The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Selection of the economically optimal parameters in the EWMA control chart

지수가중이동평균관리도의 경제적 최적모수의 선정

  • 박창순 ((156-756) 서울 동작구 흑석동 산221, 중앙대학교 정경대학 응용통계학과) ;
  • 원태연 ((156-756) 서울 동작구 흑석동 산221, 중앙대학교 정경대학 응용통계학과)
  • Published : 1996.03.01
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Abstract

Exponentially weighted moving averae(EWMA) control chart has been used widely for process monitoring and process adjustment recently, but there has not been many studies about the selection of the parameters. Design of the control chart can be classified into the statistical design and the economic design. The purpose of the economic design is to minimize the cost function in which all the possible costs occurring during the process are probability given the Type I error probability. In this paper the optimal parameters of the EWMA chart are selected for the economic design as well as for the statistical design. The optimal parameters for the economic design show significantly different from those of the statistical design, and especially the weight is always larger than that used in the statistical design. In the economic design, we divide the model into the single assignable cause model and the multiple assignable causes model caacording to number of which is used as the average context of the multiple assignable causes, it shows that the selection of the parameters may be misleading when the multiple assignable causes exist in practice.

지수가중이동평균관리도는 최근 들어 공정검색과 공정수정에 널리 이용되고 있으나 모수의 설정에 관한 연구는 많지 않다. 관리도의 설계는 통계적 설계와 경제적 설계로 분류한다. 통계적 설계는 허용된 제1종 오류하에서 제2종 오류를 최소화하는데 반해 경제적 설계는 공정에서 발생하는 모든 가능한 비용을 고려한 비용함수를 최소화한다. 이 논문에서는 지수가중이동평균관리도의 통계적 설계와 함께 경제적 설계를 정의한 다음 각 설계에서의 최적모수를 선정하여 결과를 비교한다. 경제적 설계에서 설정된 최적모수는 통계적 설계와 다르게 나타남을 알 수 있고 특히 가중치의 값은 통계적 설계에서 보다 항상 큰 값으로 나타난다. 경제적 설계에서는 고려하는 이상원인의 수에 따라 단일이상원인과 다중이상원인 모형으로 구분하여 설계한다. 다중이상원인의 평균적 개념으로 적용되는 단일이상원인 모형에서는 실제 다중이상원인이 존재할 때에 잘못된 판단을 할 수 있음을 보이고 있다.

Keywords

References

  1. Handbook of Mathemetical Functions with Formulas, Graghs and Mathemetical Tables Abramowitz, M.;Stegun, I. A.
  2. Technometrics v.34 no.3 Statistical Process Monitoring and Feedback Adjustment - A Discussion Box, G.;Kramer, T.
  3. Technometrics v.29 A Simple Method for Studying Run-Length Distribution of Exponentially Weighted Moving Average Charts Crowder, S. V.
  4. Journal of Quality Technology v.19 Average Run Length of Exponentially Weighted Moving Average Charts Crowder, S. V.
  5. Journal of Quality Technology v.24 An EWMA for Monitoring a Process Standard Deviation Crowder, S. V.;Hamilton, M.
  6. Journal of the American Statistical Association v.51 The Economic Design of X-Charts Used to Maintain Current Control of a Process Duncan, A. J.
  7. Journal of the American Statistical Association v.66 The Economic Design of X-Charts When There Is a Multiplicity of Assignable Causes Duncan, A. J.
  8. Journal of the American Statistical Association v.63 An Algorithm for the Determination of the Economic Design of X-Charts based on Duncan's Model Goel, A. L.;Jain, S. C.;Wu, S. M.
  9. ACM Transactions on Mathematical Software v.4 Design and Testing of Generalized Reduced Gradient Code for Nonlinear Programming Lasdon, L. S.;Waren, A. D.;Jain A.;Ranter M.
  10. GRG2 User's Guide Lasdon, L. S.;Waren, A. D.
  11. Technometrics v.28 no.1 The Economic Design of Control Charts; A Unified Approach Lorenzen, T. J.;Vance, L. C.
  12. Technometrics v.32 no.1 EWMA Control Chart Schemes : Properties and Enhancements Lucas, J. M.;Saccucci, M. S.
  13. Journal of Quality Technology v.12 no.2 The Economic Design of Control Charts : A Review and Literature Survey Montgomery, D. C.
  14. Journal of Quality Technology v.14 no.1 Economic Design of an X-Control Chart Montgomery, D. C.
  15. Journal of Quality Technology v.27 no.3 Statistically Constrained Economic Design of EWMA Control Charts Montgomery, D. C.;Torng, J. C.;Cochran, J. K.;Lawrence, F. P.
  16. Biometrika v.41 Continuous Inspection Schemes Page, E. S.
  17. Communication in Statistics : Simulation and Computation v.23 no.2 Economic Design of a Variable Sample Size X-Charts Park, C.;Reynolds, M. R.
  18. Technometrics v.1 Control Chart Tests based on Geometric Moving Average Roberts, S. W.
  19. Technometrics v.20 Average Run Lengths of Geometric Moving Average Charts by Numerical Methods Robinson, P. O.;Ho, T. Y.
  20. Technometrics v.31 no.3 Economic Statistical Control Charts Design with an Application to X and R Charts Saniga, E. M.
  21. Economic control of Quality of Manufactured Product Shewhart, W. A.
  22. Technometrics v.10 no.3 The Economic Design of Cumulative Sum Control Charts Taylor, H. M.