• 품질경영학회지
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• 제28권3호
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• pp.18-30
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• 2000

Recent studies have shown that the $\bar{X}$ chart with variable sampling intervals(VSI) and the $\bar{X}$ chart with variable sample size(VSS) are much quicker than Shewhart $\bar{X}$ chart in detecting shiks in the process. Shewhart $\bar{X}$ chart has been beneficial to detect large shifts but it is hard to apply Shewhart $\bar{X}$ chart in detecting moderate shifts in the process mean. In this article the $\bar{X}$ chart using variable sample size(VSS) and variable sampling Intervals(VSI) has been proposed to supplement the weak point mentioned above. So the purpose of this paper is to consider finding the design parameters which minimize expected loss costs for unit process time and measure the performance of VSSI(variable sample size and sampling interval) $\bar{X}$ chart. It is important that assignable causes be detected to maintain the process controlled. This paper has been studied under the assumption that one cycle is from starting of the process to eliminating the assignable causes in the process. The other purpose of this article is to represent the expected loss costs in one cycle with three process parameters(sample size, sampling interval and control limits) function and find the three parameters.

• 품질경영학회지
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• 제32권4호
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• pp.156-168
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• 2004

This research investigates the statistical efficiency of variable sampling size & sampling interval(VSSI) $\bar{X}$ charts under two assignable causes. Algorithms for calculating the average run length(ARL) and average time to signal(ATS) of the VSSI $\bar{X}$ chart are proposed by employing Markov chain method. States of the process are defined according to the process characteristics after the occurrence of an assignable cause. Transition probabilities are carefully derived from the state definition. Statistical properties of the proposed chart are also investigated. A simple procedure for designing the proposed chart is presented based on the properties. Extensive sensitivity analyses show that the VSSI $\bar{X}$ chart is superior to the VSS or VSI $\bar{X}$ chart as well as to the Shewhart $\bar{X}$ chart in statistical sense, even tinder two assignable causes.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2004년도 품질경영모델을 통한 가치 창출
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• pp.64-69
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• 2004

This research investigates statistical characteristics of variable sampling size & interval(VSSI) X charts under two assignable causes. Algorithms for calculating the average run length(ARL) and average time to signal(ATS) of the VSSI X chart are proposed by employing Markov chain method. Extensive sensitivity analysis shows that the VSSI. X chart is superior to the VSS or VSI X chart as well as to the Shewhart X chart in statistical sense, even under two assignable causes.

• 한국품질경영학회:학술대회논문집
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• 한국품질경영학회 2004년도 품질경영모델을 통한 가치 창출
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• pp.507-512
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• 2004

This research investigates economic-statistical characteristics of variable sampling size & interval(VSSI) X charts under two assignable causes. We propose the procedure for designing VSSI X charts, based on Lorenzen and Vance model. Computational experiments show that the VSSI X chart Is superior to the Shewhart X chart in the economic-statistical sense, even under two assignable causes

• 대한산업공학회지
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• 제31권1호
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• pp.87-98
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• 2005

This research investigates economic-statistical characteristics of variable sampling size and interval (VSSI)$\bar{X}$charts under two assignable causes. A Markov chain approach is employed in order to calculate average run length (ARL) and average time to signal (ATS). Six transient states are derived by carefully defining the state. A steady state cost rate function is constructed based on Lorenzen and Vance(1986) model. The cost rate function is optimized with respect to six design parameters for designing the VSSI $\bar{X}$ charts. Computational experiments show that the VSSI $\bar{X}$ chart is superior to the Shewhart $\bar{X}$ chart in the economic-statistical sense, even under two assignable causes. A comparative study shows that the cost rate may increase up to almost 30% by overlooking the second cause. Critical input parameters are also derived from a sensitivity study and a few guideline graphs are provided for determining the design parameters.

