

2.71

Standard Deviation (µm)

0.59

0.58

Cpk

0.80

2.37

Diameter

Roughnes Minimum y = 2.4416 d = 1.0000 Cycle Ti Minimum y = 42.3665 d = 0.52670

Cpk

Figure 5 Optimisation plot

Surface Roughness

The appropriate parameters from Minitab program converted to the actual values which calculated as showed in equation (4) to (8).

x A = ( A * 750 ) + 3,750

(4)

x B = ( B * 0.3) + 0.7

(5)

Cycle Time (seconds)

Silpakorn U Science & Tech J Vol.5(2), 2011

Parameter Setting for Rod Push Production Process

Process Capability of Diameter (using 95.0% confidence)

LSL

USL Within Ov erall

P rocess D ata LS L 4.855 Target * USL 4.89 S ample M ean 4.8775 S ample N 20 S tD ev (Within) 0.0010265 S tD ev (O v erall) 0.00232832

P otential (Within) C apability Cp 5.68 Low er C L 3.89 U pper C L 7.47 C PL 7.31 C PU 4.06 C pk 4.06 Low er C L 2.76 U pper C L 5.36 O v erall C apability

4.855 4.860 4.865 4.870 4.875 4.880 4.885 4.890 O bserv ed P erformance P P M < LS L 0.00 P P M > U S L 0.00 P P M Total 0.00

E xp. Within P erformance P P M < LS L 0.00 P P M > U S L 0.00 P P M Total 0.00

E xp. O v erall P erformance P P M < LS L 0.00 P P M > U S L 0.04 P P M Total 0.04

Pp Low er C L U pper C L PPL PPU P pk Low er C L U pper C L C pm Low er C L

2.51 1.72 3.29 3.22 1.79 1.79 1.20 2.38 * *

Figure 6 Process capability of diameter

Process Capability of Roughness (using 95.0% confidence)

USL Within Ov erall

P rocess Data LS L * Target * USL 5 S ample M ean 2.7308 S ample N 20 S tDev (Within) 0.319802 S tDev (O v erall) 0.534229

P otential (Within) C apability Cp * Low er C L * U pper C L * C PL * C PU 2.37 C pk 2.37 Low er C L 1.60 U pper C L 3.13 O v erall C apability

1.8 O bserv ed P erformance P P M < LS L * P P M > U S L 0.00 P P M Total 0.00

2.4

E xp. Within P erformance P P M < LS L * P P M > U S L 0.00 P P M Total 0.00

3.0

3.6

4.2

E xp. O v erall P erformance P P M < LS L * P P M > U S L 10.80 P P M Total 10.80

Figure 7 Process capability of surface roughness

4.8

Pp Low er C L U pper C L PPL PPU P pk Low er C L U pper C L C pm Low er C L

* * * * 1.42 1.42 0.94 1.89 * *

E. Thavorn and P. Sudasna-na-Ayudthya

Silpakorn U Science & Tech J Vol.5(2), 2011

Conclusions The aim of this research is to find appropriate parameters for Rod Push production process, which affects the diameter, surface roughness and cycle time. Central composite design was used in this research. The appropriate parameters from response optimiser were spindle speed of rough-cutting (A) = 1.11, feed rate of rough-cutting (B) = 0.60, depth of cut of rough-cutting (C) = 1.84, spindle speed of finish-cutting (D) = -0.49, and feed rate of finishcutting (E) = -0.46. The diameter was 4.8725 mm, the surface roughness of 2.44 micrometers and cycle time of 42.36 seconds, the composite desirability of

Acknowledgments The authors are very thankful to Diatec Precision Co., Ltd and Quality Report Co., Ltd, for facilities and equipment and for Cofocal Laser scanning Microscope to measure surface roughness for this research. References Montgomery, D. C. (2009) Statistical Quality Control: A Modern Introduction, 6th ed., John Wiley & Sons, New York. Montgomery, D. C. (2009) Design and Analysis of Experiment, 7th ed., John Wiley & Sons, New York. Myers, R. H., Montgomery D. C., and AndersonCook C. M. (2008) Response Surface Methodology: Product Optimization Using Designed Experiment. 3rd ed., John Wiley & Sons, New York. Sudasna-na-Ayudthya, P. and Luangpaiboon P. (2008) Design and Analysis of Experiments, 1st ed., TOP Publishing, Bangkok.

0.97. After converted to the actual values were x A , x B , xC , x D , and x E equal to 4,583 rpm, 0.72 mm/

minute, 1.25 mm, 3,379 rpm, and 0.11 mm/minute respectively. After the improvement, the results indicated that the diameter and the surface roughness were closer to the target value at confidence level of 95% and the Cpk of both response variables increase. Moreover, cycle time is reduced. Suggestions The influence of the factors to cutting tool wear has not been investigated in this research. So, further study could perform to improve the process.

Research Article The Study of Suitable Factors for Welding on Canned Food by Design of Experiment Method Prachuab Klomjit * and Paisan Chantasoponno Department of Industrial Engineering and Management, Faculty of Engineering and Industrial Technology, Silpakorn University, Nakhon Pathom, Thailand Corresponding author. E-mail address: prachuab@su.ac.th

Received October 21, 2011; Accepted January 30, 2012 Abstract

This research aimed to study the factors that affected canned food welding and the suitable condition

of the design of experiment that affected its quality and suitability which finally led to standard quality reference in real work place.

This research utilized the concept of experiment design and analysis to study 4 factors as follows; the

electric current, a spring pressure, size of copper wire and overlapping area. By testing 3 response values of welding which were welding strength, welding flexibility, and welding thickness, we found the suitable factors and conditions of the experiment. The results indicated that electric current, spring pressure, and size of copper wire had stronger influence on welding strength and flexibility, whereas only electric current and spring pressure had influence on welding, welding thickness and welding flexibility. The overlapping area had less influence comparing to other factors. The study concluded that the suitable conditions for welding were 55 Amp of electric current, a spring pressure of 60 daN, wire diameter of 2.10 mm. and overlapping area of 0.7 mm. Keywords: Suitable Factor; Design of Experiment; Welding; Canned Food Introduction

factors such as can welding, can coating, polyester-

powder coating on welding line, and can sealing.

Canned Food Containers are useful for food

preservation. Nowadays, canned food packaging is

commonly used in Thailand. There are about 900

data, it was found that the sample product with

million cans of canned food containers produced

the size of â&#x20AC;&#x153;603x700â&#x20AC;? had highest defect in can

each year. Canned food and fruit manufacturing

welding and had highest risk among all heights of

compete in quality and price to gain competitiveness

can products. The defect can be categorized into

in the global market.

3 types; hot weld, narrowed weld and cold weld

The important steps that lead to producing

by testing the 4 welding characteristics; welding

qualified canned food depend on various suitable

strength, welding coherence, welding flexibility and

Silpakorn U Science & Tech J 5 (2): 26-32, 2011

According to the manufacturing research

P. Klomjit and P. Chantasoponno

Silpakorn U Science & Tech J Vol.5(2), 2011

welding thickness. All defect types cannot be fixed

in heat transfer change. Even though the other value

and returned to manufacturing process once they

settings are normal, the heat will be easily noticed

occurred.

from the point where the heat has better flow.

Welding process is the process of forming

The best amount of electricity from the

connections between metal by the pressing of metal

power supply was measured by the flow based on

electrodes on both sides. Heat will be generated

the maximum number of beads on a piece of iron

by electricity and transferred to the plates. Heat

metal. The appropriate power supply depended on

resistance of metal plate will be higher than electrode

the can thickness that did not tear when tested by

heat. Heat distribution is common in the normal

connecting them with the power supply set at 2 / 3

welding process. E1 and E2 electrodes identify â&#x20AC;&#x153;Iâ&#x20AC;?

of the minimum value for the production.

