The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A Markov Chain Representation of Statistical Process Monitoring Procedure under an ARIMA(0,1,1) Model

ARIMA(0,1,1)모형에서 통계적 공정탐색절차의 MARKOV연쇄 표현

  • 박창순 (중앙대학교 수학통계학부)
  • Published : 2003.03.01
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Abstract

In the economic design of the process control procedure, where quality is measured at certain time intervals, its properties are difficult to derive due to the discreteness of the measurement intervals. In this paper a Markov chain representation of the process monitoring procedure is developed and used to derive its properties when the process follows an ARIMA(0,1,1) model, which is designed to describe the effect of the noise and the special cause in the process cycle. The properties of the Markov chain depend on the transition matrix, which is determined by the control procedure and the process distribution. The derived representation of the Markov chain can be adapted to most different types of control procedures and different kinds of process distributions by obtaining the corresponding transition matrix.

일정 시간간격으로 품질을 측정하는 공정관리절차의 경제적 설계에서는 그 특성의 규명이 측정시점의 이산성 (discreteness) 때문에 복잡하고 어렵다. 이 논문에서는 공정 탐색 절차를 Markov 연쇄(chain)로 표현하는 과정을 개발하였고, 공정분포가 공정주기 내에서 발생하는 잡음과 이상원인의 효과를 설명할 수 있는 ARIMA(0,1,1) 모형을 따를 때에 Markov 연쇄의 표현을 이용하여 공정탐색절차의 특성을 도출하였다. Markov 연쇄의 특성은 전이행렬에 따라 달라지며, 전이행렬은 관리절차와 공정분포에 의해 결정된다. 이 논문에서 도출된 Markov 연쇄의 표현은 많은 다른 형태의 관리절차나 공정분포에서도 그에 해당하는 전이행렬을 구하면 쉽게 적용될 수 있다.

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References

  1. Journal of Quality Technology v.29 A Comparison of Statistical Process Control and Engineering Process Control Box G. E. P.;Coleman, D. E.;Baxley R. V., Jr. https://doi.org/10.1080/00224065.1997.11979740
  2. Technometrics v.34 Statistical Process Control and Feddback Adjustment A Discussion Box, G. E. P.;Kramer, T.
  3. Technometrics v.36 Selection of Sampling Inteval and Action Limit for Discrete Feedback Adjustment Box, G. E. P;Luceno, A. https://doi.org/10.2307/1269952
  4. Technometrics v.28 The Economic Design of Control Charts : a Unified Approach Lorenzen, T. J.;Vance, L. C. https://doi.org/10.2307/1269598
  5. Journal of Quality Technology v.31 EWMA Control Charts for Monitoring the Mean of Autocorrelated Processes Lu, C. W.;Reynolds, M. R., Jr. https://doi.org/10.1080/00224065.1999.11979913
  6. Journal of Quality Technology v.21 Economic Control Chart Desings and the In-Control Time Distribution : A sensitivity Study McWilliams, T. P. https://doi.org/10.1080/00224065.1989.11979152
  7. IIE Transactions v.30 The SPRT Chart for Monitoring a Proportion Reynolds, M. F., Jr.;Stoumbos, Z. G.
  8. Applied Probability Models with Optimization Applications Ross, S. M.
  9. Technometrics v.31 Economic Statistical Control Chart Designs with an Application to and R Charts Saniga, E. M. https://doi.org/10.2307/3556141
  10. Technometrics v.26 On the Markov Chain Approach to the Two-Sides CUSUM Procedure Woodall, W. H. https://doi.org/10.2307/1268414