응용통계연구 (The Korean Journal of Applied Statistics)

  • 제30권1호
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  • Pages.1-12
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  • 2017
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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Markov 과정의 최초통과시간을 이용한 지수가중 이동평균 관리도의 평균런길이의 계산

Average run length calculation of the EWMA control chart using the first passage time of the Markov process

  • 박창순 (중앙대학교 응용통계학과)
  • 투고 : 2016.10.12
  • 심사 : 2016.11.03
  • 발행 : 2017.02.28
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⟨ 이전 논문 다음 논문 ⟩

초록

많은 확률과정이 Markov 특성을 만족하거나 근사적으로 만족하는 것으로 가정된다. Markov 과정에서 특히 관심을 끄는 것은 최초통과시간이다. 최초통과시간에 대한 연구는 Wald의 축차분석에서 시작하여 근사적 특성에 대한 많은 연구가 되어왔고 컴퓨터의 발달로 통계계산적 방법이 사용되면서 근사적 결과가 참값에 가까운 값을 계산할 수 있게 되었다. 이 논문은 Markov 과정의 예로서 지수가중 이동평균 관리도를 사용할 때 평균런길이를 계산하는 과정과 계산상의 주의점, 문제점 등을 연구하였다. 이 결과는 다른 모든 Markov 과정에 적용될 수 있으며 특히 Markov 연쇄로의 근사는 확률과정의 특성의 연구에 유용하고 계산적 접근을 용이하게 한다.

Many stochastic processes satisfy the Markov property exactly or at least approximately. An interested property in the Markov process is the first passage time. Since the sequential analysis by Wald, the approximation of the first passage time has been studied extensively. The Statistical computing technique due to the development of high-speed computers made it possible to calculate the values of the properties close to the true ones. This article introduces an exponentially weighted moving average (EWMA) control chart as an example of the Markov process, and studied how to calculate the average run length with problematic issues that should be cautioned for correct calculation. The results derived for approximation of the first passage time in this research can be applied to any of the Markov processes. Especially the approximation of the continuous time Markov process to the discrete time Markov chain is useful for the studies of the properties of the stochastic process and makes computational approaches easy.

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참고문헌

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