(volume) required heat and welding capacity in

accordance to rules of the Joule heat spots. Heat

Factorial Design that referred to the factorial design

volume Q is balanced with the performance of W

which each factor consisted of three design levels.

when welding electric current, welding power and

The symbol of the factors was represented by a

welding time are correctly set. The heat will help

capital letter and the levels of each factor were low,

weld the metal. The first process occurs between the

medium, and high. The symbols could be substituted

platesâ&#x20AC;&#x2122; joint where the heat is distributed and some

by k 0 (Low), 1 (Medium), and 2 (High). The

heat is lost to the water cooling system.

experiment of 3k designs was substituted by the

Parames Chutima (2002) presented 3k

numbers of k. For example, to design 32, number 00 meaned the experiment which both factors A and B were low. 01 referred to experiment which factor A was low and factor B was moderate. The equation was defined as follow (Mayer and Montgomery, 2002) (Figure 2).

Figure 1 Welding roll

From Figure 1, tin plate was welded with

copper wire electrode through the welding tin at the melting point of 230 oC where the wire was dissolved and prevented the contamination from welding roll.

Figure 2 Co-factor for the experiment design 33

The wire strength affects the welding characteristics; therefore the copper wire should be periodically

Equation

tested in order to maintain the highest quality.

Yij = m + Gi + eij

Normally, the design of wires has changed from

m =

Average

time to time due to machine-design development;

G =

Influence factors

the change on single side of heat surface could result

e =

discrepancy

Silpakorn U Science & Tech J Vol.5(2), 2011

The Study of Suitable Factors for Welding

experimental designs set up the

the value of factors at high and low levels within

hypothesis when y (variable) is at a normal

the 8 experimental conditions in order to pilot the

distribution. Therefore, to gain that kind of

welding by using the specified factor values. The

distribution, E needs to be set up as a normal

pipe produced by the welding process was used to

distribution and independently as well e ij ~

conduct a mechanical testing and then measured

NID(0,σ2).

the tensile strength of welding and expansion of

The independence of distribution is verified

the pipe diameter. This needed to be done together

by using a scatter plot to study the distribution

with the consideration of the welding structure.

characters. The distribution characters are then

The result was then analyzed and trial used in real

checked whether the distribution points are

workplace. In “factors that were appropriate for

independent. For the variance stability, a scatter

polyester powder coating, spray cans on the welds”

plot is also used to check whether the distribution

by Staporn Pimsarn (2004), the experimental design

points from each factor have the residual. If none of

was conducted to study the appropriate factors for

changes of the megaphone appears in a distribution

polyester spray on the can welding”. Utumporn

shape of the information, the information displays

Pongudom (2010) studied the problem in radiator

variance stability.

factory by studying the data from a prototype

Several researchers have studied in this area.

factory and found that there were several problems

“Finding the optimum conditions for coating of

that needed to be solved urgently. However, waste

lacquer on a piece of tin coated steel by means of

problem had great influence on cost. According to

experimental design” by Tosapol Kieatchareanpol

the data from the prototype factory, it was found

(1994) applied the concept of experimental design

that most of the wastes were produced during

and analysis of the experiment to study the four

the aluminum roll forming process to make raw

factors i.e. types of lacquers, lacquer weight per

material radiator. There were two main factors that

area, incubation temperature, and incubation time.

caused this waste problem i.e. the performance of

The experiment was conducted by testing six types

forming process and the value setting of a welding

of lacquer coating i.e. flexibility test, scratching

machine. The first problem occurred when material

test, rubbing resistance test, penetration of water

specification was incorrect such as the size of

resistance test, strength of adhesion between the

aluminum molding wheel. Moreover, the machine

lacquer and metal texture test and delaminating

with broad scale caused an inaccurate reading. To

of the lacquer from the heating sterilization test.

deal with this matter, the researchers modified the

The results showed the optimum condition was Z

procedure manuals in order to set the operational

lacquer weight 8-9 grams per square meter curing

standard. According to the analysis, the second

temperature 250 C and 13 minutes for incubating.

problem was pointed out that welding speed and

“A Study of the TIG welding that influences the

welding voltage were the main factors of waste.

properties of welding for stainless steel pipes

The 32 factorial Design was used to find out the

type SUS 436L ” by Sutiwat Mahakaporn (1996)

perfect conditions as a reference for machine setting.

experimented the welding according to three

From experiments using the manual operation and

factors i.e. welding electric current, welding electric

setting the appropriate welding speed at 106.1 m/

pressure, and welding speed. His experiment set

min with electrical power at 268 voltages, it was

Most

P. Klomjit and P. Chantasoponno

Silpakorn U Science & Tech J Vol.5(2), 2011

found that the waste was reduced from 9.62% to

Response Variables

2.71%. Consequently, this led to factory standard

Âľ

Average

improvement.

Factors that influence the amount of electricity

This research studied the suitable factors for

Factors that influence the pressure spring

canned-food welding size of 603x700. Statistical

Factors that influence the overlap

analysis was used to calculate the suitable value. The

Factors that influence the the size of the

significance of the study was the result of suitable

copper wire

factors that influenced canned-food welding. The

Effects caused by the interaction of G & b

suitable factors would help reducing waste which

Effects caused by the interaction of G & g

finally led to standard quality reference in real work

Effects caused by the interaction of G & d

place.

Effects caused by the interaction of b & g

Effects caused by the interaction of b & d

Procedure

Effects caused by the interaction of g & d

Gbg Effects caused by the interaction of G & b &

This research studied the properties of the

connection by rip test, ball test, post weld test, and

stretch weld test. The experiment was divided into

Gbd Effects caused by the interaction of G & b &

three levels i.e. medium, high and low. The three

levels were used to study the impact, and compared

Ggd Effects caused by the interaction of G & g &

with the manufacturing conditions at present. The

range of each variable studied was related to the

bgd Effects caused by the interaction of b & g &

interesting point in manufacturing. (Table 1)

g d d d

Gbgd Effects caused by the interaction of G & b & Table 1 The level of factors State

Factor

g&d

Errors

Experiment design plan (Table 2) 1. The main factors were electricity volume, spring

-(low)

0(medium)

+(High)

Electricity Volume

pressure, overlapping area of steel sheet, steel

Spring Pressure

sheet thickness.

Overlapping Area

0.5

0.7

0.9

Size of welding wire

2.06

2.08

2.10

2. Response variables were Rip test, Ball test, post weld test, weld stretch test 3. Reproductively, the numbers of experiments were

3x3x3x3 = 81 repeat for 2 times in total of 162

Factors that affected various features of the

testing, and the response variables tested of 4

testing can were electric current, spring pressure,

types in total of 648 testing.

size of welding wire, and the overlapping area.

4. Metric design.

Therefore, these factors have influence on the testing result. The 4 types of results from response variables are shown as follows:

Silpakorn U Science & Tech J Vol.5(2), 2011

The Study of Suitable Factors for Welding

Table 2 Experiment order

Low

- A Factor of electricity.

- The stability of the variance.

Medium 0 B The intermediate pressure spring

High

Finding the optimum conditions from the experiment

+ C Level factors, area of â&#x20AC;&#x2039;â&#x20AC;&#x2039;overlap of

the plate.

5.3 On a response (Response plot) From the welding condition experiment,

the welding strength and welding are considered.

D The thickness of the welding wire.

5. Analysis of statistical tests.

Therefore it is vital to consider the suitable

5.1 The analysis of variance (ANOVA).

conditions of each factor by evaluating response

5.2 To determine the accuracy

values to find out the good quality of welding line.

eij ~ NID(0,s ) 2

- Data were normally distributed.

- Data was independent.

The scale for each factor can be described in

the table below.

Table 3 The weight rating of the results

P. Klomjit and P. Chantasoponno

Silpakorn U Science & Tech J Vol.5(2), 2011

Results

From the experiment data, it was shown that

data variations were distributed evenly along the line indicating that data had normal data distribution.

The response variables of the welding-

strength test i.e. power volume, spring pressure, overlapping area, size of wire welding affected welding strength as follows:

- The power volume at 45 amps was the

suitable condition for the welding-strength test.

was 60 daN.

Figure 3 Error analysis of the normal distribution

- The suitable condition for spring pressure

of the results of welding strength test

- The suitable condition for overlapping area

was 0.9 mm.

From the experiment data, it was shown that

- The suitable size of wire welding was 2.08

mm.

data variations were distributed evenly along the line indicating that data had normal data distribution.

