• IE interfaces
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• v.17 no.1
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• pp.1-12
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• 2004

In a modern semiconductor device manufacturing industry, statistical bin limits on wafer level test bin data are used for minimizing value added to defective product as well as protecting end customers from potential quality and reliability excursion. Most wafer level test bin data show skewed distributions. By Monte Carlo simulation, this paper evaluates methods and sample size effect regarding determination of statistical bin limits. In the simulation, it is assumed that wafer level test bin data follow the Poisson distribution. Hence, typical shapes of the data distribution can be specified in terms of the distribution's parameter. This study examines three different methods; 1) percentile based methodology; 2) data transformation; and 3) Poisson model fitting. The mean square error is adopted as a performance measure for each simulation scenario. Then, a case study is presented. Results show that the percentile and transformation based methods give more stable statistical bin limits associated with the real dataset. However, with highly skewed distributions, the transformation based method should be used with caution in determining statistical bin limits. When the data are well fitted to a certain probability distribution, the model fitting approach can be used in the determination. As for the sample size effect, the mean square error seems to reduce exponentially according to the sample size.

• Communications for Statistical Applications and Methods
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• v.27 no.1
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• pp.65-77
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• 2020

Geometric charts are effective in monitoring the fraction nonconforming in high-quality processes. The in-control fraction nonconforming is unknown in most actual processes; therefore, it should be estimated using the Phase I sample. However, if the Phase I sample size is small the practitioner may not achieve the desired in-control performance because estimation errors can occur when the parameters are estimated. Therefore, in this paper, we adjust the control limits of geometric charts with the bootstrap algorithm to improve the in-control performance of charts with smaller sample sizes. The simulation results show that the adjustment with the bootstrap algorithm improves the in-control performance of geometric charts by controlling the probability that the in-control average run length has a value greater than the desired one. The out-of-control performance of geometric charts with adjusted limits is also discussed.

• Journal of the Korean Statistical Society
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• v.21 no.2
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• pp.127-137
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• 1992

In this paper we investigate scaling limits for associated random measures satisfying some moment conditions. No stationarity is required. Our results imply an improvement of a central limit theorem of Cox and Grimmett to associated random measure and an extension to the nonstationary case of scaling limits of Burton and Waymire. Also we prove an invariance principle for associated random measures which is an extension of the Birkel's invariance principle for associated process.

• Communications for Statistical Applications and Methods
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• v.1 no.1
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• pp.102-111
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• 1994

We Propose a method of sensitivity analysis in latent root regression analysis (LRRA). For this purpose we derive the quantities ${\beta\limits^\wedge \;_{LRR}}^{(1)}$, which correspond to the theoretical influence function $I(x, y \;;\;\beta\limits^\wedge \;_{LRR})$ for the regression coefficient ${\beta\limits^\wedge}_{LRR}$ based on LRRA. We give a numerical example for illustration and also investigate numerically the relationship between the estimated values of ${\beta\limits^\wedge \;_{LRR}}^{(1)}$ with the values of the other measures called sample influence curve(SIC) based on the recomputation for the data with a single observation deleted. We also discuss the comparision among the results of LRRA, ordinary least square regression analysis (OLSRA) and ridge regression analysis(RRA).

• Journal of Korean Society for Quality Management
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• v.32 no.4
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• pp.229-241
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• 2004

Process capability index is used to determine whether a production process is capable of producing items within a specified tolerance. The index $C_{pmk}$ is the third generation process capability index. This index is more powerful than two useful indices $C_p$ and $C_{pk}$. Whether a process distribution is clearly normal or nonnormal, there may be some questions as to which any process index is valid or should even be calculated. As far as we know, yet there is no result for statistical inference with process capability index $C_{pmk}$. However, asymptotic method and bootstrap could be studied for good statistical inference. In this paper, we propose various bootstrap confidence limits for our process capability Index $C_{pmk}$. First, we derive bootstrap asymptotic distribution of plug-in estimator $C_{pmk}$ of our capability index $C_{pmk}$. And then we construct various bootstrap confidence limits of our capability index $C_{pmk}$ for more useful process capability analysis.

• Journal of the Korean Statistical Society
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• v.26 no.1
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• pp.57-74
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• 1997

Csorgo-Revesz type theorems for Wiener process are developed to those for Gaussian process. In particular, some results of superior and inferior limits for the increments of a Gaussian process are differently obtained under mild conditions, via estimating probability inequalities on the suprema of a Gaussian process.

• Communications for Statistical Applications and Methods
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• v.12 no.1
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• pp.117-123
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• 2005

A functional central limit theorem is obtained for a stationary linear process of the form $X_{t}= \sum\limits_{j=0}^\infty{a_{j}x_{t-j}}$, where {x_t} is a strictly stationary sequence of negatively associated random variables with suitable conditions and {a_j} is a sequence of real numbers with $\sum\limits_{j=0}^\infty|a_{j}|<\infty$.

• Journal of Korean Physical Therapy Science
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• v.2 no.4
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• pp.739-747
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• 1995

The purpose of this study was to evaluate and compare the Limits of stability(LOS) in hemiplegic patients who can walking independently. The LOS was measured at stable surface, unstable surface with eye open and eye closed. In this study, 18 out-patients were evaluated who were treated at Yonsei University Medical Center Rehabilitation Hospital. In order to determine the statistical significance of results, T-test, paired t-test, and Kruskal-Wallis 1-way ANOVA were applied at 0.05 level of significance. The results were as follows: 1. The mean of lateral limits of stability was 9.89 degree. 2. The mean of anteroposterior limits of stability was 6.43 degree. 3. There was a significant difference of limits of stability between sound side and affected side(p<0.05). 4. The limits of stability was significantly decreased with eye closed(p<0.05) 5. The limits of stability was significantly decreased at unstable surface(p<0.05). 6. The limits of stability was a significant difference as spasticity degree of ankle plantar flexors(p<0.05). These results showed that the limits of stability in hemiplegic patients was more decreased than that of normal adult. In order to improve the balance in hemiplegic patients, we need to increase the limits of stability.

• Proceedings of the Korean Statistical Society Conference
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• 2000.11a
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• pp.119-121
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• 2000

A functional central limit theorem is obtained for a stationary multivariate linear process of the form $X_t=\sum\limits_{u=0}^\infty{A}_{u}Z_{t-u}$, where {$Z_t$} is a sequence of strictly stationary m-dimensional linearly positive quadrant dependent random vectors with $E Z_t = 0$ and $E{\parallel}Z_t{\parallel}^2 <{\infty}$ and {$A_u$} is a sequence of coefficient matrices with $\sum\limits_{u=0}^\infty{\parallel}A_u{\parallel}<{\infty}$ and $\sum\limits_{u=0}^\infty{A}_u{\neq}0_{m{\times}m}$. AMS 2000 subject classifications : 60F17, 60G10.

• Communications for Statistical Applications and Methods
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• v.5 no.3
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• pp.645-657
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• 1998

During the start-up of a process or in a job-shop environment conventional use of control charts may lead to erroneous results due to the limited number of subgroups used for the construction of control limits. This article considers the effect of using estimated control limits based on a limited number of subgroups. Especially we investigate the performance of $\overline{X}$ and R control charts when the data are independent, and X control chart when the data are serially correlated in terms of average run length(ARL) and standard deviation run length(SDRL) using simulation. It is found that the ARL and SDRL get larger as the number of subgroups used for the construction of the chart becomes smaller.