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

Markov 과정의 최초통과시간을 이용한 지수가중 이동평균 관리도의 평균런길이의 계산

  • 박창순 (중앙대학교 응용통계학과)
  • Received : 2016.10.12
  • Accepted : 2016.11.03
  • Published : 2017.02.28

Abstract

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.

Acknowledgement

Supported by : 한국연구재단

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