Capability Assessment for Weibull In-Cell Touch
Panel Manufacturing Processes With
Variance Change
Yu-Ting Tai, Wen Lea Pearn, Kai-Bin Huang, and Lu-Wei Liao
Abstract—Since touch panels can provide natural
user-interface, including fluent multipoint touch or advance gesture recognition, recently they have been extensively applied in various portable devices, such as smart phones and tablet PCs. In-cell touch panel is the highest integration touch technology as compared to the on-cell and typical touch panel manufacturing technologies for the thinnest and lightest structure. In in-cell manufacturing processes, manufacturing yield assessment is an essential issue. However, inevitable process variance changes could arise from equipment, material, and operation, and may not be detected within a short time. In addition, the process output usually has a Weibull distribution. To circumvent the undetected variance change causing the inaccurate manufac-turing yield calculation, we provide a yield measure index to avoid overestimating when the underlying distribution is Weibull with variance change. We also show that the accommodation of the process capability index would not be affected by the scale parameter of Weibull distribution. Applying this method, the magnitudes of the undetected variance change are incorporated into the evaluation of manufacturing yield. For illustration purposes, a real application in an in-cell manufacturing factory, which is located in the Science-based Industrial Park in Hsinchu, Taiwan, is presented.
Index Terms—In-cell touch panel, manufacturing yield, variance change, weibull distribution.
I. Introduction
I
N RECENT years, touch panels have been extensively applied in various portable devices such as smart phones and tablet PCs since they provide a natural user-interface (NUI) to enter information easily and intuitively [1]. Ca-pacitive sensors dominate touch applications due to better user experience, including fluent multi-point touch or advance gesture recognition. There are different capacitive touch panel technologies according to the stack-up of the touch sensor.Manuscript received May 30, 2013; revised September 25, 2013 and De-cember 27, 2013; accepted January 21, 2014. Date of publication February 6, 2014; date of current version May 1, 2014. This work was supported by the National Science Council of Taiwan under Grant NSC100-2410-H-424-011.
Y.-T. Tai is with the Department of Information Management, Kainan University, Taoyuan 33857, Taiwan (e-mail: yttai@mail.knu.edu.tw).
W. L. Pearn, K.-B. Huang, and L.-W. Liao are with the Depart-ment of Industrial Engineering and ManageDepart-ment, National Chiao Tung University, Hsinchu 30010, Taiwan (e-mail: wlpearn@mail.nctu.edu.tw; queueingnctu@gmail.com; s9633519.iem96g@g2.nctu.edu.tw).
Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org.
Digital Object Identifier 10.1109/TSM.2014.2303514
Fig. 1. Diagrams of touch panel product types. (a) Add-on touch panel type. (b) OGS touch panel type, (c) On-cell touch panel type. (d) In-cell touch panel type.
One of these technologies is add-on type, including GG (glass-glass), GFF (glass–film-film), G1F (glass-film), and OGS (one glass solution). Sensor for add-on touch panel is patterned on glass or film substrate, being so-called GG, GFF, G1F, or OGS. This sensor is laminated between cover lens and LCD via optically clear adhesive (OCA) by lamination process. Another touch technology is embedded type, which is dominated by LCD makers. They are on-cell and in-cell touch technologies. For on-cell type, the touch sensor is patterned between the polarizer and color filter layer. For in-cell type, the touch sensor is integrated into LCD stack by sharing LCD process. No matter which touch sensor type, all the touch electrode can be made by indium tin oxide (ITO), a transparent and conductive material. Fig. 1 shows the add-on sensor and embedded sensor on Fig. 1(a) to Fig. 1(d), respectively.
New structures of substrate involving OGS and in/on-cell have no need of extra sensor substrate due to integration. The three touch panel types take advantage of cover lens and display’s parts for patterning and they can reduce lam-ination process which is touch panel module makers’ major loss. In-cell touch panel type is the highest integration touch
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technology comparing to the other two, since it shares LCD manufacturing process or even same LCD stacks. It performs the thinnest and lightest structure, so that has become new trend for fantastic user experience. Since the in-cell touch panel being an essential part of the portable devices in current and future trend, the manufacturing yield assessment of the in-cell touch panel is a very important issue.
