• 대한산업공학회지
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• 제31권1호
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• pp.87-98
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• 2005

This research investigates economic-statistical characteristics of variable sampling size and interval (VSSI)$\bar{X}$charts under two assignable causes. A Markov chain approach is employed in order to calculate average run length (ARL) and average time to signal (ATS). Six transient states are derived by carefully defining the state. A steady state cost rate function is constructed based on Lorenzen and Vance(1986) model. The cost rate function is optimized with respect to six design parameters for designing the VSSI $\bar{X}$ charts. Computational experiments show that the VSSI $\bar{X}$ chart is superior to the Shewhart $\bar{X}$ chart in the economic-statistical sense, even under two assignable causes. A comparative study shows that the cost rate may increase up to almost 30% by overlooking the second cause. Critical input parameters are also derived from a sensitivity study and a few guideline graphs are provided for determining the design parameters.

• 대한산업공학회지
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• 제29권2호
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• pp.179-189
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• 2003

Gate poly-silicon critical dimension is a prime characteristic of a metal-oxide-semiconductor field effect transistor. It is important to achieve the uniformity of gate poly-silicon critical dimension in order that a semiconductor device has acceptable electrical test characteristics as well as a semiconductor wafer fabrication process has a competitive net-die-per-wafer yield. However, on gate poly-silicon critical dimension, the complexity associated with a semiconductor wafer fabrication process entails hierarchical variance components according to run-to-run, wafer-to-wafer and even die-to-die production unit changes. Specifically, estimates of the hierarchical variance components are required not only for disclosing dominant sources of the variation but also for testing the wafer-level uniformity. In this paper, two experimental designs, a two-stage nested design and a randomized complete block design are considered in order to estimate the hierarchical variance components. Since gate poly-silicon critical dimensions are collected from fixed die positions within wafers, a factor representing die positions can be regarded as fixed in linear statistical models for the designs. In this context, the two-stage nested design also checks the wafer-level uniformity taking all sampled runs into account. In more detail, using variance estimates derived from randomized complete block designs, Duncan's multiple range test examines the wafer-level uniformity for each run. Consequently, a framework presented in this study could provide guidelines to practitioners on estimating the hierarchical variance components and testing the wafer-level uniformity in parallel for any characteristics concerned in semiconductor wafer fabrication processes. Statistical analysis is illustrated for an experimental dataset from a real pilot semiconductor wafer fabrication process.

• Communications for Statistical Applications and Methods
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• 제9권2호
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• pp.347-354
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• 2002

An n-point design is maximal fan if all the models with n-terms satisfying the divisibility condition are estimable. Such designs tend to be space filling and look very similar to the ″Latin-hypercube″ designs used in computer experiments. Caboara, Pistone, Riccomago and Wynn (1997) conjectured that a maximal fan design on an integer grid exists for any n and m, where m is the number of factors. In this paper we examine the relationship between maximal fan design and latin-hypercube to give a partial solution for the conjecture.

• Communications for Statistical Applications and Methods
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• 제8권3호
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• pp.685-696
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• 2001

Robust design is an approach to reducing performance variation of response values in products and processes. In the Taguchl parameter design, the product-array approach using orthogonal arrays is mainly used. However, it often requires an excessive number of experiments. An alternative approach, which is called the combined-array approach, was suggested by Welch et. al. (1990) and studied by others. In these studies, only single response variable was considered. We propose how to simultaneously optimize multiple responses when there are correlations among responses, and when we use the combined-array approach to assign control and noise factors. An example is illustrated to show the difference between the Taguchi's product-array approach and the combined-array approach.

• 한국정밀공학회:학술대회논문집
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• 한국정밀공학회 2004년도 추계학술대회 논문집
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• pp.700-703
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• 2004

A reliability analysis and design procedure based on the design of experiment (DOE) is combined with the response surface method (RSM) for numerical efficiency. The procedure established is based on a 3$^n$ full factorial DOE for numerical quadrature using explicit formula of optimum levels and weights derived for general distributions. The full factorial moment method (FFMM) shows good performance in terms of accuracy and ability to treat non-normally distributed random variables. But, the FFMM becomes very inefficient because the number of function evaluation required increases exponentially as the number of random variables considered increases. To enhance the efficiency, the response surface moment method (RSMM) is proposed. In RSMM, experiments only with high probability are conducted and the rest of data are complemented by a quadratic response surface approximation without mixed terms. The response surface is updated by conducting experiments one by one until the value of failure probability is converged. It is calculated using the Pearson system and the four statistical moments obtained from the experimental data. A measure for checking the relative importance of an experimental point is proposed and named as influence index. During the update of response surface, mixed terms can be added into the formulation.

