응용통계연구 (The Korean Journal of Applied Statistics)

  • 제10권2호
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  • Pages.385-401
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  • 1997
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
권호 표지

누적합관리도에서 평균런길이의 근사와 결정구간의 설정

An approximation method for the ARL and the decision interval in CUSUM control charts

  • 이재헌 ((503-703) 광주시 남구 진월동 592-1, 광주대학교 산업정보공학과) ;
  • 박창순 ((156-756) 서울시 동작구 흑석동 221, 중앙대학교 응용통계학과)
  • 발행 : 1997.09.01
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초록

연속적인 생산공정에서 꾸준하면서도 작은 품질의 변화를 신속하게 탐지하는 통계적 절차로서 누적합(CUSUM) 관리도를 많이 사용하고 있다. 본 논문에서는 누적합 관리도의 평균런길이를 근사하는 방법과 누적합관리도의 통계적 설계, 즉 관리상태에서의 평균런길이가 일정한 값으로 고정되었을 경우 이를 만족하는 결정구간을 설정하는 방법을 제시한다. 또한 이 방법을 관측값이 정규분포와 지수분포를 따르는 경우에 적용시켜 그 정확성을 비교하고 있다.

Cumulative sum (CUSUM) control charts are widely used in industry for the statistical process control. The statistical design procedure in CUSUM charts tells how to choose the decision interval value. The decision interval is primarily determied by the desired in - control ARL - that is, by the acceptable frequency of false out-of-control signals. In this paper we propose a new approximation method for calculating the ARL and determining the decision interval. The performance of the proposed method is examined by evaluating the accuracy of estimated ARLs and decision intervals in normal and exponential cases.

키워드

참고문헌

  1. Journal of Quality Technology v.23 no.4 An Optimal Design of CUSUM Quality Control Charts Gan, F. F.
  2. Journal of Quality Technology v.26 no.2 Design of Optimal Exponential CUSUM Control Charts Gan, F. F.
  3. Technometrics v.13 no.2 Determination of A.R.L. and a Contour Nomogram for CUSUM Charts to Control Normal Mean Goel, A. L.;Wu, S. M.
  4. Journal of Statistical Planning and Inference v.2 Wald's Approximations to the Average Run Length in CUSUM Procedures Khan, R. A.
  5. Journal of the Korean Statistical Society v.23 no.1 A Heuristic Approach for Approximating the ARL of the CUSUM Chart Kim, B. C.;Park, C. S.;Park, Y. H.;Lee, J. H.
  6. Sequential Analysis v.13 no.2 An Estimation Method for the Excess over the Boundaries in the SPRT and its Applications Lee, J. H.;Park, C. S.;Kim, B. C.
  7. Annals of Statistics v.14 Optimal Stopping Times for Detecting Changes in Distributions Moustakides, G. V.
  8. Biometrika v.41 Continous Inspection Schemes Page, E. S.
  9. Sequential Analysis v.6 no.3 A Corrected Wiener Process Approximation for CUSUM ARLs Park, C. S.
  10. Sequential Analysis v.11 no.1 An Approximation Method for the Characteristics of the Sequential Probability Ratio Test Park, C. S.
  11. Journal of the Korean Statistical Society v.19 no.2 A CUSUM Chart Based on Log Probability Ratio Statistic Park, C. S.;Kim B. C.
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  15. Sequential Analysis Wald, A.
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