• 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.

• KSCE Journal of Civil and Environmental Engineering Research
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• v.5 no.2
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• pp.19-25
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• 1985

By the combined use of reduced integration and addition of nonconforming displacement modes, a highly effective new plate element has been established. The displacement field of this element was formed by adding nonconforming modes only to transverse displacement component of Ahmad-Irons' element and the element matrices are computed by the numerical integrations with modified orders. Comparing with other elements, the superiority of the both NC 8-4.1 and NC 8-5.1 elements over the elements previously studied has been observed. The solutions with these elements converge to the true solutions very rapidly as the mesh is refined. These elements are also shown to be applicable to the wide range of thick and very thin plate problems.

• Journal of Korean Society for Quality Management
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• v.30 no.1
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• pp.74-96
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• 2002

The objectives of this study is to suggest the rectifying sampling inspection plan considering quality cost. Limiting quality level(LQL) plans(also called LTPD plans) and outgoing quality(OQ) plans are considered. The Hald's linear cost model is discussed with and without a beta prior for the distribution of the fraction of nonconforming items in a lot. It is assumed that the sampling inspection is error free. We consider the design of reliability acceptance sampling plan (RASP) for failure rate level qualification at selected confidence level. The lifetime distribution of products is assumed to be exponential. MIL-STD-690C and K C 6032 standards provide this procedures. But these procedures have some questions to apply in the field. The cost of test and confidence level(1-$\beta$ risk) are the problem between supplier and user. So, we suggest that the optimal life test sampling inspection plans using simple linear cost model considering product cost, capability of environment chamber, environmental test cost, and etc. Especially, we consider a reliability of lots that contain some nonconforming items. In this case we assumed that a nonconforming item fail after environmental life test. Finally, we develope the algorithm of the optimal sampling inspection plan based on minimum costs for rectifying inspection and RASP. And computer application programs are developed So, it is shown how the desired sampling plan can be easily found.

• 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 of Industrial and Systems Engineering
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• v.20 no.42
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• pp.73-85
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• 1997

In the product liability age the demand on quality is extremely high and inspection and test are automated. The process capability indices $C_p, {\;}C_{pk}$ and p control chart widely used to provide unitless measure of process performance and process control. Traditional process capability indices $C_p, {\;}C_{pk}$ do not represent the process variation from target value. The convention p chart for control of fraction nonconforming becomes inadequate when the fraction nonconforming becomes very small such as PPM level production system. This paper proposes process performance measure considering quadratic loss function and cumulative counts control chart for control of PPM level production system.

• 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.

• 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 the Korea Safety Management & Science
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• v.18 no.2
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• pp.119-125
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• 2016

The ratio which we usually use in producing products is nonconforming proportion or percent defective. As our modern society develops, we cannot but meet another proportion in legal, managerial, and medical areas where our human beings might commit various kinds of errors though they do not want them. In this paper we will generally call the ratio 'proportion.' When the size of such proportion as percent defective is observed by persons, it is not true proportion but apparent proportion because it has been observed with human or situational errors. Past studies have not systematically covered the analysis of relations between such proportions and type 1 and 2 error, but this paper analyses and derives such various relations, and it suggests the guideline as sixteen properties for utilization and sensitive analysis of the relations. Current paper's consideration of apparent proportion in addition to true proportion as our familiar concept will open and widen existing academic and application areas where people have mainly built societal, scientific and engineering rules and methods based only on true proportion.