Journal of the Korean Data and Information Science Society

한국데이터정보과학회 (The Korean Data and Information Science Society)
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$\bar{X}$ 관리도에서 런길이의 중위수에 기초한 모수 추정의 영향

The effect of parameter estimation on $\bar{X}$ charts based on the median run length

  • 이유진 (중앙대학교 응용통계학과) ;
  • 이재헌 (중앙대학교 응용통계학과)
  • Lee, Yoojin (Department of Applied Statistics, Chung-Ang University) ;
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
  • 투고 : 2016.09.23
  • 심사 : 2016.10.25
  • 발행 : 2016.11.30
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⟨ 이전 논문 다음 논문 ⟩

초록

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.

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.

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피인용 문헌

  1. 자기출발 EWMA와 $\bar{X}$ 관리도의 관리상태 성능 vol.29, pp.4, 2016, https://doi.org/10.7465/jkdi.2018.29.4.851