International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 93

Designing Robust Parameters for

Injection-compression Molding Light-guided Plates
Based on Desirability Function and Regression Model
Tsung-Yen Lin
Fu Chun Shin Machinery Manufacture Co., LTD Tainan, Taiwan
Ming-Shyan Huang*
Department of Mechanical and Automation Engineering, National Kaohsiung First University of Science and Technology,
Kaohsiung, Taiwan
e-mail: mshuang@nkfust.edu.tw
*Corresponding author
Abstract-- This work describes a robust injection replication effect of the microstructures distributing on the
compression molding parameter design method that uses linear surface of LGPs determines the optical performance. For
regression model and desirability function to reduce the effect of v-grooves microstructures, the depth of the melt filling has a
environmental noise on injection molded parts quality. The strong correlation with the luminance of LGPs [1]. Although
design objective was to achieve a uniform geometry and injection molding (IM) is one of the most common processes
dimensions of light-guided plate (LGP) after injection molding. for manufacturing microfeatured parts, it has some inherent
In this study, an experimental 2.5-inch LGP injection problems [2-4]. The primary difficulty is that molten polymers
compression molding was performed to test the feasibility of the in a tiny cavity instanteously freeze once they touch the
desirability function, regarding its construction of a composite relatively cooler cavity wall. Increasing the plastic
quality indicator that represents the quality-loss function of temperature, mold temperature, injection speed, and packing
multiple qualities. Firstly, the experimental design and ANOVA pressure may enhance the luminance performance of an LGP
methods were employed to select parameters that affect part [5, 6] However, residual stress exists in LGPs, and the
qualities and adjustment factors. Secondly, a two-level, uniformity of the microfeatures remains a problem with IM.
statistically-designed experiment using least squared error Injection compression molding (ICM) was developed to solve
method was performed to generate a regression model between these problems [7].
part quality and adjustment factors. The mathematical model ICM introduces a compression action into the filling
was then used to optimize process parameters. The experimental process. With a reliance on pressure transmitted from the glue
findings show that the robust process parameters generated by sprue, pressure is also imposed by a compression action from
the proposed method yield a better uniform production quality the mold wall. This process has many advantages, including
than the initial and thus improved and uniform production even packing, less molding pressure, less residual stress, less
quality, which validates its feasibility. molecular orientation, less uneven shrinkage, less density
Index Term-- Desirability function; injection molding; variation, less warpage, and better dimensional accuracy than
light-guided plate; regression model. found with the IM process. On the basis of these advantages,
ICM is typically used to fabricate parts requiring a high
I. INTRODUCTION accuracy and no residual stress, such as LPGs. For instance,
A light-guided plate (LGP) is a key component of Wu and Su [8] who used ICM to reduce the shrinkage of
backlight modules in liquid crystal displays that directs light LGPs, found that the mold and barrel temperatures and
propagation to enhance luminance and uniformity. The injection speed were the key parameters for enhancing the