In the in-cell touch panel manufacturing process, ITO (Indium Tin Oxide) thin film patterning is one of the es-sential operations in which the photolithography and etching manufacturing steps are involved. ITO thin films have been commonly constructed as the transparent electrodes due to excellent photoelectrical properties. It should be noted that sur-face resistance is a very critical specification which is mainly depended on the manufacturing capability of the electrodes. It needs uniform surface resistance to obtain uniform touching performance.
As high quality requirements of the portable devices, the stringently control for surface resistance in in-cell touch panel manufacturing processes are required. In in-cell touch panel manufacturing factories, control charts are commonly applied to provide early warning for the changes in the process mean and variance for the critical specification. Yield measure index is usually used to assess the manufacturing yield. However, inevitable process variance changes which could arise from equipment, material, and operation, and may not be detected within short time. Manufacturing yield may be overestimated due to the inevitable process variance changes. In addition, the process output usually has a Weibull distribution. In this paper, we develop a yield assessment formula to obtain Weibull in-cell touch panel manufacturing yield more accurately, as it could provide feedback to in-plant practitioners on what actions need to take for manufacturing yield control and improvement.
The remainder of the paper is organized as follows. The manufacturing yield problem of in-cell touch panel manu-facturing process is presented in Section II. In Section III, we present the manufacturing yield assessment using a yield measure index method and present the statistical properties of sample variance for Weibull in-cell touch panel manufacturing processes. In addition, we present a manufacturing yield assessment to accommodate undetected variance changes. We also show the accommodation of the process capability index would not be affected by the scale parameter of Weibull distribution. To illustrate the applicability of the proposed manufacturing yield assessment, a real-world case taken from the manufacturing process in an in-cell touch panel manu-facturing factory is shown in Section IV. Finally, Section V provides the conclusions.
II. In-Cell Touch Panels Manufacturing
Yield Problem
In-cell touch panel manufacturing technologies have at-tracted many practitioners to devote their efforts since in-cell touch panels allow for slimmer and lighter devices as well as improve backlight penetration for brighter displays which are extensively applied in the high-end devices recently. Since
Fig. 2. Diagram of electrode.
the touch sensor is integrated into LCD stack by sharing LCD process, the touch electrodes are made by ITO (Indium Tin Oxide) thin film in the LCD array manufacturing process. Thus, the photolithography operation and etching operation are used to form the pattern of touch electrodes on the thin film. Fig. 2 shows the sensing ITO lines (brown) and driving ITO lines (green).
In the manufacturing process of forming the pattern of touch electrodes, it is noted that surface resistance is an essential specification. It needs uniform surface resistance to obtain uniform touching performance. Higher or lower resistance degrades touch and display performance since touch sensing signal is synchronized with periodic display signal. When resistance value changes, the synchronization between touch and display operation have been changed. Some touch panel controller could compensate un-uniform surface resistance, but the cost increases. It is indeed that touch panel maker should be compliant to the resistance specification in order to increase manufacturing yield.
In the in-cell touch panel manufacturing process, inappropriate photolithography or etching operations may cause over- or insufficient etching. When some defects occur in the ITO patterning operation, the malfunction of display (such as bridge and short) is accompanied. These situations may cause the negative side effect that is the un-uniform surface resistance may raise and the variance of surface resistance may change. Notably, data of surface resistance collected from shop floor is skewed distributions that are bounded on one side occur frequently in industry, since open or short electrodes may cause the resistance raise dramatically. It is better described by Weibull than by normal distribution. Weibull distribution is a very flexible distribution and can easily be fit to many data sets. In addition, while the integration of the touch sensor into the LCD stack by sharing the LCD manufacturing process, the difficulties of the manufacturing technology raise and some inevitable process variations regarding inadequate electrodes may occur owing to the limitations of equipments, materials, and workmanship may not be detected within short time. To avoid overestimating
TABLE I
Corresponding Yield and NCPPM for Various Values of Yield Measure Index
the manufacturing yield and successfully implement any corrective action for quality improvement programs, we present a modified yield measure index in this paper.
III. Capability Index Approach for In-cell Touch
Panel Manufacturing Yield Assessment
Manufacturing yield has been the most basic and critical criterion used in the manufacturing industry for measuring process performance. Since the fiercer competition in global portable devices market, such as smartphone and tablet PC, manufacturing yield assessment for in-cell touch panel pro-cesses is very important. It is noted that typical yield mea-sure index is applied to assess manufacturing yield under stable normal process (Montgomery [2], Pearn and Kotz [3]). However, surface resistance data collected from shop floor is better described by Weibull than by normal distribution and undetected variance changes may occur. Consequently, typical yield measure index may not be applied directly.