These response variables had been tested

(Figure 4 and Table 4 as a sample) and found the optimal conditions as follows: the power volume of electric current of 55 amp., spring pressure of 60 daN, over lapping area of 0.7 mm and wire size of 2.10 mm.

The strength of the weld. A The strength of the weld. B The strength of the weld. C The strength of the weld. D

Finally, the evaluation criteria were used to

calculate the highest value of the four test results (welding strength, welding interface, welding thickness, and welding elongation). The optimum condition for canned food packaging in test no. 26

Figure 4 Graph of the response variable and the

was showed as follows:

welding strength

1. Factor A (+) gave the electricity volume

of 55 amps.

Table 4 The welding-strength test Level

Factor A

Factor

Factor C

2. Factor B (0) gave the spring pressure of

60 daN. Factor

3. Factor C (0) gave the overlapping area of

0.7 mm.

1(-)

4.91

5.37

4.66

4.55

4. Factor D (+) gave the wire size of 2.10 mm.

2(0)

3.99

4.59

4.09

4.91

The results from the welding thickness were shown

3(+)

3.90

2.92

4.00

4.43

as follows: The score from welding-strength test was 10 points.

Silpakorn U Science & Tech J Vol.5(2), 2011

The Study of Suitable Factors for Welding

The score from welding line test was 9 points.

The score from overlapping-area test was 10 points.

research and development, thus more numbers of factors should be added in the experiment in order

The score from welding-elongation test was 9 points.

The present study attempts to perform a

to gain the optimisation.

The comparison showed that the suitable

conditions from properties experiment gave better

References

welding condition. The strength of the weld was

Chutima, P. (2002) Experimental design and

improved to 97 - 98 percent of the welding score

engineering, Chulalongkorn University,

which was better than the old condition at 89 - 90

Bangkok.

percent score. The width of the weld increased from

Kieatcharoenphol, T. (1994) To find the optimum

0.48 MM. to 0.5 mm, and elongation of the welds

conditions for the coating of lacquer on a piece

increased from 110 MPa to 106 MPa.

of tin coated steel by means of experimental design. Master’s thesis. Department of

Conclusion

Industrial Engineering. Graduate School.

Chulalongkorn University.

The result from the experiment of the suitable

factors for canned food showed that the welding

Mahakapakorn, S. (1996) The study of the

strength and the welding line were affected by the

integration process of TIG for stainless steel

electric volume and spring pressure. The welding

pipes, drums, casings of SUS436L. Master’s

thickness was affected by the overlapping area.

thesis. Chulalongkorn University. Pimsarn, S. (2004) Factors that are suitable for

And the welding line flexibility was affected by all testing factors.

application on polyester powder coating

The result from the analysis of the suitable

welding cans. Master’s thesis. Department

conditions for tin coated steel canned welding of size

of Industrial Engineering. King Mongkut’s

“603 x 700” was found as follows: electric current

University of Technology North Bangkok.

of 55 amp, spring pressure of 60 daN., copper wire

Pongudom, U. (2010) The factors that fit into

(and compressed) 2.10. mm., and the overlapping

the aluminum tube from a roll forming

area of 0.7 mm.

process. Case factory radiator Thesis Master. Department of Industrial Engineering. King

Suggestion

Mongkut’s University of Technology North

Bangkok.

The effect of electric current could be divided

into 3 levels. It should be noted that some factors

Myers, R. H, and Montgomery, D. C. (2002)

have high range of thickness. Therefore the factor

Response Surface Methodology. 2rd ed., John

adjustment should be employed in order to obtain

Wiley & Sons. New York.

narrow thickness.

Research Article A Study of Proper Conditions in Face Milling Palmyra Palm Wood by Computer Numerical Controlled Milling Machine Surasit Rawangwong*, Jaknarin Chatthong, Julaluk Rodjananugoon and Worapong Boonchouytan Department of Industrial Engineering, Faculty of Engineering, Rajamangala University of Technology Srivijaya, Songkhla, Thailand * Corresponding author. E-mail address: sitnong2@yahoo.co.th Received October 21, 2011; Accepted December 25, 2011 Abstract The purpose of this research was to investigate the effects of main factors on the surface roughness in milling process of Palmyra Palm wood face by computer numerical controlled milling machine and using shell end mill cutting tools 6 edges. The main factors including speed, feed rate, depth of cut and angle of cut were investigated for the optimum surface roughness. Generally, acceptable surface roughness was between 3.0-9.0 Âľm before sanding process. In the experiment, Palmyra Palm wood of 11-13% humidity was used at 800-1200 rpm in cutting speed and feed rate at 0.03-0.05 mm/tooth. The result of preliminary trial showed that the depth of cut and the angle of the cut had no effect on surface roughness. It was found from the experiment that the factors affecting surface roughness were feed and speed, with tendency for reduction of roughness value at a lower feed rate and greater cutting speed. Therefore, in the facing process for Palmyra Palm wood it was possible to determine a face milling condition by means of the equation Ra=0.954+20.4 feed+0.00126 speed. This equation was employed at a limited speed of 800-1200 rpm, and the feed rate of 0.03-0.05 mm/tooth. The result from the experiment of the mean absolute percentage error of the equation of surface roughness is 6.10% which is less than the margin of error, and is acceptable. Keywords: Design of Experiment; Computer Numerical Controlled Milling Machine; Palmyra Palm Wood; Surface Roughness Introduction Borassu flabellifer Linn is a scientific name of Palmyra Palm which is a tropical plant from Africa. Later, Palmyra Palm was grown throughout in the south India and then Thailand lastly (Thalabnark, 2000). Every part of Palmyra Palm is useful for human beings. For instance, its young leaves are made for child toy handicrafts, its elder leaves can be used for making a roof, and its peeled stems can be made as a rope. Moreover, both young male and

Silpakorn U Science & Tech J 5 (2): 33-39, 2011

female Palmyra Palm can produce palm sugar and their fruits are major ingredient of Thai dessert which has very nice smell. The peeled palm fruits also can be used as a kind of fuel which energizes a high energy. In addition, the palm stems can be used to make practical device and furniture including blackboards, desks, chairs, house posts or even beds. Apart from the mentioned usefulness, some souvenirs are created from Palmyra Palm woods such as spoons, dishes, vases, bracelets and candle plates.

Silpakorn U Science & Tech J Vol.5(2), 2011

The Study of Proper Conditions in Face Milling Palmyra Palm Wood

Nowadays Palmyra Palm wood products are most popular and wanted in furniture markets because they have a unique texture with their rings, strength, endurable and low prices. However, Palmyra Palm wood has a drawback point, in that its thorns in the texture cause the problems in production process. Therefore, the main challenge in using Palmyra Palm products is surface roughness in the production process. These include planning, turning or cutting processes. The surface roughness is not appropriate for target market need, thus it consumes much more time in decorating the Palmyra Palm wood products. The other factors that cause to surface roughness can be identified as cutting speed, feed rate, depth of cut and angle of cut (Bagci and Aykut, 2006; Rawangwong and Chatthong, 2007; Rawangwong and Chatthong, 2008; Routara et al. 2009; Yang et al., 2009; Rawangwong et al., 2010; Rawangwong et al., 2011). Last but not least, skillful and experienced workers are one of the important factors. The cause mentioned above can motivate the researchers in investigating the optimum surface roughness for furniture industrial manufacturers to make use of Palmyra Palm wood in the production process. In addition, a reduction of time-consumption during cutting process can increase the quantity of production and it decreases the production cost. The finding would also become a data base for further research.

1) Computer numerical controlled (CNC) milling machine of model EMCO PC Mill 50 with basic technical specifications including a maximum stable round of speed of 2500 rpm, feed rate of 0-75 mm/min as shown in Figure 1.

Figure 1 CNC milling machine 2) Wood piece Samples: Palmyra Palm wood fumigated planks with 50Ă&#x2014;50 mm in a cross section and 300 mm in a length of 11-13% with humidity in wood as shown in Figure 2.

