• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1655-1668
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• 2014

In this article, we propose and analyze a new nonconforming primal mixed finite element method for the stationary Stokes equations. The approximation is based on the pseudostress-velocity formulation. The incompressibility condition is used to eliminate the pressure variable in terms of trace-free pseudostress. The pressure is then computed from a simple post-processing technique. Unique solvability and optimal convergence are proved. Numerical examples are given to illustrate the performance of the method.

• Communications for Statistical Applications and Methods
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• v.22 no.5
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• pp.519-530
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• 2015

The geometric chart has proven more effective than Shewhart p or np charts to monitor the proportion nonconforming in high-quality processes. Implementing a geometric chart commonly requires the assumption that the in-control proportion nonconforming is known or accurately estimated. However, accurate parameter estimation is very difficult and may require a larger sample size than that available in practice in high-quality process where the proportion of nonconforming items is very small. Thus, the error in the parameter estimation increases and may lead to deterioration in the performance of the control chart if a sample size is inadequate. We suggest adjusting the control limits in order to improve the performance when a sample size is insufficient to estimate the parameter. We propose a linear function for the adjustment constant, which is a function of the sample size, the number of nonconforming items in a sample, and the false alarm rate. We also compare the performance of the geometric charts without and with adjustment using the expected value of the average run length (ARL) and the standard deviation of the ARL (SDARL).

• Proceedings of the Safety Management and Science Conference
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• 2008.04a
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• pp.283-293
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• 2008

Analysis of Means(ANOM) is a visualization tool for comparing several means to the grand mean like control chart type. This paper reviews five ANOM methods for continuous data such as ANOM, ANOME (ANOM for Treatment Effects), ANCON (Analysis of Contrasts), ANOMV (ANOM for Variance), ANOMC (ANOM for Correaltion). Three ANOM tools for discrete data such as ANOMNP (ANOM for Nonconforming Proportions), ANOMNC (ANOM for Nonconforming Unit), ANOMNPU (ANOM for Nonconfirmities Per Unit) are also developed.

• Journal of Korean Society for Quality Management
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• v.49 no.1
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• pp.81-95
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• 2021

Purpose: The purpose of this study was to analysis pattern of nonconforming farmers who is one of the factors of unconformity in residual pesticides. Methods: Pattern analysis of nonconforming farmers were analyzed through convergence of safety data and farmer's DB data. Exploratory data analysis and association rule analysis were used for extracting factors related to unconformity. Results: The results of this study are as follows; regarding the exploratory data analysis, it was found that factors of farmers influencing unconformity in residual pesticides by total 9 factors; sampling time, gender, age, cultivation region, farming career, agricultural start form, type of agriculture, cultivation area, classification of agricultural products. Regarding the association rule analysis, non-conformity association rules were found over the past three years. There was a difference in the pattern of nonconforming farmers depending on the cultivation period. Conclusion: Exploratory data analysis and association rule analysis will be useful tools to establish more efficient and economical safety management plan for agricultural products.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.1
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• pp.55-78
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• 2001

Given the anisotropic Poisson equation $-{\nabla}{\cdot}{\mathcal{K}}{\nabla}p=f$, one can convert it into a system of two first order PDEs: the Darcy law for the flux $u=-{\mathcal{K}{\nabla}p$ and conservation of mass ${\nabla}{\cdot}u=f$. A very natural mixed finite volume method for this system is to seek the pressure in the nonconforming P1 space and the Darcy velocity in the lowest order Raviart-Thomas space. The equations for these variables are obtained by integrating the two first order systems over the triangular volumes. In this paper we show that such a method is really a standard finite element method with local recovery of the flux in disguise. As a consequence, we compare two approaches in analyzing finite volume methods (FVM) and shed light on the proper way of analyzing non co-volume type of FVM. Numerical results for Dirichlet and Neumann problems are included.

• Journal of Korean Society for Quality Management
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• v.44 no.1
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• pp.167-180
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• 2016

Purpose: The problem for the traditional control chart is that it is unable to monitor the very small fraction of nonconforming and the underlying distribution is the normal distribution. $Z_p$ control chart is useful where it controls the vert small fraction on nonconforming. In this study, we will design the $Z_p$ control chart in order to use under non-normal process. Methods: $Z_p$ is calculated not by failure rate based on attribute data but using variable data. Control limit for non-normal $Z_p$ control chart is designed based on ${\alpha}$-risk calculated by cumulative distribution function of Burr distribution. ${\beta}$-risk, which is for performance evaluation, obtains in the Burr distribution's cumulative distribution function and control limit. Results: The control limit for non-normal $Z_p$ control chart is designed based on Burr distribution. The sensitivity can be checked through ARL table and OC curve. Conclusion: Non-normal $Z_p$ control chart is able to control not only the very small fraction of nonconforming, but it is also useful when $Z_p$ distribution is non-normal distribution.

• Proceedings of the Korean Society for Quality Management Conference
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• 1998.11a
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• pp.133-142
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• 1998

This paper is a brief review of the different procedures that are available for fitting theoretical distributions to data. The use of each technique is illustrated by reference to a distribution system which including the Pearson, Poission approximation of Gamma distribution and Burr functions. These functions can be used to calculate percent out of specification. Therefore, in this paper a new methods for estimating a measure of non-normal process capability for Gamma distributed variable data proposed using the percentage nonconforming. Process capability indices combines with the percentage nonconforming information can be used to evaluate more accurately process capability.

• Journal of Korean Society for Quality Management
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• v.23 no.1
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• pp.1-14
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• 1995

ISO 3951 (1989) Sampling Procedures and Charts for Inspection by Variables for Percent Nonconforming is an acceptable quality level (AQL) type sampling scheme. Sample size code letters and inspection levels in this International Standard correspond to those given in the ISO 2859 (1989), a standard for sampling plans by attributes. Two acceptance sampling procedures can be used ; tabular and graphical methods. The graphs could be used in less critical applications while the tabular method would be available for those familiar with MIL-STD-414 tables and to confirm the results of the graphs when needed. The sampling procedures of the ISO 3951 are matched to the ISO 2859 to enable us to move between them. Composite OC and ASN curves are given for AQL 2.5% and code letter F.

• Journal of Korean Society for Quality Management
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• v.45 no.2
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• pp.209-225
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• 2017

Purpose: Since traditional p chart is unable to deal with the variation of attribute data, this paper proposes a new attribute control chart for nonconforming proportions incorporating overdispersion with a beta-binomial model. Methods: Statistical theories for control chart developed under the beta-binomial model and a new approach using this control chart are presented Results: False alarm probabilities of p chart with the beta-binomial model are evaluated and demerits of p chart under overdispersion are discussed from three examples. Hence a concrete procedure for the proposed control chart is provided and illustrated with examples Conclusion: The proposed chart is more useful than traditional p chart, individual chart to treat observed proportions nonconforming as variable data and Laney p' chart.

• 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.