Abstract—Process yield is the most common criterion used in the semiconductor manufacturing industry for measuring process performance. In the globally competitive manufacturing environment, photolithography processes involving multiple man-ufacturing lines are quite common in the Science-Based Industrial Park in Hsinchu, Taiwan, due to economic scale considerations. In this paper, we develop an effective method for measuring the manufacturing yield for photolithography processes with multiple manufacturing lines. Exact distribution of the estimated measure is analytically intractable. We obtain a rather accurate approximation to the distribution. In addition, we tabulate the lower conference bounds based on the obtained approximated distributions for the convenience of industry applications. We also develop a decision-making method for process precision testing to determine whether a process meets the process yield requirement preset in the factory. For illustration purposes, an application example is included.
Index Terms—Capability index, lower confidence bound, multiple manufacturing lines, process yield.
I. Introduction
T
HE PROGRESS in semiconductor manufacturing tech-nologies has led to the wide use of electronic devices applications. Due to competition from the global semiconduc-tor manufacturing industry, smaller die size should be achieved to reduce manufacturing costs. In a wafer fabrication, the photolithography process is considered a bottleneck and has the greatest impact on manufacturing yield [1], particularly, for small-die-size product types. Photolithography is the process of transferring geometric shapes on a mask to the surface of a silicon wafer. Photolithography process results are crucial to the final functions of one product in the semiconductor manufacturing process. A typical photolithography process consists of seven major steps [2]: pretreatment or priming, spin coating, prebake, exposure, post-exposure bake, develop-ment, and metrology. Fig. 1 depicts the exposure operation, which is the operation of transferring circuit patterns on aManuscript received June 12, 2011; revised September 20, 2011; accepted November 27, 2011. Date of publication December 13, 2011; date of current version May 4, 2012.
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 is with the Department of Industrial Engineering and Man-agement, National Chiao Tung University, Hsinchu 300, Taiwan (e-mail: wlpearn@mail.nctu.edu.tw).
C.-M. Kao is with the Institute of Statistics, National Chiao Tung University, Hsinchu 406, Taiwan (e-mail: cmkao1031@gmail.com).
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.2011.2179568
Fig. 1. Exposure operation.
mask to a wafer. In the photolithography process, the most essential specification is critical dimensions (CDs), that is defined as the linewidth of the photo resist line printed on a wafer and reflects whether the exposure and development are proper to produce geometers of the correct size [3]. In wafer fabrications, it is essential to assess the manufacturing yield on the photolithography process; it could provide feedback to engineers on what actions need to take for manufacturing yield control and improvement.
Since the photolithography process requires very low frac-tion of defectives in parts per million (ppm), process capability indices (PCIs) have been widely and popularly applied in quality assurance in recent years. Capability measures for processes with a single line have been investigated extensively [4]–[9]. However, in most globally competitive wafer fabrica-tions, a process with multiple manufacturing lines is common, particularly, for the wafer fabs in the Science-Based Industrial Park in Hsinchu, Taiwan. In those wafer fabs, a photolithogra-phy process with multiple manufacturing lines consists of mul-tiple parallel independent manufacturing lines, with each man-ufacturing line having a machine or a group of machines per-forming necessary identical job operations. As the manufac-turing lines have various process averages and standard devia-tions, the values of PCIs will be different for each manufactur-ing line. The combined output of all manufacturmanufactur-ing lines leads to inaccurate yield measures of the photolithography process. In this paper, to assess the manufacturing yield for pho-tolithography process with multiple manufacturing lines, we present a new capability index (SM
pk) method for exact
man-ufacturing yield calculation. This paper is organized as fol-lows. Section II presents the manufacturing yield problem of the photolithography process with multiple manufacturing lines. Section III shows the new process capability index SpkM for processes with multiple manufacturing lines and the distribution of ˆSM
pk. Section IV provides the lower confidence
bound of SpkM and decision making on whether a process
Fig. 2. Photolithography process with multiple manufacturing lines.
with multiple manufacturing lines is capable. For illustration purposes, an application example is provided in Section V. Finally, Section VI includes the conclusions.
