• 품질경영학회지
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• 제25권3호
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• pp.74-85
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• 1997

In this paper we calculate the subgroup size necessary for detecting the change of percent defective with several detection probabilities for orginal population fraction nonconforming p, changed population fraction nonconforming $p^*$, and the ratio k=$p^*$/p in the usage of p control charts. From our calculation we can know the error level of normal a, pp.oximation in detection probability calculation and recommend the subgroup size with lower error levels of normal a, pp.oximation, and then we show the reasonable subgroup size necessary for p, $p^*$, k, and the detection probability of the change of fraction nonconforming in a process. The information that we here show in tables will be useful when p control chart users decide the subgroup size in the p control chart users decide the subgroup size in the p control chart.

• 대한안전경영과학회지
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• 제14권3호
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• pp.167-174
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• 2012

In the manufacturing process the most widely used $\bar{X}$ chart has been applied to control the process mean. Also, Accelerated Life Test(ALT) is commonly used for efficient assurance of product life in development phases, which can be applied in production reliability acceptance test. When life data has lognormal distribution, through censored ALT design so that censored ALT data has asymptotic normal distribution, $ALT\bar{X}$ control chart integrating $\bar{X}$ chart and ALT procedure could be applied to control the mean of process in the manufacturing process. In the situation that process variation is controlled, $Z_p$ control chart is an effective method for the very small fraction nonconforming of quality characteristic. A simultaneous control scheme with $ALT\bar{X}$ control chart and $Z_p$ control chart is designed for the very small fraction nonconforming of product lifetime.

• 품질경영학회지
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• 제44권1호
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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.

• 품질경영학회지
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• 제32권2호
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• pp.191-200
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• 2004

Using the p chart is not adequate in case that there are lots of data and it is difficult to divide into products conforming or nonconforming because of obscurity of binary classification. So we need to design a new control chart which represents obscure situation efficiently. This study deals with the method to performing arithmetic operation representing fuzzy data into fuzzy set by applying fuzzy set theory and designs a new control chart taking account of a concept of classification on the term set and membership function associated with term set.

• 산업경영시스템학회지
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• 제20권42호
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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.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 1999년도 추계학술대회
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• pp.247-257
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• 1999

There are several models for process quality assurance by quality system(ISO 9000), process capability analysis, acceptance control chart and so on. When a high level process capability has been achieved, it takes a long time to monitor the process shift, so it is sometimes necessary to develop a quicker monitoring system. To achieve a quicker quality assurance model for high-reliability process, this paper presents a model for process quality assurance when the fraction nonconforming is very small. We design an acceptance control chart based on variable quality characteristic and time-censored accelerated testing. The distribution of the characteristics is assumed to be normal of lognormal with a location parameter of the distribution that is a linear function of a stress. The design parameters are sample size, control limits and sample proportions allocated to low stress. These parameters are obtained under minimization of the relative variance of the MLE of location parameter subject to APL and RPL constraints.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2000년도 추계학술발표논문집
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• pp.217-234
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• 2000

Approximately normalized control charts, called Q charts, have been given Quesenberry(1991) for charting in process of short-run, job-shop, etc. We consider a Q chart with inspection error for job-shop floor under geometric distribution, which can be used for processes when a fraction nonconforming is very small. Our results would be applied for designing other control charts with inspection error.

• Communications for Statistical Applications and Methods
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• 제27권1호
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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.

• 대한안전경영과학회지
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• 제1권1호
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• pp.123-134
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• 1999

There are several models for process quality assurance by quality system (ISO 9000), process capability analysis, acceptance control chart and so on. When a high level process capability has been achieved, it takes a long time to monitor the process shift, so it is sometimes necessary to develop a quicker monitoring system. To achieve a quicker quality assurance model for high-reliability process, this paper presents a model for process quality assurance when the fraction nonconforming is very small. We design an acceptance control chart based on variable quality characteristic and time-censored accelerated testing. The distribution of the characteristics is assumed to be normal or lognormal with a location parameter of the distribution that is a linear function of a stress. The design parameters are sample size, control limits and sample proportions allocated to low stress. These paramaters are obtained under minimization of the relative variance of the MLE of location parameter subject to APL and RPL constraints.

• 대한안전경영과학회:학술대회논문집
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• 대한안전경영과학회 2013년 춘계학술대회
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• pp.533-546
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• 2013

이 논문은 미세공정변동에서 극소불량을 감지하는 관리도의 경제적 설계를 개발하기 위한 조사연구이다. 일반적인 관리도의 설계는 통계적 설계와 경제적 설계로 구분할 수 있다. 공정의 변동 원인에 따라 샘플의 간격(h), 샘플의 크기(n), 관리한계선(k) 등의 설계 모수를 최적접근방법으로 결정을 하는 경제적 설계의 모델을 조사하였다. 관리도의 경제적 설계는 공정의 관리이상상태를 효율적으로 감지하여 관리상태로 정상화 시키는 것에 대한 공정의 개선비용과 기대품질비용을 절약 할 수 있는 최적설계 방안이다. 그리고 Shewhart 관리도의 X-bar 통계량으로 극소불량을 검출 하는것에 한계가 있기 때문에 Zp 통계량과 분포를 설계하여 극소불량을 빠르게 감지할 수 있는 Zp 관리도의 설계를 적용하고, 미세공정변동을 정확하게 감지할 수 있는 CUSUM 관리도를 동시에 적용하였다. 따라서, 미세공정변동과 극소불량을 동시에 관리 할 수 있는 Zp-CUSUM 관리도의 통계적 설계 구조를 체계화 하였으며, 기존의 경제적 설계의 모델을 비교 분석하여 새로운 경제적 설계에 대한 모델을 제안하고자 한다.