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 International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 94
accuracy of the optical components and eliminating shrinkage. quality indicators. Some of these indicators can then be
Shen et al. [9] applied ICM to mold 2-inch LGPs. Their selected to construct a composite quality indicator that
investigation demonstrated that the replication effects of represents the mathematical function of the required
microstructures were improved with increasing plastic multi-quality characteristics. However, if any of the multiple
temperature and were dependent on the proper compression principal components have eigenvalues exceeding one being
distance and speed. selected, the feasible solution generated by PCA may not
Traditionally, parameter setting for injection compression satisfy each quality indicator. To resolve this problem, Liao
molding relied on statistical analyses and experimentation, [21] proposed the weighted principal component (WPC)
computer-aided simulations, or operator experience [10, 11]. method of estimating quality by the accountability proportion
However, if the setting for producing molded parts approaches of PCA. Another approach, suggested by Derringer and Suich,
the specification limits, the process is easily affected by is the desirability function (DF), which redefines composite
environmental variation, which reduces the yield rate. In such quality [22]. The desirability function approach is one of the
a case, the parameters are inadequate, and the process is not most widely used methods for solving the multi-quality
robust. Other methods such as fuzzy theory and artificial characteristics problem, first introduced by Harrington [23].
neural network (ANN) that have been proposed to address This technique involves estimating each of the characteristics
such problems generally require substantial data [12-14]. For with response surface functions and then using a
instance, ANN is an empirical modeling technique that transformation routine to simplify the problem into a single
mimics the nature of biological neural network systems and measure of performance. A number of researchers have
possesses the ability to learn using learning algorithms such as suggested improvements to the desirability function approach
back propagation. An accurate representation of the process over the past four decades [24]. This work used the DF
can be obtained by training the network using just method of generating composite quality indicators. A
experimental data, without precise understanding and regression-model based searching method was then used to set
development of a rigorous mathematical model. Because of the robust injection molding parameters proposed by Huang
the aforementioned benefits, various applications of ANN and Lin [25]. This method first uses DOE and ANOVA
have been reported for controlling the injection molding methods to select the main parameters affecting parts quality
process [15, 16]. as adjustment factors. A two-level statistically designed
The Taguchi method and response surface method have experiment using least squared error method is then performed
been developed to target a single quality by designing to generate a regression model between parts quality and
experiments to optimize process parameters [17-20]. However, adjustment factors. Based on this mathematical model, this
the Taguchi method of experimentally searching for optimal study employed the steepest decent method to optimize
process parameters is confined to the design ranges of factor process parameters. A 2.5-inch injection-compression molding
levels. The response surface method has no such limitation experiment were then performed to verify model performance.
despite its more complex experimental design.
In practice, seeking the ideal process parameters and II. DESIGN OF ROBUST PARAMETERS
focusing on multi-quality characteristics is difficult but Figure 1 shows the proposed robust parameter searching
generally necessary. When studying multi-quality method, which includes the following three phases: (1) setting
characteristics, i.e., numerous correlated quality characteristics, the composite quality indicator, (2) executing full factorial
experimental data may be contradictory and data analysis may experiments, and (3) searching for robust process parameters.
be difficult. Principal component analysis (PCA) can convert The three phases are discussed in detail below.
data for multi-quality characteristics into several independent
A. Phase 1 – Setting the Composite Quality Indicator

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Data containing information about multi-quality contribution percentage of experimental factors to the
characteristics were first collected and normalized to generate composite quality indicator  , which is determined by
dimensionless values, each of which is between 0 and 1. If the ANOVA method. The adjustment factors have two distinct
quality requirements differ, the corresponding normalization characteristics: (1) a change in adjustment factors caused by
may differ as well: (1) larger-the-better - the target value of environmental interference substantially affects parts quality.
quality objectives is uncertain but was expected to be large, (2) If the adjustment factors are controlled, the required product
smaller-the-better - the target value of quality objectives was quality is assured. By varying adjustment factors, this research
uncertain and was expected to eventually be small, and (3) discovered a process window that enables adjustment of
target-the-best – the target values of quality objectives were selected factors within the window so that molded parts meet
certain and were expected to be achieved. their quality specifications. (2) If the process parameters
Second, the DF was used in this phase to convert within the process window obtain parts with insufficient
observed data into a composite quality indicator, which quality, the range is further adjusted until quality requirements
represents a mathematical model of multi-quality are met.
characteristics. The desirability function method proposed by In this phase, the composite quality indicator  is
Derringer and Suich [22] suggests that the composite quality generated using many quality indicators with different
indicator can be defined as adjustment factors. However, this work examines only the
three most important adjustment factors. The factors are used

DF  i 1 d i  again in phases 2 and 3 to optimize the process parameters.

n 1/ n
(1)
The steps in phase 1 can be summarized as: (1) normalize the
measurements - after performing the suggested Taguchi design
where, ‘n’ denotes the number of quality characteristics; the experiment, normalize the observations of each quality. (2)
DF value becomes zero if one of the di is zero. It becomes one
Determine  - by using DF for the above normalized
only if all instances of di are one. The di represents the observations, the composite quality DF can be generated using
desirability value of the ith quality characteristic defined by Eq. (1). (3) Select the three most significant adjustment factors
Derringer and Suich[22] as follows: - adjustment factors are selected according to their
proportional contribution to the composite quality indicator as
0 x i  xi , LSL revealed by ANOVA analysis. These adjustment factors were
 t then used as the experimental factors in the 2 K full factorial
 x i  xi , LSL 
d i    xi , LSL  x i  xi ,USL (2) experiments in phase 2, where K is less than 3 considering
 