II. Manufacturing Yield of the Wafer Photolithography Process
In semiconductor manufacturing processes, the wafer pho-tolithography process is the most essential process; it requires high resolution, precise alignment, and low defect density. In general, a common thin-film transistor liquid crystal display (TFT-LCD) driver integrated circuit (IC) chip used in smart phone usually needs more than 30 masks for the exposure and developing steps which is a complex process and needs precise process yield assessment and control. In the photolithography process, CDs are the most important specification. To control the photolithography process effectively, CD measurements must be made on each layer in the manufacturing process [10]. For example, in CMOS semiconductor manufacturing process, poly layer is mainly used to fabricate the gate terminal of CMOS devices. Poly width is a CD in photolithography process that affects the manufacturing yield in two ways. First, thinner poly width of a random access memory (RAM) cell used in TFT-LCD driver IC may cause device leakage current in the order of several tens of times. It is noted that a TFT-LCD driver IC of high definition 720 (HD720) (720RGB×1280) product type involves 720×1280×24 RAM cells. That means total leakage current would be 100 million times when comparing original requirement. It is unexpected since more power consumption resulting from greater leakage current could shorten battery duration on portable devices.
In addition, wider poly width would consume larger device layout area, especially, for a high-definition application. Take HD720 TFT-LCD driver IC for example, if poly width on each RAM cell has been increased, it would cause same proportion area increasing. It is uncompetitive and cannot satisfy the trend of smaller portable devices applications. In the shop floor, if the process parameter is out of control, some yield improve-ment actions must be initiated immediately. Consequently, ob-taining the accurate process yield is very essential which could feedback to internal photo process engineers or external prac-titioners in IC design houses and make yield improvements.
It should be noted that a photolithography process usually consists of multiple manufacturing lines in the Science-Based
Industrial Park. Fig. 2 depicts four manufacturing lines in-volved in a photolithography process. Since the manufacturing lines have various process averages and standard deviations, the values of process capability indices will be different for each manufacturing line. To access the manufacturing yield of the combined output of all manufacturing lines for the photolithography process, we provide a new overall index SM
pk
to obtain the exact yield measure in the subsequent section. III. Overall Manufacturing Yield Measures for
Photolithography Processes with Multiple Manufacturing Lines
Process yield, the percentage of processed product unit passing the inspection, has been the most basic and common criterion used in the semiconductor manufacturing industry for measuring process performance. Due to competition in wafer fabrications, the manufacturing yield of a photolithography process demands very low fraction of defective, normally mea-sured by ppm or parts per billion. Bolyes [6] considered the yield measurement index Spkfor normal processes with single
manufacturing line. It provides exact measure of the process yield for a normally distributed process with a fixed value of Spk. To assess the photolithography process with multiple
manufacturing lines, we present the new yield measure index SM
pk and show its distribution.
A. Yield Measure Index SM pk
For the process with multiple manufacturing lines, we con-sider a k-lines process with k yield measures P1, P2, . . . , and Pk. We propose the overall capability index for the multiple
manufacturing lines process, referred to as SM
pk, as follows: SpkM = 1 3 −1 ⎧ ⎨ ⎩ ⎡ ⎣1 k k j=1 (2(3Spkj)− 1) + 1 ⎤ ⎦ /2 ⎫ ⎬ ⎭ (1)
where Spkjis the Spk value of the jth line for j = 1, 2, . . . , k.
The new index, SM
pk, can be viewed as a generalization of
multiple manufacturing lines yield index. From (1), given SM pk = c, we have ⎧ ⎨ ⎩ 1 k k j=1 (2(3Spkj)− 1) ⎫ ⎬ ⎭= 2(3SMpk)− 1 = 2(3c) − 1. (2)
2.00 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002 0.002
A one-to-one correspondence relationship between the index SM
pk and the overall process yield P can be established as
P = 1 k k j=1 Pj = 1 k k j=1 [2(3Spkj)− 1] = 2(3c) − 1. (3)
Consequently, the new index SM
pkprovides an exact measure of
the manufacturing lines yield. It is noted that if SM
pk= 1.00, the
overall process yield would be exactly 99.73%. The number of nonconformities in parts per million (NCPPM) is 2699.8. We tabulated various commonly capability requirements and corresponding overall process yield in Table I. It can be seen from the definition that the weighted average is, indeed, independent of the number of manufacturing lines.