Equipment and Tools This research study aimed to investigate the effect of main factor on the surface roughness of Palmyra Palm wood in the face milling process by computer numerical controlled milling machine and using shell end mill cutting tools of 6 edges. The following equipment and instrument were used.

Figure 2 Palmyra palm wood work-piece 3) Cutting tools: A high speed steel (HSS) model Co 8% with 40 millimeter diameter of 6 edges, as shown in Figure 3.

S. Rawangwong et al.

Silpakorn U Science & Tech J Vol.5(2), 2011

process. Third, it was a pilot treatment to examine the optimum surface roughness and last procedure was to take the real treatment in order to confirm the results. These were detailed in the following. Procedures no. 1: To investigate the sample size for designing the Palmyra Palm milling machine by using Minitab R.15 with statistic reliability and significance at 95% and 5% respectively Procedures no. 2: To study the factors affecting surface roughness in the Palmyra Palm wood milling process by using Completely Randomized Factorial Designs with 3 repeated treatments for reducing the variation of sampling. Minitab R.15 was employed to calculate statistic values and to analyze the 24 Factorial Design (Ploypanichjaroen, 2003), (Montgomery, 2005), (Sudasna Na Ayuthaya and Luangpaiboon, 2008). The 4 factors and the responsive surface roughness value as shown in Table 1.

Figure 3 Shell end mill 4) A surface roughness measuring device of model Mitutoyo Surf Test 301 as shown in Figure 4.

Table 1 The allocated variation in procedure no.2

Figure 4 Surface roughness tester

Factor

High

Low

Speed (rpm)

1000

800

Feed (mm/tooth)

0.05

0.03

Depth (mm)

Angle (degree)

Procedures no. 3: As General Factorial Design was used for identifying the optimum surface roughness with the allocated speed of 3 levels: 800, 1000 and 1200 rpm; the allocated feed classified into 3 levels; 0.03, 0.04 and 0.05 mm/ tooth; but the direction of cutting was stable at 0 degree. Further, the depth of cutting was stable at 1 mm which did not affect the surface roughness from the first treatment. The findings were shown in Table 2.

5) Humidity measuring instrument: Model DT-129 6) Digital vernier caliper Methodology There were four main procedures that served the purposes of conducting this research study. First, it was to investigate the sample size for designing the Palmyra Palm milling machine. Second, it was to study the factors expected to make an effect on surface roughness in the Palmyra Palm wood milling

Silpakorn U Science & Tech J Vol.5(2), 2011

The Study of Proper Conditions in Face Milling Palmyra Palm Wood

Table 2 The allocated variation in procedure no.3 Factor

Level 1

Level 2

Level 3

Speed (rpm)

1200

1000

800

Feed (mm/tooth)

0.05

0.04

0.03

Depth (mm)

Angle (degree)

Procedure no. 4: To take the real treatment in order to confirm the results. This treatment was tried out to confirm the conformation of each treatment by using a linear equation of procedure no.3 to predict the surface roughness. Condition was sampling selected with 6 times of a replication without margin errors lower than 10%.

Figure 5 Analyzed results of surface roughness values

Results Results of sampling sizes. The statistic values used in data analysis were reliability at 95% or significance at 5%. The feed was at 0.03 mm/ tooth; the speed was 1000 rpm; the depth of cut was at 2 mm; and the direction of cutting was at 0 degree. The twelve repeated treatments revealed that the mean average of surface roughness was at 2.75 µm and the standard deviation was 0.732 µm. Furthermore, the result of sample size investigation was a 5-sampled size. According to procedure no.2, the analysis of the variance of surface roughness R2 was of 67.71 % and the Adjust R2 was of 59.10 %. This meant that the data variance value was at 100 µm2. For the variance value at 67.71 µm2 could be explained with regression model and the remaining value was not explainable due to the uncontrollable variables. The details are as follows: it is obviously seen that the most variance of surface roughness is implied as a regression model. This can be said that the design of each treatment is appropriate and accurate as shown in Figure 5.

Figure 6 The interaction effects plot of surface roughness

Figure 7 The main effects plot of surface roughness

S. Rawangwong et al.

Silpakorn U Science & Tech J Vol.5(2), 2011

Figure 5 and Figure 7 reveal that the main factors affecting the surface roughness of Palmyra Palm are feed and speed with tendency of higher surface roughness when feed and speed increase from 0.03 to 0.05 mm/tooth and 1000 to 1200 rpm respectively. The surface roughness reduced when the feed decreases and the decreased speed decreases the surface roughness of Palmyra Palm as shown in Figure 6 and Figure 7. shows that no other factors affect the surface roughness. Based on procedure no. 3 and data analysis in order to identify the variation of surface roughness of Palmyra Palm and adjust for variance analysis. The findings revealed that the designing surface roughness measurement was decision making coefficient of 64.23 % and Adjust R2 was of 54.25%. This meant that the variance value was at 100 Âľm2 and 64.23 Âľm2 was implied by the regression model and the rest of data could not be interpreted because of the uncontrolled variable. Therefore, the data variance to measure the surface roughness could be implied from the feed and speed. These brought about the accurate designing treatment and appropriate for data analysis. The analysis of variance for Ra is shown in Figure 8.

Figure 9 The interaction effects plot of surface roughness

Figure 10 The main effects plot of surface roughness The basic treatment shown in Figure 8, Figure 9 and Figure 10 presents that the main factors influencing the surface roughness of Palmyra Palm are feed and speed. The surface roughness reduces when the feed decreases and the decreased speed decreases the surface roughness of Palmyra Palm as shown in Figure 10 and Figure 11. The other factors do not have effects on the surface roughness. The regression analysis of the surface roughness of Palmyra Palm wood, and feed and speed by adjusting the variation. The ratio of feed is classified into 3 levels: 0.03, 0.04 and 0.05 mm/ tooth; the speed is set into 3 levels: 800, 1000 and 1200 rpm. Further, the depth of measurement is stable at 1 mm and direction of cutting is at 0 degree

Figure 8 Analyzed results of surface roughness values

Silpakorn U Science & Tech J Vol.5(2), 2011

The Study of Proper Conditions in Face Milling Palmyra Palm Wood

stability. The recessive test is Minitab R.15. The findings are shown in Figure 11.

1) Cutting speed significantly effects the surface roughness of Palmyra Palm wood followed by feed rate. The result also indicates that lower value of speed and lower feed tended to decrease the surface roughness. 2) The linear equation in this research was as follows:

This equation could be applied with shell end mill tool and high speed steel with mill cutting tools 6 edges speed was at 800-1200 rpm and the feed rate at 0.03-0.05 mm/tooth. 3) When comparing the treatment for confirming the results to the findings using the formulation displayed, the measurement was 10 % of errors. The percentage of average error was of 6.10% fewer than the margin of error that could be acceptable.

Figure 11 Regression analysis: surface roughness values, speed and feed The analysis of regression model can be related to the main factors and the surface roughness (Ra) as shown in this linear equation:

Ra = 0.954 + 20.4 feed + 0.00126 speed

Ra = 0.954 + 20.4 feed + 0.00126 speed (1)

Suggestions 1) The measurement for piece of work revealed that the Palmyra Palm wood had much vary which affected on the surface roughness measurement. This is an uncontrolled factor and time-consuming for the treatment. It is better to avoid measuring roughness of the core texture. 2) This research limitation is that the CNC milling machine used is of a small size that enables to produce a few power in milling.

The result of procedure no.4 is confirming all treatments by using an algebraic equation to predict the surface roughness of Palmyra Palm. The sampling of cutting process within the limited area can be compared to the real means. The deviation lessens than 10 % but it is just 6.10%. This is acceptable. Conclusion The study of investigating the surface roughness in Palmyra Palm wood face milling process by CNC milling machine and using shell end mill cutting tools of 6 edges in order to identify the means of the surface roughness of Palmyra Palm wood face milling process in furniture production. The completely randomized block factorial design was applied to the research. The main factors including speed, feed, depth of cut and angle of cut were investigated for the optimum surface roughness. It could be concluded as following;

Acknowledgement This research study was sponsored by Rajamangala University of Technology Srivijaya, fellowship and it is also under the Office of Higher Education Commission grant in 2009. My deep appreciation goes to the Automatic Machine laboratory, Faculty of Engineering for supporting to using various kinds of practical machine in conducting this research.