 xi ,USL  xi , LSL  experimental cost.
1 x i  xi ,USL

B. Phase 2 – Executing Full Factorial Experiments
As mentioned above, environmental noise may degrade
where x i represents the mean value of the ith quality the quality of injection molded parts. For quality
characteristics to meet quality specification limits, the process
characteristics; xi ,USL and xi , LSL are the upper window must be robust and allow varying adjustment factors.
By varying the adjustment factors caused by environmental
specification limit and lower specification limit of the ith
interference and by performing the 2K full factorial
quality characteristics, respectively. The value t is the
experiments, a robust process window can be identified. The
relaxation factor, and its value is set between 0 and 10.
experimental runs were designed to combine the extreme
Adjustment factors are selected according to the
points of a three-dimension process window. If a defect occurs
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 International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 96
at extreme points in the process window, a better region can be
0 
found by using the steepest decent method to relocate the  
parameter settings. β   1 (4)
K

The steps of phase 2 are: (1) design the 2 full factorial  
experiments - the experiments were designed according to the  k 
number and the possible ranges of adjustment factors. The
initial central point for 2K full factorial experiment was where Y represents the vector of observation, which may be
obtained by referring to the optimal parameter setting of DOE DFnew or wnew here; X represents the matrix of experimental
suggested in phase 1. (2) Obtain the new new by using PCA runs; xnk represents the kth process parameter in the
for observation after normalization - the new quality indicators experimental run ‘n’. β represents the vector of estimated
new are obtained. (3) Check robustness - if all the new for coefficients of the regression model, and ε represents the
running 2K full factorial experiments meet the quality random error vector.
specification levels, this means that the set-points of the The β vector can be estimated by the least squared error
process parameters of this experimental group could be robust method as follows:
for the new. However, if the robustness confirmation fails at
this point, the next step is to repeat phase 3 and search for β
1
 X' X 1 X' Y
another set of process parameters by employing the regression 2
model-based robust parameter search method. (5)

C. Phase 3 – Searching for Robust Process Parameters [25] The composite equation of the relationship between the

After establishing a regression model based on the process parameters and the product quality can then be

relationship between the process parameters and quality determined. Additionally, Y and matrix X in Eq. (8) must be

observations, the steepest decent method was used to converted into Eq. (9) to get coefficient β in the regression

determine the distance and direction to the target. For any model.

given quality observation, y and k number of process The steps of phase 3 are as follows: Step 1: establish the

parameters were assumed to significantly affect quality, such regression model – Eq. (7) represents the relationship between
process parameters and parts quality. The Y and X in Eq. (8)
as x1 ,x2 , ,xk . The sample data of full factorial experiment can also be substituted into the following equations:

in the previous phase could be used to fit the regression model.

Therefore, the following matrix can be used to obtain the data  y1 
sample that fits the model:
y 
Y   2 ;

Y  Xβ  ε  
 y8 
(3)

 y1  1 x11 x12  x1k 

y  1 x x22  x2k 
Y   2 ; X  21
;
      
   
 yn  1 xn1 xn2  xnk 

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 International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 97
1 1 1 1 1 1 1  1 III. EVALUATION OF 2.5-INCH LGP INJECTION
1 1 1 1 1 1 1 1 COMPRESSION MOLDING

1 1 1 1 1 1 1 1
  A. Experimental Setup
1 1 1 1 1 1 1  1
X  This study analyzed the
(6) injection compression of a
1 1 1 1 1 1 1 1
  2.5-inch LGP, which is characterized by V-shaped
1 1 1 1 1 1 1  1 micro-structure. The objective of the experiment was to
1 1 1 1 1 1 1  1 replicate these micro-structures. Figure 2 shows that the
 