B. Distribution of ˆSM pk
To evaluate the overall yield measure index SM
pk, we consider
the following ˆSM
pk that can be expressed as
ˆSM pk = 1 3 −1 ⎧ ⎨ ⎩ ⎡ ⎣1 k k j=1 (2(3 ˆSpkj)− 1) + 1 ⎤ ⎦ /2 ⎫ ⎬ ⎭ (4)
where ˆSpkj denotes the estimator of Spkj. It should be noted
that the exact distribution of the overall yield index SMpk is
an-alytically intractable. Thus, we apply the Taylor expansion of k-variate and taking the first order, the asymptotic distribution of ˆSM pk can be expressed as ˆSM pk∼ N ⎛ ⎝SM pk, 1 36k2nφ(3SM pk) 2 k j=1 a2j + b2j ⎞⎠ (5) where aj={[(USL − μj)/ √ 2σj]φ[(USL− μj)/σj] +[(μj− LSL)/ √ 2σj]φ[(μj− LSL)/σj]}, bj ={φ[(USL − μj)/σj]− φ[(μj− LSL)/σj].
Variables aj and bj are the corresponding parameters of the
jth manufacturing line (see Appendix).
C. Accuracy of Yield Measure
To measure how accurate the normal approximation is, we conduct a simulation study using the statistical package as follows. For convenience to present our new development, we consider two manufacturing lines of a process. In the simulation scenario, the value of SM
pk is 1.00 and process
mean of the two investigated manufacturing lines are unequal. We simulate 10 000 000 random sample of size n = 60, 100, 500, 1000 from N2(μ1, μ2,σ12, σ22,0), a normal process with two independent lines. In addition, we compute 10 000 000 ˆSM
pk using (4). Figs. 3 and 4 depict approximate
and exact distributions, it is clear that as the sample size n = 1000, the approximate and simulated distributions are almost indistinguishable. In fact, even with n = 60, the approximation is quite reasonable for practical purposes.
IV. Decision Making on Photo Processes With Multiple Manufacturing Lines
For in-plant applications, to calculate the yield index with multiple manufacturing lines, sample data must be collected. It is noted that a great degree of uncertainty may be introduced into capability assessments due to sampling errors. Conse-quently, conclusions based on the calculated values will lead to make unreliable decisions as the sampling errors have been ignored. A reliable approach for assessing the true value of process index is to construct the lower confidence bound. The lower confidence bound is not only essential to manufacturing yield assurance but also can be used in capability testing for decision making.
A. Lower Confidence Bound
It should be noted that the variance of ˆSM
pk is not identical
for a fixed value of SM
pk. Since the sampling distribution of ˆSpkM
can be presented in 2k + 1 parameters, aj, bj, j = 1, . . . , k, and
SpkM (5), the lower confidence bound (SpkMLB) is also a function
of those parameters. Thus, we have to consider the effect of all the parameters in the calculation of lower confidence bound to ensure that the lower bounds obtained are reliable. The word “reliable” here means that the probability that the obtained lower bound (subject to the sample estimate) is smaller than the actual capability index SM
pk and is greater than the desired
confidence level. For a process with two manufacturing lines, i.e., k = 2, we note that for an identical value of SM
pk, there are
numerous combinations of Spk1and Spk2. Fig. 5 shows the
Fig. 3. Comparison of normal approximate and exact densities via simulations.
For a fixed value of Spkj, there are numerous combinations
of aj and bj. Table II displays some combinations of the
parameters Spk1, Spk2, a1, a2, b1, and b2 under SpkM = 1,
and the corresponding lower confidence bounds of SMpk. Our
extensive calculation results show that: 1) the lower confidence bound of SM
pkobtains its maximum at Spk1=Spk2, and minimum at Spk1 ≥ 2.5 and Spk2 = (1 3)−1[2 (3SM pk)− 1 (or Spk1 = (1 3)−12(3SM pk)− 1
and Spk2 ≥ 2.5); and 2) for fixed values of Spk1 and Spk2, the lower confidence bound of
Fig. 4. Comparison of (a) approximate and (b) exact cumulative distribution function.
SpkM reaches its minimum at b1 = b2 = 0. Figs. 6 and 7 show lower confidence bounds plot of a two manufacturing-line process and plane curve for SM
pk = 1.00, 1.33, 1.50, 1.67, 2.00.