• 대한산업공학회지
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• 제7권2호
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• pp.55-59
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• 1981

An Application of Experimental Designs to Improve the quality of Industrial product : optimization Methodology of statistical model. The primary object of this paper is to aid scientists and Engineers, in applying response surface procedures to obtain operating conditions for many technical fields, particularly for industrial manufacturing processes. The problem considered in this paper is to select technically and scientifically some important factors affecting the quality of products through the experimental design and analysis of response surface. Even though the mathematical model is unknown these statistical analysis can be applicable to control the quality of industrial products and to determine optimum operating conditions for many technical fields, particularly, for industrial manufacturing processes. This paper proposes a method to obtain the optimum operating condition, and how to find the condition by using table of orthogonal array experiments, and optimization methodology of statistical model.

• 한국통신학회논문지
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• 제27권5C호
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• pp.465-473
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• 2002

In this paper the authors propose a theoretic framework to design the Virtual Private Network (VPN) via which the Quality of Services (QoSs) are guaranteed over IP networks. The required QoS is a very strict packet loss probability or a probability that packet delay does not exceed a certain target value in a statistical manner. QoSs are guaranteed by providing a statistical bandwidth similar to equivalent bandwidth, which is computed so that the provided bandwidth is sufficient to guarantee those requirements. Two typical network architectures are considered in constructing VPN, the customer pipe scheme and the Hose scheme, and we propose a method to compute the amount of the required bandwidth for the two schemes. Finally, we investigate the implication of the scheme via numerical experiments.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.983-989
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• 2005

Secondary batteries with high performance are essential in widespread use of modern portable devices such as cellular phones and laptop computers. High energy density, long cycle life, and safety are some of important requirements for secondary battery. To achieve such characteristics, a mixing proportion of electrolyte solution ingredients in the battery should be carefully chosen. In this paper, using statistical design of mixture experiments (DOME), we attempt to find an optimum condition of designing the secondary battery. DOME has a distinct feature in that the experimental region is represented by simplex, rather than hypercube, because the sum of blend proportions should be unity. Several designs based upon this point have been proposed for mixture experiments. Among them, an extreme vertices design is employed in this paper because there are a couple of blend constraints to be considered. In order to investigate how the mixing proportion interacts with other manufacturing factors, a fractional factorial design is also included across the extreme vertices design. As a result, we find that the blend proportion of solution ingredients has a significant effect on battery performances. By simultaneously optimizing two battery capacities, this paper proposes an optimum blend proportion according to process factor settings.

• Journal of the Korean Statistical Society
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• 제36권2호
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• pp.209-228
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• 2007

Given scattered surface air temperatures observed by a network of weather stations, it is an important problem to estimate the entire temperature field for every location on the globe. Recently, a multi-scale spherical basis function (SBF) representation was proposed by Li (1999) for representing scattered data on the sphere. However, for a successful application of Li (1999)'s method, some practical issues such as network design, bandwidth selection of SBFs and initial coefficients are to be resolved. This paper proposes automatic procedures to design network and to select bandwidths. This paper also considers a preprocessing problem to obtain a stable initial coefficients from scattered data. Experiments with real temperature data demonstrate the promising empirical properties of the proposed approaches.

• 한국염색가공학회지
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• 제20권2호
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• pp.19-28
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• 2008

The objective of this study was to apply the statistical technique known as design of experiments to optimize the % exhaustion variables for phthalocyanine dyeing of nylon fiber. In this study, a three-factor Central Composite Rotatable Design (CCRD) was used to establish the optimum conditions for the phthalocyanine reactive dyeing of nylon fiber. Temperature, pH and liquor ratio were considered as the variable of interest. Acidic solution with higher temperature and lower liquor ratio were found to be suitable conditions for higher % exhaustion. These three variables were used as independent variables, whose effects on % exhaustion were evaluated. Significant polynomial regression models describing the changes on % exhaustion and % fixation with respect to independent variables were established with coefficient of determination, R2, greater than 0.90. Close agreement between experimental and predicted yields was obtained. Optimum conditions were obtained using surface plots and Monte Carlo simulation techniques where maximum dyeing efficiency is achieved. The significant level of both the main effects and interaction was observed by analysis of variance (ANOVA) approach. Based on the statistical analysis, the results have provided much valuable information on the relationship between response variables and independent variables. This study demonstrates that the CCRD could be efficiently applied for the empirical modeling of % exhaustion and % fixation in dyeing. It also shows that it is an economical way of obtaining the maximum amount of information in a short period of time with least number of experiments.