1 1 1 1 1 1 1 1 light-guided plates was 55 mm long, 41 mm wide, and 0.7 mm
thick. The V-shaped micro-structure had a depth of 15 μm, a
The X matrix contains the values 1 and -1, which represent the width of 52 μm, and an included angle of 120°. The LGP
upper and lower levels of each control factor, respectively. stamper was clipped to the core of the mold and was filled by
The second, third, and fourth columns represent control factor a fan gate. The mold design was single cavity with two
levels x1, x2, and x3, respectively. The fifth, sixth, and seventh cooling channels. The molding material was PMMA (Japan),
columns represent interaction effect levels x1 to x2, x1 to x3, and the molding machine was a FANUC ROBOSHOT α-30iA.
and x2 to x3, respectively. The eighth column indicates the Injection compression molding technology was used to
interaction effect among x1, x2, and x3. Entering vector Y and experimentally increase the replication ability of the
matrix X into Eq. (9) obtains the coefficient vector of the micro-structure. The eight experimental parameters included
regression model, β. Step 2: estimate the responses for all filling speed, melt temperature, mold temperature,
possible treatments in the varying ranges. The set-point of the compression distance, compression speed, holding pressure,
process parameters (or the predicted points of the robust holding time and cooling time, and the Taguchi’s L18
molding parameters) and the least resolution of machine orthogonal array was used for verification. Table 1 shows the
control are used as the basis for arranging all possible combinations of the eight parameters in the L18 orthogonal
treatments in the varying ranges. For example, if there are array and measured observations. Three samples were
three adjustment factors and if the upper and lower limits are obtained in each experimental run. Figure 3 shows the points
five times the least resolution of the injection molding of the molded micro-structure of LGP that were measured by a
K
machine, the number of treatments is 5 . Step 3: determine 3D profiler. The two observed objectives were based on the
whether or not the inference process should be continued - this average and range value of micro-structure height of the nine
step determines whether or not the inference of the robust measured points. The measured points were fixed in the same
molding parameters should continue. By substituting all micro-structure by making clips, and the average range and
treatments to construct coefficient vectors of the regression maximum deviation in range were larger than 13.5 m and
model and to generate predicted values, stopping the inference smaller than 0.41 m, respectively, which was in accordance
process has two conditions: either all predicted values meet with industrial specifications.
the quality specifications or only some predicted values do. In
the latter case, the set-point should be selected in the inference B. Taguchi Analysis
process before proceeding to step 4. In the former case, phase Table 2 shows the L18 experimental results of 2.5-inch
2 is performed to test robustness. Step 4: Infer the next robust LGP injection compression molding, including the average
molding parameter - set the search direction by using steepest normalized values of average/range of nine-point heights and
decent method. The forward distance relies on the least the composite quality indicator DF. Of these eighteen
resolution of the machine control. Return to step 2. combinations of Taguchi orthogonal array, the best
combination was that in Exp. No. 3. Table 3 shows the

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 International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 98
ANOVA results for these DF values. Since the results showed parameters of an injection molding process for multi-quality
that compression distance, compression speed, and cooling characteristics, but also meets the requirements of
time significantly affected the DF values, these three factors multi-quality characteristics of molded parts. A light-guided
were selected for adjustment. plate experiment was performed to examine this method. The
Tables 4(a) and 4(b) show the results of the full factorial proposed search method was based on a DF method that can
experiment for the first two inferences of robust parameters. In successfully construct a composite quality indicator, which
the two failed tests in the full factorial experiment, the set represents the mathematical model of multi-quality
points were compression distances of 5.0 mm and 3.9 mm, characteristics and a regression model-based search method
compression speeds of 100% and 98%, and cooling times of that can reflect variables to adjust search distance and
45 s and 44.5 s. The DF values in the tables did not meet all direction.
robustness criteria in this phase. Thus, the search was repeated The proposed method has five major advantages:
until a set-point that met the robustness criteria was found (see 1) The operator is not required to use complex experimental
Table 4(c)). designs.
2) The regression model for describing the mathematical
C. Verification relationship between part quality and process parameters is
The additional verification was performed to test the simple and the inference of robust process parameters is
robustness of the optimal process parameters found by the DF efficient.
method. The two set points, the initial central point of Table 3) The ratio of products disqualified due to unstable
4(a) and the robust central point of Table 4(c), were used to machines and non-uniform materials is decreased, and the
inject fifty molds as measurement samples, i.e., the initial effectiveness of the molding process is improved.
setting of robust process parameters were compression 4) The treatment applied in the full-factorial experiments can
distance of 5 mm, compression speed of 100%, and cooling be confirmed to ensure that the molding process is robust.
time of 45 s. The robust process parameters were compression 5) The search for robust parameters is not restricted to the
distance of 4.8 mm, compression speed of 99.6%, and cooling designed levels of controlled factors.
time of 45.4 s. results of robustness testing. Figures 4(a) and In summary, the experimental results indicate that the
4(b) show the normal distribution of quality characteristics in proposed method effectively solves the problem of
terms of probability density function. The dashed and solid multi-quality characteristics, significantly improves the
lines indicate the initial setting of process parameters and the stability of the molding process, and increases yield.
robust setting of process parameters, respectively. In this case
study, the initial setting of process parameters obtained almost REFERENCES
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height, and eighteen of fifty parts were unqualified within the injection-molded V-groove light guide plates. Polym. Eng. Sci. 2008,