A. Manufacturing Yield for Stable Normal Process
In many in-plant applications, yield-based index Cpk is commonly used as an effective tool to assess manufacturing yield, which can provides bounds of the process yield for a normally distributed process with a fixed value of Cpk. This approach can measure the process departures from the target value and the magnitude of process variance. The index Cpk proposed by Kane [4] and defined as min{(USL − μ)/3σ, (μ− LSL)/3σ}, where USL and LSL are the upper and lower specification limits, respectively; μ is the process mean and
σ is the process standard deviation. Table I presents various commonly used capability requirement and the corresponding overall process yield associated with non-conformities (NC in parts per million, NCPPM).
In Table I, it is no more than 2700 NCPPM while the value of Cpk is equal to 1. As the value of Cpk is equal to 1.33, the defect rate drops to 66 ppm. To attain less than 0.002 ppm defect rate, a Cpk value of 2.00 is required (see Montgomery [2]).
B. Manufacturing Yield for Weibull in-Cell Touch Panel Manufacturing Process with Undetected Variance Changes
In-cell touch panel is a Weibull-distributed process with undetected variance changes resulting from the limitations
of equipments, materials, and workmanship. However, typical yield-based index Cpk has two essential assumptions that are the process is in a state of stable and normal. Bothe [5] consid-ered mean shifts and Pearn et al. [6] investigated the variance changes for normal processes, respectively. However, the in-cell touch panel manufacturing process is not approximately normal-distributed. In addition, Hsu et al. [7] and Pearn et al. [8] investigated mean shifts and variance changes for Gamma manufacturing process environments, respectively. In fact, in many real situations, the surface resistance data collected from some in-cell touch panel shop floors are Weibull-distributed. It should be noted that Weibull distribution, with various values of α and β, is a very flexible distribution and can cover a wide class of non-normal applications in the industry (Rinne [9]).
The Weibull distribution can be denoted as Weibull (α, β) with cumulative distribution function and the probability den-sity function given by
FX(x) = 1− e−(x/α)
β
, x≥0,
and
f(x) = βα−βxβ−1e−(xα)β, x≥0,
where α(>0) is the scale parameter, and β(>0) is the shape parameter. The mean and variance of Weibull distribution are
μ= α[(1 + β−1)] and
σ2= α2(1 + 2β−1) −2(1 + β−1),
respectively. As it can be seen in Fig. 3, the Weibull distribu-tion covers a wide class of non-normal applicadistribu-tions.
1) Stability Control Using S2 Chart for Weibull in-Cell Touch Panel Process: Control chart is widely used to identify
shifts or drifts in processes. In this paper, we investigate the effects on the manufacturing yield assessments for in-cell touch panel manufacturing process in which the manufacturing data is a Weibull distribution with undetected variance change. The S2 control chart is a common and effective tool to
monitor process variability. However, when we apply the control chart, some essential assumptions should be satisfied, such as the process characteristics must follow normal dis-tribution. Since the in-cell touch panel process investigated in this paper is Weibull-distributed, violating the assumption, we need to replace the traditional upper and lower control limits, ¯S2n− 1χ2
α/2,n−1 and
¯S2n− 1χ2
1−(α/2),n−1, as quantiles of the cumulative distribution function from different parameters of Weibull (α, β), where ¯S2 is an unbiased
estimator of σ2.
It should be noted that the explicit close forms regarding the probabilities of detecting variance change using the S2 control chart are rather complicated for Weibull-distributed data. To avoid overestimating manufacturing yield, we suggest the power of the S2 chart for in-cell touch panel Weibull-distributed data based on the UCL and LCL be obtained using the simulation technique. In the paper, to investigate the behavior of sampling distribution of variance for Weibull data and determine the estimated upper and lower control limits, the Monte-Carlo simulation method is applied. Three steps of
Fig. 3. Probability density functions for Weibull distribution with different parameter combinations.
the Monte-Carlo algorithm to determine the control limits of
S2 control chart are summarized as follows:
Step1: Generate N preliminary samples from Weibull (α, β),
each of size k. Let Sibe the variance of the ith sample.
Step2: Sort Si and obtain S(1)<S(2)<...<S(N). Let ˆtp be the percentile for Si.