Consequently, to obtain the reliable lower bound, we set Spk1 = 2.5, Spk2 = (1 3)−1(2 (3SM pk) − 1), a1 = √ 2(3Spk1)φ(3Spk1), a2= √ 2(3Spk2)φ(3Spk2), and b1= b2= 0. For general cases, two essential results are listed as fol-lows: 1) for an identical value of SM
pk, the lower confidence
bound of SM
pk is minimum at Spki = (1
3)−1k(2(3SM pk)
1.00 1.00 0.0163711 0.0163711 −0.0083220 −0.0083220 0.9761508 1.00 1.00 0.0163711 0.0163711 −0.0083220 −0.0083220 0.9761508 1.00 1.00 0.0163711 0.0163711 −0.0083220 −0.0083220 0.9761508 1.00 1.00 0.0163711 0.0163711 −0.0083220 −0.0083220 0.9761508 1.33 0.9287227 0.0007859 0.0324173 0.0000000 0.0000000 0.9628229 1.33 0.9287227 0.0007314 0.0316824 0.0002593 −0.0067986 0.9628548 1.33 0.9287227 0.0007249 0.0283878 −0.0002676 −0.0145563 0.9639949 1.33 0.9287227 0.0007245 0.0277405 −0.0002680 −0.0152509 0.9645474 1.33 0.9287227 0.0007245 0.0276590 −0.0002680 −0.0153112 0.9646420 1.33 0.9287227 0.0007245 0.0276524 −0.0002680 −0.0153149 0.9646509 1.33 0.9287227 0.0007245 0.0276520 −0.0002680 −0.0153151 0.9646514 1.33 0.9287227 0.0007245 0.0276520 −0.0002680 −0.0153151 0.9646514
Fig. 5. Combinations of Spk1and Spk2for SpkM= 1.00, 1.33, 1.50, 1.67, 2.00
(from bottom to top).
Fig. 6. Lower confidence bounds plot of a two manufacturing-line process for SM
pk= 1.00, 1.33, 1.50, 1.67, 2.00 (from bottom to top).
−1) − (k − 2)]2and Spkj ≥ 2.5, where j = i; and 2) for fixed value of Spkj, the lower confidence bound of SMpkreaches
its minimum at bj = 0, i.e., the mean is on-center.
Conse-quently, in the calculation of lower confidence bound of SM pk, we set Spki= (1 3)−1k(2(3SM pk)− 1) − (k − 2) 2and Spkj ≥ 2.5, for all j = i, aj = √ 2{3Spkjφ(3Spkj)}, and bj = 0
for all j = 1, . . . , k. In this way, the level of confidence can be ensured, and the decisions (lower confidence bound) made based on such an approach are indeed more reliable.
We note that with the above parameters setting, the sampling distribution of SMpkcan be written in a shorter and simpler form,
that is ˆSM pk∼ N SpkM, D 2φ2(3D) 2k2nφ2(3SM pk) (6) where D = (13)−1k(2(3SM pk)− 1) − (k − 2) /2}. Thus, given an estimated value of SMpk, a sample size n, the
number of manufacturing line k, a confidence level 1− α, and the lower confidence bound of SM
pk (denoted as S M LB pk ) can be obtained as follows: SMpkLB = ˆSpkM − Zα ˆ Dφ(3 ˆD) k√2nφ(3 ˆSM pk) (7) where Zα is the upper 100α percentile of the standard normal
distribution.
B. Test for Decision Making on Photolithography Process Yield Measure
Using the index SM
pk, engineers can access the process
performance and monitor the manufacturing process on a routine basis. To test whether a given process with multiple manufacturing lines is capable, we consider that
H0: SpkM ≤ c versus H1: S M
Fig. 7. Plane curves of SMLB
pk versus Spk1 for S M
pk= 1.00, 1.33, 1.50, 1.67,
2.00 (from bottom to top).
can be executed by considering the testing statistic T = ( ˆS M pk− c)k √ 2nφ(3 ˆSM pk) ˆ Dφ(3 ˆD) (9) where ˆD = (13)−1k(2(3 ˆSM pk)− 1) − (k − 2) /2} . The null hypothesis H0 is rejected at α level if T > zα, where zα
is the upper 100α% point of the standard normal distribution. For more general cases with unequal production quantity for each line, our method can be easily extended as follows. We first take weighted average of the overall yield. We then convert the average of the overall yield into the corresponding value of SM
pk.