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method for optimizing process parameters generated 100% [2] Xu, G.; Yu, L.; Lee, J.; Koelling, K.W. Experimental and numerical

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proposed method. [3] Sha, B.; Dimov, S.; Griffiths, C.; Packianather, M.S. Investigation of

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[26]

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 International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 100
Get the optimal setting and
normalize the observations from
Taguchi D.O.E.
Phase 1
Get  and choose adjustment
factors by ANOVA analysis

Construct the 23 full factorial

experiments

Get new
Phase 2
Yes
Satisfy Finish
robustness?
No
Buildup regression model

Estimate the response for all

possible treatments in their
varying range

Phase 3 Yes
Stop the inference
process?
No
Inferring next robust process
parameters

Fig. 1. Flowchart of the robust parameter searching method for multi-quality characteristics.

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Round sprue

Cooling
channels Fan gate

8 mm
0.7 mm

41 mm
55 mm

(a)
0.015 mm

0.052 mm
120°

(b)

Fig. 2. 2.5-inch LGP molding: (a) geometry of the injection compression mold; (b) micro-structure of the LGP stamper for injection compression molding
(Materials: Beryllium copper alloy).

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Unit: mm

Fig. 3. Measuring positions of 2.5-inch LGP microstructures.

Lower Specification Limit: 13.50 m

Robust setting
60
Initial setting NG Good
Mean50 StDev N
13.62 0.008 50
12.71
40 0.010 50
Frequency

30

20

10

0
60 12.80 13.00
12.60 13.20
12.80 13.40
13.00 13.60
13.20 13.80
13.40 13.60
Averaged LGP’s 9-point micro-structure height (m)
(a)

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 Upper Specification
International Journal of Engineering Limit:
& Technology 0.41 m Vol:14 No:01
IJET-IJENS 103

20
Robust setting
Initial setting Good NG
Mean StDev N
0.3815 0.024 50
0.40 0.024 50
Frequency

10

0
0.28 0.3 0.32 0.34 0.36 0.38 0.4 0.42 0.44 0.46 0.48
Range of LGP’s 9-point micro-structure height (m)

(b)

Fig. 4. Heights of 2.5-inch LGP 9-point micro-structures: (a) average, (b) range.

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TABLE I
1 7
The L18 (2 ×3 ) experiment for 2.5-inch LGP injection compression molding

Control factors Observations (gray digits).

Exp. Filling Melt Mold Compress. Compress. Holding Holding Cooling Avg. Avg. Avg. Range Range Range
No. speed temp. temp. distance speed pressure time time 9-point 9-point 9-point 9-point 9-point 9-point
heights1 heights2 heights3 heights1 heights2 heights3
(μm) (μm) (μm) (μm) (μm) (μm)
(mm/s) (oC) (oC) (mm) (%) (kgf/cm2) (s) (s)
1 50 240 70 3 80 700 3 35 12.72 12.71 12.71 0.42 0.36 0.41
2 50 240 80 4 90 800 4 40 13.18 13.19 13.19 0.54 0.50 0.46
3 50 240 90 5 100 900 5 45 13.55 13.59 13.54 0.49 0.36 0.35
4 50 250 70 3 90 800 5 45 13.09 13.10 13.12 0.48 0.42 0.44
5 50 250 80 4 100 900 3 35 13.50 13.45 13.45 0.55 0.41 0.38
6 50 250 90 5 80 700 4 40 13.61 13.62 13.62 0.46 0.45 0.45
7 50 260 70 4 80 900 4 45 13.26 13.26 13.26 0.43 0.31 0.34
8 50 260 80 5 90 700 5 35 13.48 13.45 13.50 0.48 0.43 0.55
9 50 260 90 3 100 800 3 40 13.45 13.50 13.51 0.49 0.43 0.32
10 55 240 70 5 100 800 4 35 13.20 13.16 13.18 0.34 0.38 0.39
11 55 240 80 3 80 900 5 40 13.19 13.20 13.18 0.47 0.50 0.43
12 55 240 90 4 90 700 3 45 13.45 13.46 13.45 0.44 0.58 0.37
13 55 250 70 4 100 700 5 40 13.34 13.36 13.34 0.46 0.45 0.42
14 55 250 80 5 80 800 3 45 13.52 13.47 13.53 0.49 0.35 0.46
15 55 250 90 3 90 900 4 35 13.58 13.61 13.62 0.50 0.49 0.49
16 55 260 70 5 90 900 3 40 13.47 13.46 13.45 0.47 0.41 0.49
17 55 260 80 3 100 700 4 45 13.47 13.48 13.45 0.42 0.44 0.40
18 55 260 90 4 80 800 5 35 13.61 13.68 13.66 0.56 0.49 0.53
1, 2, 3
mean sample 1, 2, and 3 at the same run, respectively.

