The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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Performance of CCC-r charts with bootstrap adjusted control limits

붓스트랩에 기초하여 조정한 관리한계를 사용하는 CCC-r 관리도의 성능

  • Kim, Minji (Department of Applied Statistics, Chung-Ang University) ;
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
  • 김민지 (중앙대학교 응용통계학과) ;
  • 이재헌 (중앙대학교 응용통계학과)
  • Received : 2020.06.23
  • Accepted : 2020.07.02
  • Published : 2020.08.31
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Abstract

CCC-r chart is effective for high-quality processes with a very low fraction nonconforming. The values of process parameters should be estimated from the Phase I sample since they are often not known. However, if the Phase I sample size is not sufficiently large, an estimation error may occur when the parameter is estimated and the practitioner may not achieve the desired in-control performance. Therefore, we adjust the control limits of CCC-r charts using the bootstrap algorithm to improve the in-control performance of charts with smaller sample sizes. The simulation results show that the adjustment with the bootstrap algorithm improves the in-control performance of CCC-r charts by controlling the probability that the in-control average number of observations to signal (ANOS) has a value greater than the desired one.

CCC-r 관리도는 불량률이 매우 낮은 고품질 공정을 관리하는 데 효율적이라고 알려져 있다. 대부분의 공정에서 공정 모수의 값은 알려져 있지 않기 때문에 제1국면에서 이를 추정해야 하는데, 표본의 크기가 충분히 크지 않은 경우 추정 오차가 발생하여 원하는 관리상태에서의 성능을 만족하지 못하는 경우가 발생한다. 뿐만 아니라 제1국면에서 추출하는 표본에 따른 산포로 인하여 관리상태일 때의 성능의 산포 또한 커지게 된다. 이러한 문제를 해결하기 위해 이 논문에서는 관리상태일 때 신호까지의 평균관측개수가 사전에 정한 확률로 목표하는 값보다 큰 값을 갖도록, 붓스트랩 알고리즘을 사용하여 CCC-r 관리도의 관리한계를 조정하는 절차를 제안하였다. 이때 고품질 공정에 적용하기 위하여 최대우도추정량 대신 베이즈추정량을 사용하여 불량률을 추정하였다. 다양한 상황에 대해 모의실험을 수행한 결과, 제안된 절차는 CCC-r 관리도의 관리상태 성능을 크게 향상시킴을 알 수 있었다.

Keywords

References

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