• Journal of the Korean Data and Information Science Society
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• 제27권6호
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• pp.1487-1498
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• 2016

관리도를 사용하여 공정을 관리할 때, 일반적으로 공정 모수의 정확한 값은 알 수 없기 때문에 제1국면의 표본을 통하여 이를 추정해서 사용하고 있다. 또한 추정된 공정 모수를 이용하여 관리도를 설계하는 경우 관리한계는 관리상태에서의 런길이의 평균인 ARL (average run length)이 미리 지정한 값을 만족하도록 설정하고 있다. 그러나 런길이의 분포는 일반적으로 치우쳐져 있기 때문에, 런길이의 평균 대신 중위수를 사용하는 것이 바람직할 수 있다. 이 논문에서는 제1국면에서 추정한 모수를 사용하는 경우 부그룹의 크기에 따른 $\bar{X}$ 관리도의 성능에 대해 연구하였고, 이때 공정 평균에 대한 추정량은 전체 표본평균을 사용하고 공정 표준편차에 대해서는 5가지 추정량을 사용하여 이에 대한 영향을 살펴보았다. 기존 연구와 다른 점은 여러 가지의 부그룹 크기에 대해 모수 추정의 영향을 ARL 대신 런길이의 중위수인 MRL (median run length)에 기초하여 살펴보았으며, 두 가지 방법에 대해 그 결과를 비교하였다.

• 대한산업공학회지
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• 제39권5호
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• pp.422-428
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• 2013

In many cases, an $\bar{X}$ control chart which is based on the performance variable is used in industrial fields. However, if the performance variable is too costly or impossible to measure and a less expensive surrogate variable is available, the process may be more efficiently controlled using surrogate variables. In this paper, we propose a model for the economic design of a VSI (Variable Sampling Interval) $\bar{X}$ control chart using a surrogate variable that is linearly correlated with the performance variable. The total average profit model is constructed, which involves the profit per cycle time, the cost of sampling and testing, the cost of detecting and eliminating an assignable cause, and the cost associated with production during out-of-control state. The VSI $\bar{X}$ control charts using surrogate variables are expected to be superior to the Shewhart FSI (Fixed Sampling Interval) $\bar{X}$ control charts using surrogate variables with respect to the expected profit per unit cycle time from economic viewpoint.

• 산업경영시스템학회지
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• 제22권52호
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• pp.347-354
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• 1999

Statistical Process Control(SPC) which uses control charts is widely used to inspect and improve manufacturing process as a effective method. A parametric method is the most common in statistical process control. Shewhart chart was made under the assumption that measurements are independent and normal distribution. In practice, this assumption is often excluded, for example, in case of (equation omitted) chart, when the subgroup sample is small or correlation, it happens that measured data have bias or rejection of the normality test. A bootstrap method can be used in such a situation, which is calculated by resampling procedure without pre-distribution assumption. In this study, applying bootstrap percentile method to (equation omitted) chart, it is compared and evaluated standard process control limit with bootstrap percentile control limit. Also, under the normal and non-normal distributions, where parameter is 0.5, using computer simulation, it is compared standard parametric with bootstrap method which is used to decide process control limits in process quality.

• 응용통계연구
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• 제30권3호
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• pp.487-501
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• 2017

최근 산업의 생산공정에서는 머신비전시스템을 통하여 제품의 품질특성치에 대한 정보를 이미지 데이터로 제공하는 경우가 많다. 따라서 산업과 의학 현장에서 이미지 데이터의 모니터링을 위해 관리도 절차의 필요성이 많이 대두되고 있다. 이미지 데이터를 모니터링하는 관리도 절차는 전통적으로 사용하는 관리도 절차와 유사한 점도 있지만, 데이터의 구조를 비롯하여 각 이미지에서 ROI를 설정하여 관리도 절차를 적용하는 등 서로 다른 점도 많이 있다. 이 논문에서는 생산공정에서 제공되는 이미지 데이터에 대해 관리도를 사용하는 절차를 소개하고, 이미지 또는 ROI 크기의 확대와 축소가 제품의 이상원인을 탐지하는데 어떠한 영향이 주는지를 모의실험을 통하여 알아보았고 각 관리도의 성능 또한 비교하였다.

• 품질경영학회지
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• 제28권2호
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• pp.39-56
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• 2000

${\overline{X}}$ control chart has proven to be an effective tool to improve the product quality. Shewhart charts assume that the observations are independent and normally distributed. Under the presence of positive autocorrelation and severe skewness, the control limits are not accurate because assumptions are violated- Autocorrelation in process measurements results in frequent false alarms when standard control chats are applied in process monitoring. In this paper, Threshold Bootstrap and Moving Block Bootstrap are used for constructing a confidence interval of correlated observations. Monte Carlo simulation studies are conducted to compare the performance of the bootstrap methods and that of standard method for constructing control charts under several conditions.