V. Manufacturing Yield Assessment for Photolithography Processes
In this section, to demonstrate the applicability of the pro-posed method, we consider a real-world application taken from a wafer fab located in the Science-Based Industrial Park. For the case investigated, a high-voltage manufacturing process is applied on the product type that includes 32 various masks. To control the photolithography process effectively, CD measure-ments are made on each layer in the manufacturing process. In the case, we focus on the specification of poly width on RAM cells in the essential poly layer for TFT-LCD driver IC product series. It is noted that three manufacturing lines are involved in the process. The upper and lower specification limits of the critical dimension parameter for the high-density product type are set to 118 nm and 102 nm, respectively. Measurement data are collected from the shop floor via the designate sampling plans. In the case, 100 sample observations of the critical dimension are collected from each manufacturing line in the photolithography process. Sample mean, sample standard deviation, and the values of ˆSpkj are shown in Table III.
Using the proposed method in this paper, we can assess the value of ˆSM
pk that is equal to 1.2089. The process yield
of the photolithography process is 99.9713% and the number of NCPPM is 287.066. For testing the null hypothesis H0 with c = 1 against the alternative hypothesis as given in (8), the testing statistic T , as given in (9), can be calculated as
TABLE III
Calculated Statistics of the Three Manufacturing Lines (Unit:nm)
Lines ¯xj sj ˆSpkj
1 112.5494 1.7383 1.1112
2 108.1011 1.3645 1.5391
3 111.9718 0.9383 2.1764
2.864724. Since 2.864724 is greater than the value of Z0.05, the null hypothesis H0is rejected at α=0.05. We may conclude that the process satisfies the capability requirement SM
pk ≥ 1.00.
A. Discussion
In existing literature [11], [12], the authors considered a yield index with multiple process streams. In the application and calculation in Wang et al. [12], they calculated the estimated yield using ˆSM
pk =
1k kj=1 ˆSpkj. The estimator
of SM
pk, considered by Wang et al. [12], would certainly
overestimate the process yield as stated in Wang et al. [11]. Further, the variance of ˆSM
pk considered in Wang et al. [12]
remained random variables as ˆa and ˆb. This problem can be resolved by analyzing the combination of values of SpkjM ,
j= 1, . . . , k, which is accomplished in this paper.
VI. Conclusion
Process yield is the most common and standard criterion for use in the manufacturing industry for measuring process performance. Capability measures for processes with a single manufacturing line have been investigated extensively. As many industry cases today, it is common that a process simultaneously involves more than one manufacturing line. In this paper, the yield index SpkM provided an exact measure on
the manufacturing yield for photolithography processes with the multiple manufacturing lines. Unfortunately, the distribu-tion properties of the estimated SM
pk were mathematically
in-tractable. We used Taylor expansion technique, taking the first order, to obtain rather accurate approximate distribution. Con-sequently, the lower confidence bounds based on the developed distribution can be obtained. In addition, hypothesis testing was performed for implementing the method we proposed. Using the provided yield measure method, the practitioners can determine whether a process with multiple manufacturing lines meets the process yield requirement preset in the factory. The results obtained could help the practitioners to make more reliable decisions on what yield improvement actions need to be initiated in controlling the photolithography process with multiple manufacturing lines.
Appendix Taylor Expansion of ˆSM pk SpkM = 1 3 −1 ⎧ ⎨ ⎩ ⎡ ⎣1 k k j=1 (2(3Spkj)− 1) + 1 ⎤ ⎦ /2 ⎫ ⎬ ⎭
+
i=1 ∂ˆσ 2
i
( ˆσi − σi).