Step3: Calculate the ˆt0.99865 and ˆt0.00135. Let ˆt0.99865 be the
upper control limit and ˆt0.00135 be the lower control
limit for Weibull (α, β).
Applying the Monte-Carlo approach, we can obtain the
UCL and LCL. Then, the power of S2 for Weibull process
data is derived. Type II error β is
β= PLCL≤S2≤UCL|σ1= kσ0
= PF0.00135≤S2≤F0.99865|σ1= kσ0
= GS2(F0.99865)− GS2(F0.00135) ,
where 1− β is the detection power of the process and σ1
is the new standard deviation after the variance change (σ0
is the standard deviation of the original process). In addi-tion, GS2(·) represents the empirical cumulative distribution
function of sample variance from Weibull distribution with variance change. The F0.99865 and F0.00135 are the percentile
points of the cumulative distribution function (CDF) of the Weibull-distributed process. The control limits LCL and UCL are calculated as F0.00135 and F0.99865, respectively.
We develop a MATLAB program to compute the probabil-ity of process variance out of control limits. When process variance changes from σ2 to (kσ)2 and mean is fixed, the
parameters α and β will change to new parameters α and
β. We can obtain the detection power under the situation that
the process variance changes. The parameters α and β can be obtained using the following steps:
Step1: Assume the new standard deviation σ1= k×σ, and k, μ, and σ are all known.
Step2: The mean and variance of Weibull distribution are μ = α[(1 + β−1)] and σ2= α2[(1 + 2β−1)− 2(1 + β−1)].
Then, we compute σ1 divided by μ as follows: σ1 μ = α2[(1 + 2β−1)− 2(1 + β−1)] α[(1 + β−1)] = [(1 + 2β−1)− 2(1 + β−1)] [(1 + β−1)] .
Step3: The new scale parameter (α) and shape parameter (β) can be obtained.
Table II shows the detection power when the surface re-sistance data of an in-cell touch panel process is Weibull-distributed and α = 1 as well as β =3, 4, and 5. The various magnitudes of variance change in σ are 1.0(0.5)3.5. In Table II, it should be noted that for the S2 chart with
sample subgroup size n = 9 in Weibull (1,5), the chance of catching a σ0 variance change would only 0.26 percent.
Such low probabilities indicate that small changes of variance may not be detected within short time in in-cell touch panel manufacturing process.
2) Manufacturing Yield Assessment: For the Weibull
in-cell touch panel manufacturing processes with variance change, to circumvent the undetected variance change causing the incorrect manufacturing yield calculation, we consider the magnitude of standard deviation change. AS50is the magnitude
of standard deviation change we need to accommodate when the detection power is fifty percent. In this paper, we set
TABLE II
Detection Powers of theS2Chart for Various Weibull
Distributions with Various Sample Subgroup Sizes
the detection power is equal to 0.5 since the most common industrial applications are to set average run length to 2. In addition, we develop a MATLAB program to compute the accommodation for various variance changes. We fix detection power which can be shown as PLCL≤S2≤UCL |σ1= kσ0)
= 0.5 and find k. Tables II and IV display the magnitude of standard deviation change (AS50) in which data come
from various Weibull (1, β) distributions for various values of β =1(1)24 and n = 10(1)32.
In Table III, we can find that if β is 3 with n = 10, the value of AS50 is 1.785. When β = 1, AS50 are all greater than 2.5.
It can be found that changes in σ smaller than AS50σ would
likely be missed. Consequently, AS50 would be the marginal
size of the undetected standard deviation change we should accommodate.
3) Discussion: It is particularly noted that the calculation of AS50 would not be affected by the scale parameter (α)
of a Weibull distribution. In the paper, we apply a cubic polynomial approximation method provided by Lu [10]. The essential idea of the cubic polynomial approximation method is to use the three quantiles to approximate the sum of multiple Weibull distributions. Applying a cubic polynomial approxi-mation method, we can compute the probability of ¯Xn when
X1, ..., Xnis a random sample from Weibull (α, β), and if we let Yi = Xi/αthen we have Yi= Xi/α∼ Weibull(1,β) and
¯ Y = n i=1 Yi n = n i=1 (Xi/α) n ∼ Weibull 1 n, β . (1) From Eq. (1) we can obtain
P LCL≤ ¯X≤UCL = P LCL α ≤ ¯Y≤ UCL α = P FX¯(0.00135)≤ ¯X≤FX¯(0.99865) . (2) The control limits LCL and UCL are calculated as
FX¯(0.00135) and FX¯(0.99865) are 0.135th and 99.865th percentiles
Fig. 4. The AS50curves of the Weibull process with different α values for
various n values on the horizontal. (a) α = 1. (b) α = 3.
