• International Journal of Precision Engineering and Manufacturing
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• v.9 no.1
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• pp.12-18
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• 2008

This paper describes two run-to-run controllers, a nonlinear multiple exponential-weight moving-average (NMEWMA) controller and a dynamic model-tuning minimum-variance (DMTMV) controller, for photolithography processes. The relationships between the input recipes (exposure dose and focus) and output variables (critical dimensions) were formed using an experimental design method, and the photolithography process model was built using a multiple regression analysis. Both the NMEWMA and DMTMV controllers could update the process model and obtain the optimal recipes for the next run. Quantified improvements were obtained from simulations and real photolithography processes.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.35 no.3
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• pp.129-135
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• 2012

Companies strive for quality improvement and use process data obtained through measurement process to monitor and control the process. Measurement data contain variation due to error of operator and instrument. The total variation is sum of product variation and measurement variation. Gage R&R is for repeatability and reproducibility of measurement system. Gage R&R study is usually conducted to analyze the measurement process. In performing the gage R&R study, several parameters such as the appropriate number of operators (o), sample size of parts (p), and replicate (r) are used. In this paper we propose how to determine the optimal combination of number of operators (o), sample size of parts (p), and replicates (r) considering measurement time and cost by statistical method.

• Journal of Korean Society for Quality Management
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• v.26 no.1
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• pp.126-142
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• 1998

Traditional statistical process control(SPC) assumes that consective observations from a process are independent. In industrial practice, however, observations are ofter serially correlated. A common a, pp.oach to building control charts for autocorrelatd data is to a, pp.y classical SPC to the residuals from a time series model fitted. Unfortunately, one cannot completely escape the effects of autocorrelation by using charts based on residuals of time series model. For the detection of variance change in the process we propose a CUSUM of squares control chart which does not require the model identification. The proposed CUSUM of squares chart and the conventional control charts are compared by a Monte Carlo simulation. It is shown that the CUSUM of squares chart is more effective in the presence of dependency in the processes.

• Journal of the Korean Operations Research and Management Science Society
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• v.21 no.3
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• pp.47-61
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• 1996

An ATM switch must deal with various kinds of input sources having different traffic characteristics and it must guarantee very small value of cel loss probability, about 10$^{8}$ -10$^{12}$ , to deal with loss-sensitive traffics. In order to estimate such a rate event probability with simulation procedure, a variance reduction technique is essential for obtaining an appropriate level of precision with reduced cost. In this paper, we propose a hybrid simulation technique to achieve reduction of variance of cell loss probability estimator, where hybrid means the combination of analytical method and simulation procedure. A discrete time queueing model with multiple input sources and a finite shared buffer is considered, where the arrival process at an input source and a finite shared buffer is considered, where the arrival process at an input source is governed by an Interrupted Bernoulli Process and the service rate is constant. We deal with heterogeneous input sources as well as homogeneous case. The performance of the proposed hybrid simulation estimator is compared with those of the raw simulation estimator and the importance sampling estimator in terms of variance reduction ratios.

• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.575-589
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• 2010

Exponential L$\acute{e}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.

• Journal of Korean Institute of Industrial Engineers
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• v.24 no.1
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• pp.145-156
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• 1998

In a classical clustering problem, grouping is done on the basis of similarities or distances (dissimilarities) among the elements. Therefore, the objective is to minimize the variance within each group while maximizing the between-group variance among all groups. In this paper, however, a new class of clustering problem is introduced. We call this a laydown grouping problem (LGP). In LGP, the objective is to minimize both the within-group and between-group variances. Furthermore, the problem is expanded to a multi-dimensional case where the two-way minimization process must be considered for each dimension simultaneously for all measurement characteristics. At first, the problem is assessed by analyzing its variance structures and their complexities by conjecturing that LGP is NP-complete. Then, the simulated annealing (SA) algorithm is applied and the results are compared against that from others.

• Proceedings of the KIEE Conference
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• 2006.07d
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• pp.1858-1859
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• 2006

This paper presents a new fuzzy-neural-network based interacting multiple model (FNNBIMM) algorithm for tracking a maneuvering target. To effectively handle the unknown target acceleration, this paper regards it as additional noise, time-varying variance to target model. Each sub model characterized by the variance of the overall process noise, which is obtained on the basis of each acceleration interval. Since it is hard to approximate this time-varying variance adaptively owing to the unknown acceleration, the FNN is utilized to precisely approximate this time-varying variance. The gradient descendant method is utilized to optimize each FNN. To show the feasibility of the proposed algorithm, a numerical example is provided.

• Proceedings of the KSME Conference
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• 2000.11a
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• pp.693-698
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• 2000

Aspects of classical information theory, such as rate distortion theory, investigate how to encode and decode information from an independently identically distributed source so that the asymptotic distortion rate between the source and its quantized representation is minimized. However, in most natural dynamics, the source state is highly corrupted by disturbances, and the measurement contains the noise. In recent coder-estimator sequence is developed for state estimation problem based on observations transmitted with finite communication capacity constraints. Unlike classical estimation problems where the observation is a continuous process corrupted by additive noises, the condition is that the observations must be coded and transmitted over a digital communication channel with finite capacity. However, coder-estimator sequence does not provide such a quantitative analysis as a variance for estimation error. In this paper, under the assumption that the estimation error is Gaussian distribution, a variance for coder-estimation sequence is proposed and its fitness is evaluated through simulations with a simple example.

• Journal of the Korea Society for Simulation
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• v.10 no.4
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• pp.41-50
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• 2001

When optimizing a complex system by determining the optimum condition of the system parameters of interest, we often employ the process of estimating the unknown objective function, which is assumed to be a second order spline function. In doing so, we normally use common random numbers for different set of the controllable factors resulting in more accurate parameter estimation for the objective function. In this paper, we will show some mathematical result for the analysis of variance when using common random numbers in terms of the regression error, the residual error and the pure error terms. In fact, if we can realize the special structure of the covariance matrix of the error terms, we can use the result of analysis of variance for the uncorrelated experiments only by applying minor changes.

• Fibers and Polymers
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• v.7 no.4
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• pp.424-431
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• 2006

Roll drafting, a mechanical operation attenuating fiber bundles to an appropriate thickness, is an important operation unit for manufacturing staple yams. It influences not only the linear density regularity of the slivers or staple yams that are produced, but also the quality of the textile product and the efficiency of the thereafter processes. In this research, the dynamic states of the fiber bundle in the roll drafting zone were analyzed by simulation, based on the mathematical model that describes the dynamic behavior of the flowing bundle. The state variables are the linear density and velocity of the fiber bundles and we simulated the dynamics states of the bundle flow, e.g., the profiles of the linear density and velocity in the draft zone for various values of the model parameters and boundary conditions, including the initial conditions to obtain their influence on the dynamic state. Results showed that the mean velocity profile of the fiber bundle was strongly influenced by draft ratio and process speed, while the input sliver linear density has hardly affected the process dynamics. Velocity variance of individual fibers that could be supposed to be a disturbing factor in drafting was also influenced by the process speed. But the major disturbance occurred due to the velocity slope discontinuity at the front roll, which was strongly influenced by the process speed. Thickness of input sliver didn't play any important role in the process dynamics.