The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Effects of Parameter Estimation in Phase I on Phase II Control Limits for Monitoring Autocorrelated Data

자기상관 데이터 모니터링에서 일단계 모수 추정이 이단계 관리한계선에 미치는 영향 연구

  • Lee, Sungim (Department of Applied Statistics, Dankook University)
  • Received : 2015.08.28
  • Accepted : 2015.09.09
  • Published : 2015.10.31
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Abstract

Traditional Shewhart control charts assume that the observations are independent over time. Current progress in measurement and data collection technology lead to the presence of autocorrelated process data that may affect poor performance in statistical process control. One of the most popular charts for autocorrelated data is to model a correlative structure with an appropriate time series model and apply control chart to the sequence of residuals. Model parameters are estimated by an in-control Phase I reference sample since they are usually unknown in practice. This paper deals with the effects of parameter estimation on Phase II control limits to monitor autocorrelated data.

1920년대에 소개되었던 Shewhart 관리도는 관측치가 서로 독립임을 가정했다. 오늘날은 데이터 측정과 자료수집 기술이 발전하면서 자기상관 공정 데이터가 많이 발생하고 있으며, 이것은 통계적 공정 관리의 성능에 부정적인 영향을 끼치게 된다. 자기상관이 존재하는 데이터에 대하여 가장 쉽게 접근할 수 있는 관리도는 먼저 자기상관구조를 모형화할 수 있는 적절한 시계열 모형을 가정한 다음 잔차를 구하여, 그 잔차에 기반한 Shewhart 관리도를 적용하는 것이다. 실제 문제에서 시계열 모형의 참 모수값은 알려져 있지 않으므로, 이 값은 일단계 표본(과거의 관리상태 표본)으로부터 추정된다. 본 논문에서는 이러한 모수추정이 이단계 표본을 모니터링하는데 어떠한 영향이 있는지 살펴보았다.

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References

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