of ¯Xof sampling distribution. We can obtain the approximate CDF of ¯Xdistribution which Lu [10] provided. Consequently, from Eq. (2), without loss of generality, we can set α = 1 to obtain the value of AS50. We can infer the accommodations
in standard deviation change, AS50, would not be affected by
the scale parameter α. Fig. 4 depicts the AS50 curves of the
two Weibull processes with scale parameters α = 1 and α = 3 for subgroup sizes n = 10, 15, and 20. It can be seen that the magnitude of standard deviation change would not change for α values.
C. Manufacturing Yield Calculation
It is noted that in-cell touch panel manufacturing pro-cess is better described by Weibull-distributed. In addition, manufacturing yield may be overestimated due to inevitable process variance changes. Chen and Pearn [11] considered come generalizations of these basic capability indices to cover non-normal distributions. In the non-normal case, if we are able to find a better distribution from the data, which provides a satisfactory fit, we can obtain more accurate measures of the
TABLE III
AS50Values for Various Subgroup sizen and β=1(1)12
TABLE IV
AS50Values for Various Subgroup sizen and β = 13(1)24
three quantiles (F0.00135,F0.5, and F0.99865) under consideration,
the corresponding Cpu and Cpl are defined as:
Cpu= USL− F0.5 F0.99865− F0.5 , and Cpl= F0.5− LSL F0.5− F0.00135 .
The index Cpk can be calculated as the minimum of Cpu and Cpl, namely: Cpk = min Cpu, Cpl = min USL− F0.5 F0.99865− F0.5 , F0.5− LSL F0.5− F0.00135
Since standard deviation change ranging from 0 up to AS50σ
may not be detected by control chart within short time and overestimation of the manufacturing yield may give incorrect
feedback to the process control, the optimal approach is to simply accommodate any standard deviation change no greater than AS50σ. When yield is calculated via the capability index,
the AS50 must be incorporated into the capability assessment.
Consequently, in this paper, we incorporate AS50 into the
manufacturing yield assessment. We replace F0.99865 − F0.5
and F0.5− F0.00135 with AS50(F0.99865− F0.5) and AS50(F0.5− F0.00135) in the new Cpk formula and present in the following:
Cpk = min F0.5− LSL AS50(F0.5− F0.00135) , USL− F0.5 AS50(F0.99865− F0.5) = min F0.5− LSL AS50×F0.5− AS50×F0.00135 , USL− F0.5 AS50×F0.99865− AS50×F0.5 .
Fig. 5. Weibull probability plot of the data.
where F0.00135, F0.5, and F0.99865 are the percentile points
of the CDF of the Weibull -distributed in-cell touch panel manufacturing process. The methodologies used in this paper, is quite general. It can be applied to Gamma distributions, normal distributions, non-central chi-square distributions, and other distributions [6], [8], [12], [13].
IV. Manufacturing Yield Assessment for In-cell
Touch Panel Manufacturing Process
To demonstrate the applicability of the proposed manufac-turing yield assessment method, we consider a factory appli-cation taken from an in-cell touch panel manufacturing fac-tory located in the Science-based Industrial Park at Hsinchu, Taiwan. In the case investigated, we consider the product type of TOD3205, which belongs to touch in display TID product series. Surface resistance is a critical specification in the in-cell touch panel manufacturing process. Higher or lower resistance degrades touch and display performance since touch sensing signal is synchronized with periodic display signal. Consequently, it is necessary to monitor the manufacturing stability of the electrode and control the surface resistance into the designated control limits.
In the section, we present a case to illustrate the application of the new capability index with variance change when the data of surface resistance collected from in-cell touch panel manufacturing processes are Weibull-distributed. In the case, specifications on surface resistance for the TOD3205 product are 5, 7.5, and 10 k for LSL, Target, and USL, respectively. We collect 100 observations. Using the probability plot, the result indicates that the data approximates to be distributed as Weibull distribution since the p-value is greater than 0.250 (see Fig. 5). It is evident to conclude that the data collected from the in-cell touch panel shop floor is not Gamma-distributed by observing the probability plot in Fig. 6. In the Weibull distribution, values of the scale and shape parameters can be obtained as ˆα = 6.973 and ˆβ = 19.04, respectively.