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Silpakorn U Science & Tech J Vol.5(2), 2011

References Abou-El-Hossein, K. A., Kadirgamaa, K., Hamdib, M., and Benyounis, K.Y. (2007) Prediction of cutting force in end-milling operation of modified AISI P20 tool steel. Journal of Materials Processing Technology 182: 241-247. Arlai, T., Kaewtatip, P., and Prommul, K. (2003) Influencs of various working parameter in routing process of rubber wood using tungsten carbide routers. ME-network National Conference Phuket, Thailand: 74-79. Bagci, E. and Aykut, S. (2006) A study of taguchi optimization method for identifying optimum surface roughness in CNC face milling of cobalt-based alloy (stellite 6). International Journal of Advanced Manufacturing Technology 29(9-10): 940947. Bailey, J. A., Bayoumi, A.-M. E., and Stewart, J. S. (1983) Wear of some cemented tungsten carbide tools in machining oak. Wear 85: 69-79. Bayoumi, A.-M. E. and Bailey, J. A. (1985) The role of tool composition and tool geometry in controlling the surface finish in machining of Wood. Wear 103: 311-320. Routara, B. C., Bandyopadhyay, A., and Sahoo P. (2009) Roughness modeling and optimization in CNC end milling using response surface method : effect of workpiece material variation. Journal of Advanced Manufacturing Technology 40(11-12): 1166-1180. Miklaszewski, S., Beer, P., Zbie, M., Wendler, B. G., Mitura, S., and Michalski, A. (2000) Micromechanism of polycrystalline cemented diamond tool were during milling of woodbased materials. Journal of Diamond and Related Materials 9: 1125-1128. Montgomery, D. C. (2005) Design and analysis of experiments, 6th ed., John Wiley & Sons, New York.

Ploypanichjaroen, K. (2003) Engineering Statistics Volume 2. Minitab processed, 4 th ed., Technology Promotion Association (ThaiJapanese), Bangkok. Prommul, K., Kaewtatip, P., and Arlai, T. (2002) Study on optimum wood cutting condition using PCD. ME-network National Conference Phuket, Thailand: 526-530. Rawangwong, S. and Chatthong, J. (2007) The study favorable conditions for the cutting text on para wood by computer numerical controlled milling. IE-network National Conference Phuket, Thailand: 121-129. Rawangwong, S. and Chatthong, J. (2008) The study of proper conditions for Palmyra Palm wood turning by carbide cutting tool. IE-network National Conference Songkhla, Thailand: 787-795. Rawangwong, S., Chatthong, J., Rodjananugoon, J., and Jaidumrong, J. (2010) The study favorable conditions for text engraving on coconut wood using computer numerical controlled milling machine. IE-network National Conference Ubon Ratchathani, Thailand. Rawangwong S., Chatthong, J., and Rodjananugoon, J. (2011) The study of proper conditions in face coconut wood by CNC milling machine. IEEE International Conference on Quality and Reliability (ICQR) Bangkok, Thailand: 455-459 Sutus Na Ayuthaya, P. and Luengpaiboon, P. (2008) Design and analysis of experiment, Top publishing, Bangkok. Thalabnark, D. (2000) Palmyra palm tree and Its values, Petchburi Rajabhat University printing, Petchburi. Yang, Y.-K., Chuang, M.-T., and Lin S.-S. (2009) Optimization of dry machining parameters for high-purity graphite in end milling process via design of experiments methods. Journal of Materials Processing Technology 209: 4395-4400 39

Research Article Optimisation Using a Central Composite Rotatable Design for Lacquer Production Process Chanpen Anurattananon *, Suchavadee Pattanavatcharakul and Manit Soypetch Department of Industrial Engineering and Management, Faculty of Engineering and Industrial Technology, Silpakorn University, Nakhon Pathom, Thailand * Corresponding author. E-mail address: j_pen2000@hotmail.com Received October 21, 2011; Accepted December 28, 2011

Abstract The objective of this research is to study the controllable factors affecting the lacquer quality and to find out the optimum conditions of the controllable factors by Central Composite Rotatable Design. For the crushing in Lacquer process, three controllable factors such as the quantity of solvent (x1), cooling temperature (x2), and the specific time frame of crushing (x3) were investigated. Response factor was the smoothness of lacquer surface. The relationship between response and controllable factors was determined. From the results, it was found that the optimal controllable factors were as followed: solvent of 95.59 kilograms, the cooling water temperature of 14.7 째C, and specific crushing time of 23.25 minutes. These controllable factors led to obtain the optimum smoothness of lacquer surface of 6.5 Hexman. The validation of the experiment by using such optimum setting of controllable factors from the Central Composite Rotatable Design, resulted in the 4.6% error of the lacquer surface smoothness.

Keywords : Optimization; Smoothness of lacquer surface; Central composite rotatable design; Lacquer production process Introduction

components are exactly fixed, they cannot be

Lacquer production process consists of

adjusted and other processes have no effect on

mixing process, crushing process, and quality

paint quality. Therefore, only crushing process is

adjustment process. The obstacle in the production

considered in this study.

is quality testing of paint which is not acceptable

by customer requirement. This makes the operators

which affects paint quality. There are many factors

to rework by adding some substances in case the

influencing the production of good paint quality

paint intensity does not correspond to quality

such as solvent quantity, cooling water temperature

requirement. For whole consideration about the

and crushing time. These factor condition levels

production process, crushing process and mixing

would be varied appropriately with paint quality

process are important processes which affect paint

property requirement. In crushing process, the

quality change. In the mixing process, mixing

operators have to work with skills and trial and

Silpakorn U Science & Tech J 5 (2): 40-45, 2011

Crushing process is important process

C. Anurattananon et al.

Silpakorn U Science & Tech J Vol.5(2), 2011

error for setting factor condition levels. This is the

regression analysis (Wiesberg, 1985) was used

problem to control paint quality, especially when

as the tool for building relationship between

the customer wants new various paint property.

controllable factors and response. The estimated

If paint property is not qualified by customer,

function was in form of polynomial function.

the product is reworked. This makes loss time in

The performance measures were the coefficient

production and increases production cost. The

of Determination (R2) and Mean Square Error

application of statistical experimental design

(MSE). This research illustrated the optimisation

(Montgomery, 1997) in lacquer process production

procedure with two stages. In the first stage, the

can result in improving product quality, reducing

RSM was introduced as powerful method to

process variability, i.e., closer confirmation of the

build the statistical approximation to provide for

output response to nominal and target requirements

the description of the relationship between the

and reducing development time and overall costs.

controllable factors and response. In the second

Conventional practice of classical method of

stage, the predictive model would be defined as the

maintaining other factors involved at an unspecified

objective function of optimisation to accomplish

constant level does not depict the combined

the optimisation procedure using Optimiser in

effect of all the factors involved. This method is

MINITAB.

also a time consuming process and requires a

number of experiments to determine optimum

the controllable factors which influence on paint

levels, which are unreliable. These limitations of

quality in crushing process and to find optimum

a classical method process can be eliminated by

controllable factor conditions by using a Central

optimising all the affecting parameters collectively

Composite Rotatable Design for crushing process

by statistical experimental design using response

in lacquer process production.

The objectives of this research are to study

surface methodology (RSM). Response surface methodology (Myers and Montgomery, 1995)

Methods

is the statistical and mathematical technique

useful for developing, improving and optimising

experimental design and analysis and Response

processes.It also has important applications in

Surface Methodology were the tools of procedure

the design, development, and formulation of new

design and analysis of experimental data. The

products, as well as in the improvement of existing

relationship between response and controllable

product designs. This approach can help the

factors was developed in form of polynomial model.

crushing process operators in Quality Control area

and can control the consistency of product quality

experimental design used in this research. The

with less effort. Moreover, it can help them in new

Central Composite Design was proposed by Box

product development in case they do not know the

and Wilson (Box and Wilson, 1951). It consists

exact optimum crushing process conditions used in

of 2 k full factorial points or 2 k â&#x2C6;&#x2019; q resolution V fraction factorial points called cubic points, 2k

the process.