TABLE II

The composite quality indicators DF generated by DF method in the L18 experiment of 2.5-inch LGP injection compression molding
Exp. No. Average normalized averaged Average normalized range of DF
nine-point heights nine-point heights

1 0.004 0.68 0.05

2 0.487 0.30 0.38
3 0.876 0.67 0.76*
4 0.403 0.49 0.45
5 0.779 0.49 0.62
6 0.928 0.47 0.66
7 0.563 0.81 0.68
8 0.789 0.35 0.52
9 0.795 0.62 0.70
10 0.482 0.78 0.61
11 0.488 0.42 0.45
12 0.762 0.43 0.57
13 0.652 0.51 0.57
14 0.818 0.54 0.67
15 0.915 0.32 0.54
16 0.770 0.46 0.59
17 0.774 0.59 0.68
18 0.969 0.20 0.44

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TABLE III
The ANOVA analysis of the composite quality indicator DF in 2.5-inch LGP injection compression molding
SV DOF SS MS F PSS CP (%)
Filling speed 1 0.01
Melt temp. 2 0.06 0.03 2.49 0.04 7.86
Mold temp. 2 0.04 0.02 1.83 0.02 4.40
Compression distance 2 0.08 0.04 3.19 0.05 11.57
Compression speed 2 0.10 0.05 4.25 0.08 17.17
Holding pressure 2 0.03
Holding time 2 0.01
Cooling time 2 0.09 0.04 3.67 0.06 14.10
Error 2 0.01
Pooled error (7) (0.08) (0.01) 0.20 44.90
Total 17 0.45 0.16 100.00
SV, source of variation; DOF, degrees of freedom; SS, sum of squares; MS, mean square; PSS, pure of sum squares; CP,
contribution percentage; F1,7,0.01=12.25, F2,7,0.01=9.55.

TABLE IV
Full-factorial experiment and principal component analysis in 2.5-inch LGP injection compression molding
(a) The first inference of robust parameters by the proposed method.

Initial central point Average Average DF

normalized normalized
averaged range of
nine-point heights nine-point
heights
Exp. Compression Compression speed Cooling time
No. distance 100% 45 s 0.90 0.68 0.78
5 mm
1 +0.5 +1% +0.5 0.91 0.70 0.80
2 -0.5 +1% +0.5 0.67 0.28 0.44
3 +0.5 -1% +0.5 0.88 0.21 0.43
4 -0.5 -1% +0.5 0.85 0.20 0.41
5 +0.5 +1% -0.5 0.97 0.88 0.92
6 -0.5 +1% -0.5 0.94 0.67 0.79
7 +0.5 -1% -0.5 0.97 0.67 0.80
8 -0.5 -1% -0.5 0.70 0.37 0.51
Normalized lower specification limit ≧0.81 ≧0.63 ≧0.71

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 International Journal of Engineering & Technology IJET-IJENS Vol:14 No:01 106
(b) The second inference of robust parameters by the proposed method

Initial central point Average Average DF

normalized normalized
averaged range of
nine-point heights nine-point
heights
Exp. Compression Compression speed Cooling time
No. distance 98% 44.5 s 0.82 0.64 0.73
3.9 mm
1 +0.5 +1% +0.5 0.49 0.30 0.38
2 -0.5 +1% +0.5 0.93 0.47 0.66
3 +0.5 -1% +0.5 0.80 0.59 0.69
4 -0.5 -1% +0.5 0.92 0.60 0.75
5 +0.5 +1% -0.5 0.78 0.43 0.58
6 -0.5 +1% -0.5 0.92 0.56 0.72
7 +0.5 -1% -0.5 0.80 0.62 0.70
8 -0.5 -1% -0.5 0.87 0.65 0.76
Normalized lower specification limit ≧0.81 ≧0.63 ≧0.71

