• Journal of Korean Society for Quality Management
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• v.25 no.3
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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.

• Journal of Korean Society for Quality Management
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• v.34 no.1
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• pp.73-77
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• 2006

In this paper, the Bayesian procedure for the multiple test of fraction nonconforming, p, is proposed. It is the procedure for checking whether the process is out of control, in control, or under the permissible level for p. The procedure is as follows: first, setting up three types of models, $M_1:p=p_0,\;M_2:pp_0$, second, computing the posterior probability of each model. and then choosing the model with the largest posterior probability as a model most fitted for the observed sample among three competitive models. Finally, the simulation study is performed to examine the proposed method.

• Journal of the Korea Safety Management & Science
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• v.14 no.3
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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.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.325-329
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• 2006

In this paper, the Bayesian procedure for the multiple test of fraction nonconforming, p, is proposed. It is the procedure for checking whether the process is out of control, in control, or under the permissible level for p. The procedure is as follows: first, setting up three types of models, $M_1:p=p_0,\;M_2:pp_0$, second, computing the posterior probability of each model. and then choosing the model with the largest posterior probability as a model most fitted for the observed sample among three competitive models. Finally, the simulation study is performed to examine the proposed method.

• Proceedings of the Korean Society for Quality Management Conference
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• 2006.04a
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• pp.319-324
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• 2006

In this paper, we propose Bayesian procedure for the multiple change points analysis in a sequence of fractions nonconforming. We first compute the Bayes factor for detecting the existence of no change, a single change or multiple changes. The Gibbs sampler with the Metropolis-Hastings subchain is run to estimate parameters of the change point model, once the number of change points is identified. Finally, we apply the results developed in this paper to both a real and simulated data.

• 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.

• Journal of Korean Society for Quality Management
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• v.32 no.2
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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.

• 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.

• 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.

• Proceedings of the Safety Management and Science Conference
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• 1999.11a
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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.