This study was empirical research. The

Central Composite Rotatable Design is the

Rotatable Design (CCRD) was employed as

axial or star points and n0 â&#x2030;Ľ 2 runs in the design center (Draper, 1982) (where k is the number of

RSM tools for optimising crushing process. The

controllable factors, q is the number of fraction,

In this study, the Central Composite

Silpakorn U Science & Tech J Vol.5(2), 2011

Optimization Using a Central Composite Rotatable Design

and n0 is the number of design center runs).

Table 2 Experimental data of solvent quantity,

CCRD with the rotatability property is conducted

colling water temperature, crushing time

by choosing an appropriate axial distance (Myers

and smoothness of lacquer surface

and Montgomery, 1995). Rotatability property is

x1(kg) x2 (Â°C) x3 (min.)

important for a second-order design to posses a

Run

reasonably stable distribution of scaled prediction

7.2

6.5

variance throughout the experimental design region.

112

7.2

5.5

12.8

5.5

112

12.8

5.3

7.2

7.5

112

7.2

6.0

12.8

6.2

112

12.8

5.8

58.36

5.5

10 125.64

4.9

center points in design. The design was rotatable

5.3

5.6

14.7

6.0

was measured as smoothness of lacquer surface (y)

6.35

4.8

in unit of Hexman. There were three controllable

23.25

5.5

factors affecting response, i.e. solvent quantity

5.1

( x1 ) in unit of kilograms, cooling water temperature

5.4

5.2

5.4

The reasonably stable scaled prediction variance provides asssurance that the quality of the predicted response values is roughly the same throughout the region of interest.

A 23 full factorial central composite design

(Myers and Montgomery, 1995) with five coded levels leading to 19 runs of experiments was performed. There were 8 cubic points of 23 full factorial points, 6 axial points (star points) and 5 CCRD, using an axial distance Îą = 1.682 . Response

( x 2 ) in unit of degree celcius and crushing time ( x3 ) in unit of minutes.

The coded variable levels and natural variable

levels used in this study were illustrated in Table 1.

Results and Discussions

Table 1 Coded variable levels and natural variable levels

Results

The model adequacy checking consists of 3

components as followed

Coded variable levels Factors

-1.682

-1

x1 (kg) x2(Â°C) x3(min.)

58.36

112

125.64

y (Hexman)

1. Normal probability plot of residual.

1.682

5.3

7.2

10.0

12.8

14.7

6.35

23.25

2. Fitted value versus residual plot. 3. Observation order versus residual plot.

The experimental data was illustrated in

Table 2.

C. Anurattananon et al.

Silpakorn U Science & Tech J Vol.5(2), 2011

Figure 1 Normal probability plot of residual

Figure 3 Observation order versus residual plot

Normal probability plot of residual was

In this study, the influence of solvent quantity

( x1 ), cooling water temperature ( x 2 ), and crushing

illustrated in Figure 1. The data were distributed

time ( x3 ) were studied on the smoothness of lacquer

near the straight line, which indicated that the

surface (y) at 5% significance level ( Îą ). This was

residual was normal distribution.

done by hypothesis testing. The hypotheses were as followed (1) H0 : Solvent quantity affected smoothness of lacquer surface. H1 : Solvent quantity had no effect on smoothness of lacquer surface. (2) H0 : Cooling water temperature affected smoothness of lacquer surface. H1 : Cooling water temperature had no effect on smoothness of lacquer surface.

Figure 2 Fitted value versus residual plot

(3) H0 : Crushing time affected smoothness of lacquer surface.

The fitted value versus residual plot was

H1 : Crushing time had no effect on

illustrated in Figure 2. The data were randomly

smoothness of lacquer surface.

scattered around zero-centered line. They had no

open-ended funnel patterns. It indicated that the

variance of residual was constant.

Lack-of-Fit Test was used for consideration

of appropriate regression model. The hypotheses

The observation order versus residual plot

were as followed

was illustrated in Figure 3. The data were randomly

H0 : The equation model was appropriate.

scattered around zero-centered line. It indicated that

H1 : The equation model was not appropriate.

the residual was independently random variable and

uncorrelated.

Silpakorn U Science & Tech J Vol.5(2), 2011

Optimization Using a Central Composite Rotatable Design

The relationship between response and

controllable factors was analysed in the form of polynomial model which was expressed in equation (1). 3

y = b 0 + ∑ b i xi + ∑ b i xi2 + ∑ i =1

i =1

∑b

i =1 j =i +1

xi x j (1)

Where b 0 was intercept on y-axis, b i was linear coefficients, b ii was quadratic coefficients, b ij was

cross-product coefficients, and xi , x j were uncoded

Figure 4 Parameter optimization graph

independent variables.

The polynomial equation which represented

The analysis results were illustrated as below.

the relationship between response and three Estimated Regression Coefficients for Response

controllable factors was expressed in equation (2)

Term

SE Coef

Constant 5.08413

0.08333

61.013

0.000

0.165672 x3 + 0.000459871x +

-0.28464

0.09032

-3.152

0.016

0.0695257 x22 − 5.52735 x10−5 x32 +

0.10781

0.09027

1.194

0.271

0.40761

0.10285

3.963

0.005

X1*X1

0.33079

0.12691

2.606

0.035

X2*X2

0.97770

0.12687

7.707

0.000

X3*X3

-0.00395

0.15161

-0.026

0.980

This regression equation explained that when

X1*X2

0.42655

0.12103

3.524

0.010

x1 changed 1 unit, yˆ decreased 0.134992 units, when x 2 changed 1 unit, yˆ decreased 1.87332 units and when x3 changed 1 unit, yˆ increased 0.165672

X1*X3

-0.19830 0.15273

-1.298

0.235

X2*X3

-0.08488

-0.556

0.595

units with 91.72% of R-squared. This indicated that

S = 0.190612 PRESS = 2.76367

the polynomial equation was capable to explain the

R-Sq = 96.38%

smoothness of lacquer surface well with 91.72%.

R-Sq(adj) = 91.72%

yˆ = 20.7946 − 0.134992 x1 − 1.87332 x2 + 2 1

0.00424107 x1 x2 − 8.75 x10−4 x1 x3 −

0.00267857x2 x 3

(2)

Coef

0.15253

R-Sq(pred) = 60.62%

ANOVA result Source

Seq SS

Adj SS

Adj MS

Regression

6.76449

0.75161

20.69

0.000

Linear

3.32432

1.03834

0.34611

9.53

0.007

2.91643

0.97214

26.76

0.000

Interaction 3

0.52375

0.17458

4.81

0.040

Residual Error 7

0.25433

0.03633

0.18233

0.06078

3.38

0.135

0.07200

0.01800

7.01882

Square

Lack-of-Fit Pure Error

Total

C. Anurattananon et al.

Silpakorn U Science & Tech J Vol.5(2), 2011

The controllable factors which affected paint

p-value 0.271 (more than α = 0.05) and crushing

quality in crushing process were optimised using

time ( x3 ) affected smoothness of lacquer surface

(y) with p-value 0.005 (less than α = 0.05). For

CCRD as shown in Figure 4. It was found that the optimised values of solvent quantity ( x1 ), cooling

Lack-of-Fit test, it indicated that the regression

water temperature ( x 2 ) and crushing time ( x3 ) were 95.59 kg., 14.7 °C and 23.25 min., respectively.

model was appropriate with p-value 0.135 (more

These led to the response of 6.5 Hexman which

was the target response requirement.

followed: solvent quantity ( x1 ) was 95.59 kg., cooling water temperature ( x 2 ) was 14.7 °C and

The Validation of Experiment

The crushing process operators used the

than α = 0.05). The optimum factor conditions were as

crushing time ( x3 ) was 23.25 min. with fitted value

optimum factor conditions of solvent quantity ( x1 )

of smoothness of lacquer surface 6.5 Hexman and

95.59 kg, cooling water temperature ( x 2 ) 14.7 C

it made 4% error of smoothness of lacquer surface.

lacquer. It was found that the smoothness of lacquer

Acknowledgement

surface (y) was 6.2 Hexman. It had 4.6% error of

smoothness of lacquer surface compared to the

Co., Ltd. (Thailand) for producing sample and

results from CCRD.

information used in this research.