(c) The third inference of robust parameters by the proposed method

Initial central point Average Average DF

normalized normalized
averaged range of
nine-point heights nine-point
heights
Exp. Compression Compression speed Cooling time
No. distance 99.6% 45.4 s 0.93 0.70 0.81
4.8 mm
1 +0.5 +1% +0.5 0.88 0.64 0.75
2 -0.5 +1% +0.5 0.88 0.78 0.83
3 +0.5 -1% +0.5 0.89 0.65 0.76
4 -0.5 -1% +0.5 0.96 0.83 0.89
5 +0.5 +1% -0.5 0.88 0.67 0.77
6 -0.5 +1% -0.5 0.98 0.77 0.86
7 +0.5 -1% -0.5 0.98 0.70 0.83
8 -0.5 -1% -0.5 1.03 0.88 0.95
Normalized lower specification limit ≧0.81 ≧0.63 ≧0.71

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TABLE V
Robustness quality of 2.5-inch LGP injection compression molding obtained using the proposed method

The initial setting The robust setting

Exp. Average Range of Exp. Average Range of Exp. Average Range of Exp. Average Range of
No. nine-point nine-point No nine-point nine-point No. nine-point nine-point No nine-point nine-point
heights heights heights heights heights heights heights heights
(μm) (μm) (μm) (μm) (μm) (μm) (μm) (μm)
1 (12.71) 0.36 26 (12.71) (0.44) 1 13.62 0.39 26 13.63 0.41
2 (12.72) 0.35 27 (12.70) 0.40 2 13.62 0.39 27 13.62 0.39
3 (12.72) 0.40 28 (12.70) 0.38 3 13.61 0.34 28 13.64 0.39
4 (12.70) 0.40 29 (12.72) (0.43) 4 13.61 0.38 29 13.63 0.35
5 (12.70) 0.40 30 (12.70) 0.39 5 13.61 0.36 30 13.60 0.33
6 (12.70) (0.44) 31 (12.73) 0.39 6 13.63 0.38 31 13.62 0.38
7 (12.69) (0.43) 32 (12.70) (0.43) 7 13.62 0.42 32 13.64 0.36
8 (12.72) (0.43) 33 (12.69) 0.36 8 13.63 0.39 33 13.63 0.40
9 (12.71) 0.40 34 (12.71) 0.38 9 13.62 0.37 34 13.62 0.38
10 (12.71) 0.34 35 (12.73) 0.40 10 13.63 0.41 35 13.62 0.36
11 (12.72) (0.42) 36 (12.71) 0.36 11 13.63 0.39 36 13.62 0.38
12 (12.70) 0.37 37 (12.70) (0.42) 12 13.62 0.39 37 13.60 0.35
13 (12.72) 0.39 38 (12.73) 0.38 13 13.61 0.39 38 13.62 0.37
14 (12.73) (0.41) 39 (12.71) (0.42) 14 13.62 0.36 39 13.62 0.33
15 (12.72) 0.37 40 (12.70) (0.41) 15 13.63 0.39 40 13.63 0.40
16 (12.71) 0.39 41 (12.72) 0.39 16 13.62 0.34 41 13.63 0.37
17 (12.72) 0.40 42 (12.72) 0.36 17 13.62 0.41 42 13.62 0.37
18 (12.72) 0.40 43 (12.73) 0.39 18 13.62 0.33 43 13.61 0.33
19 (12.70) 0.39 44 (12.71) (0.42) 19 13.62 0.39 44 13.61 0.37
20 (12.70) (0.41) 45 (12.71) 0.38 20 13.62 0.39 45 13.63 0.37
21 (12.71) (0.42) 46 (12.71) (0.41) 21 13.63 0.40 46 13.62 0.38
22 (12.72) 0.38 47 (12.70) 0.38 22 13.62 0.39 47 13.63 0.38
23 (12.71) (0.41) 48 (12.71) (0.43) 23 13.62 0.37 48 13.62 0.35
24 (12.72) 0.38 49 (12.71) (0.42) 24 13.63 0.39 49 13.62 0.33
25 (12.71) 0.37 50 (12.72) 0.40 25 13.62 0.35 50 13.62 0.41

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