• Title, Summary, Keyword: Average run length

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Cumulative Weighted Score Control Schemes for Controlling the Mean of a Continuous Production Process

  • Park, Byoung-Chul;Park, Sung H.
    • Journal of the Korean Statistical Society
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    • v.18 no.2
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    • pp.135-148
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    • 1989
  • Cumulative sum schemes based on a weighted score are considered for controlling the mean of a continuous production process; in which both the one-sided and two-sided schemes are proposed. The average run lengths and the run length distributions for the proposed schemes are obtained by the Markov chain approach. Comparisons by the average run length show that the proposed schemes perform nearly as well as the standard cumulative sum schemes in detecting changes in the process mean. Comparisons of the one-sided schemes by the run length distribution are also presented.

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

  • Lee, Yoojin;Lee, Jaeheon
    • Journal of the Korean Data and Information Science Society
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    • v.27 no.6
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    • pp.1487-1498
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    • 2016
  • In monitoring a process, in-control process parameters must be estimated from the Phase I data. When we design the control chart based on the estimated process parameters, the control limits are usually chosen to satisfy a specific in-control average run length (ARL). However, as the run length distribution is skewed when the process is either in-control or out-of-control, the median run length (MRL) can be used as alternative measure instead of the ARL. In this paper, we evaluate the performance of Shewhart $\bar{X}$ chart with estimated parameters in terms of the average of median run length (AMRL) and the standard deviation of MRL (SDMRL) metrics. In simualtion study, the grand sample mean is used as a process mean estimator, and several competing process standard deviation estimators are used to evaluate the in-control performance for various amounts of Phase I data.

Demerit-EWMA Control Charts

  • Cho, Gyo-Young;Jeon, Young-Mok
    • 한국데이터정보과학회:학술대회논문집
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    • pp.7-14
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    • 2004
  • In this paper, we present an effective method for process control using the Demerit-EWMA control chart in the process where nonconforming units or nonconformities are occurred by various types. We compare performance of Demerit control chart, Demerit-CUSUM control chart and Demerit-EWMA control chart based on the average run length.

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A Study of Demerit-EWMA Control Charts

  • Cho, Gyo-Young;Jeon, Young-Mok
    • Journal of the Korean Data and Information Science Society
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    • v.15 no.2
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    • pp.431-439
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    • 2004
  • In this paper, we present an effective method for process control using the Demerit-EWMA control chart in the process where nonconforming units or nonconformities are occurred by various types. We compare performance of Demerit control chart, Demerit-CUSUM control chart and Demerit-EWMA control chart based on the average run length(ARL).

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Multivariate Shewhart control charts for monitoring the variance-covariance matrix

  • Jeong, Jeong-Im;Cho, Gyo-Young
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.3
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    • pp.617-626
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    • 2012
  • Multivariate Shewhart control charts are considered for the simultaneous monitoring the variance-covariance matrix when the joint distribution of process variables is multivariate normal. The performances of the multivariate Shewhart control charts based on control statistic proposed by Hotelling (1947) are evaluated in term of average run length (ARL) for 2 or 4 correlated variables, 2 or 4 samples at each sampling point. The performance is investigated in three cases, that is, the variances, covariances, and variances and covariances are changed respectively.

Statistical design of Shewhart control chart with runs rules (런 규칙이 혼합된 슈와르트 관리도의 통계적 설계)

  • Kim, Young-Bok;Hong, Jung-Sik;Lie, Chang-Hoon
    • Journal of the Korean Society for Quality Management
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    • v.36 no.3
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    • pp.34-44
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    • 2008
  • This research proposes a design method based on the statistical characteristics of the Shewhart control chart incorporated with 2 of 2 and 2 of 3 runs rules respectively. A Markov chain approach is employed in order to calculate the in-control and out-of-control average run lengths(ARL). Two different control limit coefficients for the Shewhart scheme and the runs rule scheme are derived simultaneously to minimize the out-of-control average run length subject to the reasonable in-control average run length. Numerical examples show that the statistical performance of the hybrid control scheme are superior to that of the original Shewhart control chart.

The Effect of Short Production Runs on the Average Outgoing Quality of Skip-Lot Sampling Plan (Skip-Lot 샘풀링 검사(檢査)에서 생산기간(生産期間)이 평균출검품질(平均出檢品質)에 미치는 영향)

  • Lee, Jong-Seong
    • Journal of Korean Institute of Industrial Engineers
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    • v.13 no.2
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    • pp.97-103
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    • 1987
  • Skip-Lot sampling plan is formulated in terms of renewal process. This approach facilitates studying the average outgoing quality in a short production run of length t, AOQ (t). By numerical studies it is found that the long-run average outgoing quality (AOQ) greatly overestimates AOQ (t) for short runs.

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Statistical Design of CV Control Charts witn Approximate Distribution (근사분포를 이용한 CV 관리도의 통계적 설계)

  • Lee Man-Sik;Kang Chang-Wook;Sim Seong-Bo
    • Journal of the Society of Korea Industrial and Systems Engineering
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    • v.27 no.3
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    • pp.14-20
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    • 2004
  • The coefficient of variation(CV) which is a relatively dimensionless measure of variability is widely used to describe the variation of sample data. However, the properties of CV distribution are little available and few research has been done on estimation and interpretation of CV. In this paper, we give an outline of statistical properties of coefficient of variation and design of control chart based on this statistic. Construction procedures of control chart are presented. The proposed control chart is an efficient method to monitor a process variation for short production run situation. Futhermore, we evaluated the performance of CV control chart by average run length(ARL).

Multivariate EWMA control charts for monitoring the variance-covariance matrix

  • Jeong, Jeong-Im;Cho, Gyo-Young
    • Journal of the Korean Data and Information Science Society
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    • v.23 no.4
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    • pp.807-814
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    • 2012
  • We know that the exponentially weighted moving average (EWMA) control charts are sensitive to detecting relatively small shifts. Multivariate EWMA control charts are considered for monitoring of variance-covariance matrix when the distribution of process variables is multivariate normal. The performances of the proposed EWMA control charts are evaluated in term of average run length (ARL). The performance is investigated in three types of shifts in the variance-covariance matrix, that is, the variances, covariances, and variances and covariances are changed respectively. Numerical results show that all multivariate EWMA control charts considered in this paper are effective in detecting several kinds of shifts in the variance-covariance matrix.

The in-control performance of the CCC-r chart with estimated parameters (추정된 모수를 사용한 CCC-r 관리도에서 관리상태의 성능)

  • Kim, Jaeyeon;Kim, Minji;Lee, Jaeheon
    • The Korean Journal of Applied Statistics
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    • v.31 no.4
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    • pp.485-495
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    • 2018
  • The CCC-r chart is more effective than traditional attribute control charts for monitoring high-quality processes. In-control process parameters are typically unknown and should be estimated when implementing a CCC-r chart. Phase II control chart performance can deteriorate due to the effect of the estimation error. In this paper, we used the standard deviation of average run length (ARL) as well as the average of ARL to quantify the between-practitioner variability in the CCC-r chart performance. The results indicate that the CCC-r chart requires larger Phase I data than previously recommended in the literature in order to have consistent chart in-control performance among practitioners.