Discussions

References

Crushing time was the most influenced

Box, G. E. P., and Wilson, K. B. (1951) On the

factor to smoothness of lacquer surface. This

experimental attainment of optimum

might be caused by the homogeneous paint quality

conditions. Journal of the Royal Statistical

requirement in crushing process. Therefore, the

Society, Series B. 13 : .1-45.

and crushing time ( x3 ) 23.25 min. to produce the

The authors would like to thank TOA Paint

crushing time was the most significant factor in

Draper, N. R. (1982) Center points in second-order

crushing process with p-value 0.005 (less than

response surface designs. Technometrics

α = 0.05).

24 : 127-133. Montgomery, D. C. (1997) Design and Analysis of

Conclusions

Experiments, John Wiley & Sons, New York.

The model adequacy checking was approved

Myers, R. H., and Montgomery, D. C. (1995)

corresponding to the assumption. The Student-t

Response Surface Methodology: Process

hypothesis testing of regression coefficients indicated

and Product: Optimization Using Designed

that solvent quantity ( x1 ) affected smoothness

Experiments, John Wiley & Sons, New York.

of lacquer surface (y) with p-value 0.016 (less than

Wiesberg S. (1985) Applied Linear Regression,

α = 0.05), cooling water temperature ( x 2 ) had no

John Wiley & Sons, New York.

effect on smoothness of lacquer surface (y) with

Research Article The Development of Mathematical Model for a University Course Timetabling Problem Ronnakit Wattanamano, Kanjana Thongsanit * and Patipat Hongsuwan Department of Industrial Engineering and Management, Faculty of Engineering and Technology, Silpakorn University, Nakhon Pathom, Thailand * Corresponding author. E-mail address:kanjanath7@yahoo.com Received October 21, 2011; Accepted December 21, 2011 Abstract This research is to study the problem of classroom timetable generating due to an increase amount of student. The generator of classroom timetable needs to arrange it properly according to the limited resources , i.e., a number of classrooms, loading capacity of classroom, periods, and number of teachers. Importantly, the generating of this timetable construction has to be considered together-with the proportion between capacity of classroom and number of students; otherwise it will increase expense and extra-period requiring. An inappropriate assignment between courses to classrooms will require more classroom utilization. The expense will increase since fee is charged and forwarded to the faculty of Engineering for classroom utilization. In addition inappropriate assignment will also cause requiring extra periods between 3:45 and 6:25 PM. This occurs often at present and leads to ineffective learning. Consequently, the generating of timetable needs to be concerned about expense and time. This research is to study a course timetabling problem of Silpakorn University by building up mathematical model to find out an optimal solution. The main objectives are 1) the lowest expense generating; and 2) the least extraperiod spending. The programs used for the mathematical solution in this research are IBM ILOG CPLEX 12.2. The result was found that solving the classroom timetable problem using a mathematical model could reduce the costs of 8,115 baht / week and the extra-periods required could be reduced from 10 periods to 6 periods. Keywords: Classroom Timetable; Mathematical Model; Integer Linear Programming Introduction Course timetabling is a multi-dimensional assignment problem which is the assignment of courses to faculty members and then, the assignment of these courses to classroom and time slots. Problem encountered in academic departments such as school, college and university. Nowadays, the number of students has increased substantially.

Silpakorn U Science & Tech J 5 (2): 46-52, 2011

The compulsory and elective course may be in the same and/or different faculties. The timetabling problem has become much more complex. This problem is solved based on many restrictions such as the period time, the available number of classrooms, capacity of the classrooms or number of seats in each, amount of the registered student and other restrictions from faculty members.

K. Thongsanit et al.

Silpakorn U Science & Tech J Vol.5(2), 2011

Because of the reasons mentioned, a scheduler, a human decision-maker, consumes time to solve the problem. Furthermore, the assignment of the students to classrooms requires concerning of the suitable number of students for the classroom since it may increase cost and waste opportunity for other appropriate classroom. Some courses may be shifted to the extra-periods, such as 3:45 PM – 6:25 PM, because of inefficient assignment. This affects student’s preference. Furthermore, generating of timetable needs to be concerned about time and expense. This research is to study a course timetabling problem of Silpakorn University by building up mathematical model to find out an optimal solution with the multi objectives in order to the lowest expense generating; and the least extra-period spending.

mathematical model, e.g. f(x1,x2,.., xn) ≤ b , f(x1,x2,.., xn) ≥ b (Ragsdale et al., 2004). Linear programming (LP) involves an optimisation problem with linear objective functions and linear constraints. LP model has three basic components (Hamdy A. Taha., 2003) 1) Objective of goal that is aimed to optimise 2) Constraints or restrictions that are needed to satisfy, for example a limited amount of raw materials or labors. 3) Decision variables or the solutions, the non-negativity restrictions accounting for this requirement. Integer linear programming (ILP) is linear programming in which some or all the variables are restricted to integer value. Assignment Problem An assignment problem is a special case of a transportation model in which the workers represent the sources and the jobs represent the destinations (Ragsdale et al., 2004). e.g. the resource allocation of labors, equipments or machine to workplaces. The course time tabling problem is an assignment of courses to classrooms and time slots with restrictions in order to minimizing cost or maximizing utilization. Table 1 shows literature review about course timetabling problem.

Theory and Literature Review Integer Linear Programming (ILP) Optimisation problem is the problem involving one or more decisions with restrictions. A goal or an objective is considered. The objective is represented by an objective function which identifies the function of the decision variables. The decision maker may want to either maximize or minimize the objective e.g. minimizing cost and maximize profit. The constraint is represented in a Table 1 Literature review Reference Nakasuwan et al., 1999

Institution(student, courses, faculty, section, rooms) Thammasat University

Problem Description

Algorithm

Schedule courses and assign them to room

ILP

- Multi-objective Optimisation - Schedule courses and assign them to room subject to several side constraints Schedule class

ILP

Oladokun and Badmus, 2008

University of Ibadan

Wasfy and Aloul, 2007 Daskalaki et al., 2004 Gunawan et al., 2007

American University of Sharjah University of Patras University of Singapore

Schedule courses and assign them to room Satisfy teacher preferences

Dammak et al., 2006

University of Sharjah

Problem of assigning exams to timeslots

ILP ILP hybrid algorithm Heuristic

Silpakorn U Science & Tech J Vol.5(2), 2011

The Development of Mathematical Model

Research Methodology 1. Studying the course timetabling in practical application The relevant persons, scheduler and faculty member, were interviewed. It was found that firstly the courses are assigned in period slots. Then, each course will be assigned in a time slots and classrooms. The data about courses, lecturers, groups of student are required e.g. the number of course, faculty member, classrooms and classroom capacity etc. 2. Developing mathematical model with multi objectives minimizing classroom cost and minimizing study in the extra-period. 3. Testing the numerical model by using a case problem of Industrial Engineering department, Silpakorn university 4. Conclusion The results of the test were analyzed.

Table 2 Classroom capacity and classroom cost Room

Classroom

Cost Cj (baht/

( j)

capacity Fj

a time slot)

515

513

100

135

270

136

270

137

270

138

270

139

270

140-1

120

360

142-3

120

360

144-6

180

540

Table 3 Example data of the course data

Problem Statement This problem concerns a course timetabling problem which is a multi-dimension assignment problem. These are an assignment of courses, students, faculty members, class rooms, and period times. Courses are subjects taught one time a week. This problem assumes that each course has one section and each course is lectured by one faculty member. A faculty member can teach more than one course. Each course is designed for a group of students such as a section of 1st years student, 2nd years student, 3rd years student and 4th years student. The number of the students in a course are varied which depend on the number of registered students. There are k periods in a day which consists of general period and extra-period. There are j class rooms. The capacity of each class room is known. The cost of each class room depends on its capacity. Cost of classroom means money charge by the Faculty of Engineering due to classroom utilization. Table 2-5 provides the example of data applied in the problem.