Differentiating implicitly with respect to ˆμj and ˆσj2, j =
1, . . . , k gives ∂f(μ1, . . . , μk, σ12, . . . , σk2) ∂μˆk = −1 6kφ(3SM pk) ×1 σj φ USL− μj σj −φ μj− LSL σj , j=1, . . . , k ∂f(μ1, . . . , μk, σ12, . . . , σk2) ∂ˆσ2k = −1 6kφ(3SM pk) 1 2σj2 × USL− μj σ2 j φ USL− μj σ2 j + μj− LSL σj2 φ μj− LSL σj2 . Consequently, we can obtain
ˆSM pk ≈ S M pk+ −1 6kφ(3SM pk) k j=1 Wj + Gj where SpkM = 1 3 −1 ⎧ ⎨ ⎩[ 1 k k j=1 (2(3Spkj)− 1) + 1]/2 ⎫ ⎬ ⎭ Wj = Xj− μj σj bjand Gj= S2 j−σj2 √ 2σ2 j aj aj= ! USL− μj √ 2σj φ USL− μj σj +μj√− LSL 2σj φ μj− LSL σj " bj = # φ USL− μj σj − φ μj− LSL σj " , j= 1, . . . , k. Let Zj = √ nXj− μj and Yj = √ nS2j − σj2, j = 1, . . . , k. Then, Zj and Yj are independent. Since the first two
moments of Xj and Sj2 exist, by the central limit theorem, Zj
and Yj converge to N 0 , σ2 j and N0 , 2σ4 j , respectively, where j = 1, . . . , k. Consequently, we can obtain E( ˆSpkM) ≈
E(SM pk) = SpkM and Var( ˆSpkM)≈ Var ⎧ ⎨ ⎩SpkM + −1 6kφ(3SM pk) k j=1 Wj + Gj ⎫⎬ ⎭ ≈ 1 36k2nφ(3SM pk) 2 k j=1 a2j+ b2j .
[4] F. K. Wang, “A general procedure for process yield with multiple characteristics,” IEEE Trans. Semicond. Manuf., vol. 23, no. 4, pp. 503– 508, Nov. 2010.
[5] J. C. Lee, H. N. Hung, W. L. Pearn, and T. L. Kueng, “On the distribution of the estimated process yield index Spk,” Qual. Reliab. Eng. Int., vol.
18, no. 1, pp. 111–116, 2002.
[6] R. A. Boyles, “Process capability with asymmetric tolerances,” Commun.
Statist.: Simul. Computat., vol. 23, no. 3, pp. 615–643, 1994.
[7] S. Kotz and N. L. Johnson, “Process capability indices-review, 1992– 2000,” J. Qual. Technol., vol. 34, no. 1, pp. 1–19, 2002.
[8] V. E. Kane, “Process capability indices,” J. Qual. Technol., vol. 18, no. 1, pp. 41–52, 1986.
[9] W. L. Pearn, S. Kotz, and N. L. Johnson, “Distributional and inferential properties of process capability indices,” J. Qual. Technol., vol. 24, no. 4, pp. 216–231, 1992.
[10] H. Y. Kang and A. H. I. Lee, “Critical dimension control in photolithog-raphy based on the yield by a simulation program,” Microelectron.
Reliab., vol. 46, nos. 5–6, pp. 1006–1012, 2006.
[11] D. S. Wang, T. Y. Koo, and C. Y. Chou, “Yield measure for the process with multiple streams,” Qual. Quantity, vol. 43, no. 4, pp. 661–668, 2009.
[12] D. S. Wang, T. Y. Koo, and C. Y. Chou, “Statistical inference on the multiple-stream yield index Spkm,” J. Statist. Manag. Syst., vol. 12, no. 4, pp. 671–678, 2009.
Y. T. Tai received the Ph.D. degree in industrial
engineering and management from National Chiao-Tung University, Hsinchu, Taiwan.
She is currently an Assistant Professor with the Department of Information Management, Kainan University, Taoyuan, Taiwan. Her current research interests include process capability indices, schedul-ing, and semiconductor manufacturing management.
W. L. Pearn received the Ph.D. degree in operations
research from the University of Maryland, College Park.
He is currently a Professor of operations research and quality assurance with National Chiao-Tung University (NCTU), Hsinchu, Taiwan. He was with Bell Laboratories, Holmdel, NJ, as a Quality Re-search Scientist before joining NCTU. His current research interests include process capability, network optimization, and production management. His pub-lications have appeared in the Journal of the Royal
Statistical Society, Series C, the Journal of Quality Technology, the European Journal of Operational Research, the Journal of the Operational Research Society, Operations Research Letters, Omega, Networks, and the International Journal of Productions Research.
Chun-Min Kao received the Masters degree in
statistics from the National Chiao-Tung University, Hsinchu, Taiwan.
She is currently a Product Engineer with the Video Solutions Integration Division, AU Optronics Corpo-ration, Taichung, Taiwan. Her current research inter-ests include statistical process control, experimental design, and applied statistics.
