• 제목/요약/키워드: $\bar{X}$ control chart

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대용변수를 이용한 가변형 부분군 채취 간격 X 관리도의 경제적 설계 (Economic Design of Variable Sampling Interval X Control Chart Using a Surrogate Variable)

  • 이태훈;이주호;이민구
    • 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.

The Exponentially Weighted Moving Average Control Charts

  • Jeon, Jae-Kyeong;Goo, Bon-chul;Song, Suh-ill
    • 품질경영학회지
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    • 제19권2호
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    • pp.172-180
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    • 1991
  • The null hypothesis being tested by $the{\bar{X}}$ control chart is that the process is in control at a quality level ${\mu}o$. An ${\bar{X}}control$ chart is a tool for detecting process average changes due to assingnable causes. The major weakness of $the{\bar{X}}$ control chart is that it is relatively insensitive to small changes in the population mean. This paper presents one way to remedy this weakness is to allow each plotted value to depend not only on the most recent subgroup average but on some of the other subgroup averages as well. Two approaches for doing this are based on (1) moving averages and (2) exponentially weighted moving averages of forecasting method.

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두 개의 이상원인을 고려한 VSSI$\bar{X}$ 관리도의 경제적-통계적 설계 (Economic-Statistical Design of VSSI$\bar{X}$ Control Charts Considering Two Assignable Causes)

  • 이호중;임태진
    • 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.

상관관계의 존재하에서 붓스트랩 기법을 이용한 $\bar{x}$ 와 EWMA관리도의 수행도 평가 (Performance Evaluation of $\bar{x}$ and EWMA Control Charts using Bootstrap Technique in the Presence of Correlation)

  • 손한덕;송서일
    • 한국산업경영시스템학회:학술대회논문집
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    • 한국산업경영시스템학회 2002년도 춘계학술대회
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    • pp.365-370
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    • 2002
  • In this study, according to MARMA(1,0) model which was suggested by Seppala, in case of existing autocorrelation in X control chart and EWMA control chart, the standard method and the non-parametric bootstrap method were compared and analysed using the bootstrap method which use the resampling prediction residual.

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$\bar{x}$-chart 의 경제적(經濟的) 파라메터 설정(設定)에 관한 연구(硏究) (A Study on defermination of the economic Parameter in $\bar{x}$-control chart)

  • 한병돈;황의철
    • 품질경영학회지
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    • 제11권1호
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    • pp.44-50
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    • 1983
  • The main factors of determining the Control Line of the Control Chart can be classified as follows: 1) sample size (n), 2) the factor that determines the spread of Control Limits (B), (3) sampling frequency (h). The determination of these factors can be explained according to the extent that occurrences of assignable cause should be detected. The purpose of this paper are two: one is for composing a model of which use should be designated for economic decision on the size of these factors leading to the Control Line of the Control Chart, the other is about what influence increasing or decreasing condition, according to changeability of the size of these factors, of expect cost can have on the economy when the Control Chart is used.

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대용변수를 이용한 $\bar{X}$ 관리도의 경제적 설계 (Economic Design of $\bar{X}$ Control Chart Using a Surrogate Variable)

  • 이태훈;이재훈;이민구;이주호
    • 품질경영학회지
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    • 제37권2호
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    • pp.46-57
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    • 2009
  • The traditional approach to economic design of control charts is based on the assumption that a process is monitored using a performance variable. However, various types of automatic test equipments recently introduced as a part of factory automation usually measure surrogate variables instead of performance variables that are costly to measure. In this article we propose a model for economic design of a control chart which uses a surrogate variable that is highly correlated with the performance variable. The optimum values of the design parameters are determined by maximizing the total average income per cycle time. Numerical studies are performed to compare the proposed $\bar{X}$ control charts with the traditional model using the examples in Panagos et al. (1985).

$\bar{X}$ 관리도에서 런길이의 중위수에 기초한 모수 추정의 영향 (The effect of parameter estimation on $\bar{X}$ charts based on the median run length)

  • 이유진;이재헌
    • 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.

$\bar{x}$ 관리도의 표준관리한계와 부트스트랩 백분률 관리한계의 수행도 비교평가 (Comparison and Evaluation of Performance for Standard Control Limits and Bootstrap Percentile Control Limits in $\bar{x}$ Control Chart)

  • 송서일;이만웅
    • 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.

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개선된 3 중 2 주 및 보조 런 규칙을 가진 X관리도의 통계적 설계 (Statistical Design of X Control Chart with Improved 2-of-3 Main and Supplementary Runs Rules)

  • 박진영;서순근
    • 품질경영학회지
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    • 제40권4호
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    • pp.467-480
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    • 2012
  • Purpose: This paper introduces new 2-of-3 main and supplementary runs rules to increase the performance of the classical $\bar{X}$ control chart for detecting small process shifts. Methods: The proposed runs rules are compared with other competitive runs rules by numerical experiments. Nonlinear optimization problem to minimize the out-of-control ARL at a specified shift of process mean for determining action and warning limits at a time is formulated and a procedure to find two limits is illustrated with a numerical example. Results: The proposed 2-of-3 main and supplementary runs rules demonstrate an improved performance over other runs rules in detecting a sudden shift of process mean by simultaneous changes of mean and standard deviation. Conclusion: To increase the performance in the detection of small to moderate shifts, the proposed runs rules will be used with $\bar{X}$ control charts.

Capability Analysis of Sensory Quality of Jajang Sauce

  • Imm, Bue-Young;Lee, Ji-Hye;Yeo, Ik-Hyun
    • Food Science and Biotechnology
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    • 제18권3호
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    • pp.745-748
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    • 2009
  • Sensory quality variations of jajang sauce were monitored by the $\bar{X}-chart$ and capability analysis based on specifications of each sensory attributes. For sensory quality control (QC) of the sauce which has a strong sweetness and sourness, the ratio of sourness/sweetness was examined as a necessary QC factor to maintain the balance of sweetness and sourness. For the sensory QC factors, all the sensory data were divided into individual sensory score of reference which was a pack of sauce manufactured a week ago. The ratio form of sensory data was useful for decreasing individual variations and for increasing normality of data measured by category scale. The overall proportion of out-spec products under normal manufacturing conditions was obtained by capability analysis of sensory data with normal distribution. Out-spec samples were monitored by the $\bar{X}-chart$ of each sensory attributes.