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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

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.

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