Course (i)

Faculty member (r)

Group of students (s)

No. registered student (Ni)

614442

IE 4th year

614352

IE 3nd year

619352

IML 3nd year

619353

IML 3nd year

Table 4 Example data of the faculty member (Rir) Faculty member ( r )

Course (i)

614442, 614432, 614346, 614341, 614343

614352, 614351, 614212

614330, 614331

619353, 619492

Table 5 Example data of group of students (Sis)

Group of students ( s )

Course( i )

IE 4th year

614442, 614351, 614362, 614413, 614442

IML 3nd year

614331, 614101, 614322, 614341, 614344, 619352, 619353, 619311

K. Thongsanit et al.

Silpakorn U Science & Tech J Vol.5(2), 2011

We want to solve a course timetabling problem where all courses must be assigned to class rooms. Each class room in a period can be used for only one course and the faculty member who teaches the course cannot lecture another course at the same time. At a particular period time, each group of students can register only one course. The number of students in each class rooms is limited by class room capacity. The objectives are to minimize cost and extra-period studying. The problem is formulated in a mathematical model. The mathematical model presented below determines which course { i =1,…, I } and class room { j =1,…, J } have to be assigned to a period { k =1,…, K }. The model uses a binary decision variable ( xijk ), The integer linear programming problem for this problem will be defined using the following notations: Indices r = Faculty member , r = 1, 2, …, R s = Group of students , s = 1, 2, … S i = Course , i = 1, 2, …, I j = Class room , j = 1, 2, …, J k = Period , k = 1, 2, …,K Parameters Fj = capacity of class room j Ni = the registered student of course i Air = the course i taught by faculty member r Bis = the course i studied by a group of students Tk = weight of the extra-period Cj = Classroom Cost j Decision Variables

This problem is multi objective problem which is designed to minimize classroom cost and the extra-period of studying. Function (1) represents a formulation to transform the cost in a proportion. Tar1 is a target value which derived from the optimal solution when only one objective function, minimizing cost is considered. And Tar2 is the optimal solution obtained from minimizing the extra-period study. In Function (2), the weight of each period, Tk is added to obtain the solution. The extra-period will have higher weight level than the general period in order to minimize selecting the extra-period. Formulation (3) shows the multi objective problem which is linear function to minimize the weighted percentage deviation from the goals’ target value.

(3)

and to set The weights assigned to the priority of each objective. This problem sets 3) Constrained (4) Constraints (4) force all classrooms in each period to be assigned to at least one task. (5) Constraints (5) represent that all courses have to be assigned in the timetable.

2) Objective Function Minimizing Classroom cost

(6) Constraints (6) limit the capacity. The number of students in each class rooms has to less than classroom capacity.

Minimizing study in the extra-period 49

Silpakorn U Science & Tech J Vol.5(2), 2011

The Development of Mathematical Model

studying. The priority of each objective is equal, which means that the issues of cost and extra-period are equally important, so the weight 0.5 is assigned to w1 and w2.

(7) Constraint (7) represents that the faculty member who teaches a course cannot lecture another course at the same time.

Computational Result and Conclusion To test the improvement of the optimal solution obtained from the mathematical model by using IBM ILOG CPLEX 12.2 software, it is compared to the solution which is from the practical application. We test the problem size (i × j × k) of 8,640 variables. Table 6 - Table 11 presents examples of the solution. The course 614323, 614437, 614445, 614395, 619352 and 619313 are assigned in extra period of classroom no. 515 and 513. The total cost of the proposed method is compared to the solution obtained in the practical application. It was found that the proposed method can improve the cost 8,115 Baht/ week and the extra-periods were reduced by 4 periods as shown in Table 7.

(8) Constraint (8) force that each group of student can register a course at a period time. (9) Case Study A course timetabling problem of Industrial Engineering Department, Silpakorn University is a case problem. There are j = 10 classrooms available to be assigned. Two classrooms are located inside the Industrial Engineering Department, and the other 8 classrooms are in the central area of the Faculty of Engineering. Scheduler has to assign forty eight courses (i) to classrooms (j) and time slots (k). Faculty member teaches from Monday to Friday, 9:25 AM - 6:25 PM. There are three time slots 9:25 AM - 12:05 PM, 1:00 PM – 3:40 PM and 3:45 PM – 6:25 PM. This is a timetabling problem for 1st year student to 4th year Industrial Engineering (IE) students and Industrial Management and Logistics (IML) students in year 2010. Table 2 shows the cost and capacity of the available classrooms. List of courses, the faculty members, groups of students and the number of registered students in each group are given as shown in Table 3. Table 4 presents the courses (i) which are taught by each lecturer. Table 5 shows the courses that each group of students will study. Two objectives are to minimize cost and extra-period

Table 6 Timetable of classroom no. 515 9:25 AM 12:05 PM

1:00 PM 3:40 PM

3:45 PM 6:25 PM

Mon

614202

619316

614323

Tue

614101

614413

Wed

614301

619492

614432

Thu

614101

614432

614445

Fri

619314

614362

Sat

614395

Table 7 Timetable of classroom no. 513

9:25 AM 12:05 PM

1:00 PM 3:40 PM

3:45 PM 6:25 PM

Mon

614331

614231

619352

Tue

614454

614344

619313

Wed

619353

619311

Thu

614203

614322

Fri

614101

614341

Sat

K. Thongsanit et al.

Silpakorn U Science & Tech J Vol.5(2), 2011

Table 8 Timetable of classroom no. 135 9:25 AM 12:05 PM

1:00 PM 3:40 PM

3:45 PM 6:25 PM

Mon

614394

614343

Tue

614330

614352

Wed

614442

Thu

614351

Fri

614452

614322

Sat

Conclusion and Suggestion We have described a model that can be used to schedule courses in universities. The of timetable achieved by use the model comparing to the solution in the practical application. This study assumes one to one assignment between a course and faculty member. In further study, the constraint of a course having more than one faculty member will be considered for more practical approach. Problem concerns multi objectives which are to minimize cost and extra-period studying. A mathematical model of the timetabling problem is proposed. There is an improvement

Table 9 Timetable of classroom no. 142-3 9:25 AM 12:05 PM

1:00 PM 3:40 PM

3:45 PM 6:25 PM

Mon

614211

Tue

614211

614232

Wed

614101

614212

Thu

614213

619254

Fri

614291

614232

Sat

References Dammak, A., Elloumi, A., and Kamoun, H. (2006) Classroom assignment for exam timetabling. Advances in Engineering Software 37: 659-666 Daskalaki, S., Birbas, T., and Housos, E. (2004) An integer programming formulation for a case study in university timetabling, European Journal of Operational Research 153: 117-135. Gunawan, A., Ng, K. M., and Poh, K. L. (2007) Solving the Teacher Assignment-Course Scheduling Problem by a Hybrid Algorithm, World Academy of Science, Engineering and Technology 33: 259-264. Nakasuwan, J., Srithip, P. and Komolavanij, S. (1999) Class Scheduling Optimization. Thammasat International Journal of Science and Technology 4: 88-98. Oladokun, V. O. and Badmus, S. O. (2008) An Integer Linear Programming Model of a University Course Timetabling Problem. The Pacific Journal of Science and Technology 9: 426-431.

Table 10 Timetable of classroom no. 144-6 9:25 AM 12:05 PM

1:00 PM - 3:40 PM

3:45 PM 6:25 PM

Mon

619211

Tue

619251

Wed

614111

Thu

Fri

619253

Sat

Table 11 The comparison of the quality of the solution Total Cost (baht)

No. extra period

The practical method

18,615

The proposed method

10,500

Silpakorn U Science & Tech J Vol.5(2), 2011

The Development of Mathematical Model

Ragsdale, C. T. (2004) Spreadsheet Modeling & Decision Analysis. A practical introduction to management science, Thomson Southwestern, Canada. Taha, H. A. (2003) Operations Research: An Introduction, Prentice Hall, England.

Wasfy, A. and Aloul, F. (2007) Solving the University Class Scheduling Problem Using Advanced ILP Techniques, In IEEE GCC Conference, Bahrain, November 2007.

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