As the case is a Weibull process, the three percentiles can be obtained in the following: ˆF0.00135= 5.2985, ˆF0.5= 6.8134,
and ˆF0.99865= 7.6237. The calculated value of the conventional
ˆ
Cpk is 1.1970. Thus, the corresponding manufacturing yield
Fig. 6. Gamma probability plot of the data.
is 99.967% and the number of non-conformities in parts per million (NCPPM) is 329.412. The value of the conventional
ˆ
Cpkis not incorporated the accommodation of variance change and the yield would be overestimated.
As the value of ˆβ is 19.04, the value of AS50 is 1.756
when subgroup size n = 20 (see Table IV). The value of the modified process capability ˆCpk can be calculated as 0.6817. The value of the manufacturing yield is 95.916% and the number of non-conformities in parts per million (NCPPM) is 40845. It is noted that as the subgroup size is increased to 25, the value of AS50 is 1.660. The value of the modified
process capability ˆCpk can be calculated as 0.7211. The value of the manufacturing yield is 96.948% as well as the number of non-conformities in parts per million is 30518. Using our method, the process capability and manufacturing yield can be obtained more accurately and the decisions are made more reliably.
V. Conclusion
In-cell touch panel manufacturing process performs the thinnest and lightest structure and has become new trend for fantastic user experience. The requirement of integration of in-cell touch panel manufacturing process would increase the difficulties of manufacturing. In in-cell touch panel manufac-turing factories, surface resistance is a critical specification for uniform touch performance. Data of surface resistance is better described by Weibull- distrbuted. In addition, the typical yield measure approach ignored the fact that the variance of surface resistance may change. For the Weibull in-cell touch panel manufacturing processes, we applied the Monte-Carlo simula-tion method to determine the control limits of S2 control chart
and calculated the accommodations for various subgroup sizes (n) and Weibull parameter (β) with the designated detection power. We also showed the accommodation of the process capability index would not be affected by the scale parameter of a Weibull distribution. To avoid the overestimation of manufacturing yield, we presented a capability index method to calculate the manufacturing yield incorporating the factor of variance change. To demonstrate the applicability of the proposed method, we considered a real-world in-cell touch panel shop floor applications taken from the factory located
in the Science-based Industrial Park at Hsinchu, Taiwan. The computational results showed that changing the sample subgroup sizes n, different values of capability indices would be obtained. Consequently, the corresponding manufacturing yields can be obtained more accurately. The results obtained could help the practitioners to make more reliable decisions on what actions need to take in controlling their in-cell touch panel manufacturing processes.
Acknowledgements
The authors would like to thank the anonymous referees for their helpful comments and careful reading, which signif-icantly improved the paper.
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Yu-Ting Tai received the Ph.D. degree in industrial
engineering and management from National Chiao-Tung University, Hsinchu, Taiwan. She is currently an Associate Professor with the Department of Infor-mation Management, Kainan University, Taoyuan, Taiwan. Her research interests include process capa-bility indices, scheduling, and semiconductor manu-facturing management.
Wen Lea Pearn received the Ph.D. degree in
op-erations research from the University of Maryland, College Park, MD, USA.
He is currently a Professor of Operations Research and Quality Assurance at National Chiao-Tung Uni-versity (NCTU), Hsinchu, Taiwan. He was with Bell Laboratories as a member of Quality Research Sci-entist before joining NCTU. His research interests include process capability, network optimization, and production management. His publications have appeared in the Journal of the Royal Statistical
Soci-ety, Series C, Journal of Quality Technology, European Journal of Operational Research, Journal of the Operational Research Society, Operations Research Letters, Omega, Networks, International Journal of Productions Research, and
others.
Kai-Bin Huang received the Ph.D. degree in
in-dustrial engineering and management from Na-tional Chiao-Tung University, Hsinchu, Taiwan. He is currently an Engineer with the Measure-ment/Calibration Technology Department, Electron-ics Testing Center, Taiwan. His research interests include queueing theory, optimization theory, quality engineering, and applied statistics.
Lu-Wei Liao received the master’s degree in
in-dustrial engineering and management from National Chiao-Tung University, Hsinchu, Taiwan. He is currently a Senior Engineer in the Manufacturing Department, Taiwan Semiconductor Manufacturing Company, Hsinchu. His research interests include process capability indices, quality engineering, and applied statistics.
