응용통계연구 (The Korean Journal of Applied Statistics)

  • 제33권2호
  • /
  • Pages.161-170
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  • 2020
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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관리한계 설정에 따른 ${\bar{X}}-S^2$ 관리도의 성능

Performance of the combined ${\bar{X}}-S^2$ chart according to determining individual control limits

  • 홍휘주 (중앙대학교 응용통계학과) ;
  • 이재헌 (중앙대학교 응용통계학과)
  • Hong, Hwi Ju (Department of Applied Statistics, Chung-Ang University) ;
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
  • 투고 : 2020.02.04
  • 심사 : 2020.02.28
  • 발행 : 2020.04.30
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⟨ 이전 논문 다음 논문 ⟩

초록

${\bar{X}}-S^2$ 관리도는 공정 평균과 산포의 변화를 동시에 탐지하는 전통적인 관리도들 중 하나이다. 일반적으로 사용하는 ${\bar{X}}-S^2$ 관리도의 설계 방법은 병행하는 관리도의 오경보율은 주어진 값을 만족하면서 각 관리도는 동일한 개별적인 오경보율을 갖도록 설정하는 것이다. 이 논문에서는 각 관리도의 개별 오경보율을 다르게 설정하고 이것이 ${\bar{X}}-S^2$ 관리도의 성능에 어떠한 영향을 주는지 살펴보았다. 이를 위해 ${\bar{X}}$ 관리도의 오경보율을 S2 관리도의 오경보율에 γ배한 경우를 고려하였고, γ값에 따른 ${\bar{X}}-S^2$ 관리도 성능을 비교하였다. 관리도의 성능을 평가하는 측도로는 특정한 변화에 대한 성능을 판단하는 경우 이상상태에서의 평균런길이를 사용하였고, 전반적인 성능을 판단하는 경우 RMI(relative mean index)를 사용하였다.

The combined ${\bar{X}}-S^2$ chart is a traditional control chart for simultaneously detecting mean and variance. Control limits for the combined ${\bar{X}}-S^2$ chart are determined so that each chart has the same individual false alarm rate while maintaining the required false alarm rate for the combined chart. In this paper, we provide flexibility to allow the two charts to have different individual false alarm rates as well as evaluate the effect of flexibility. The individual false alarm rate of the ${\bar{X}}$ chart is taken to be γ times the individual false alarm rate of the S2 chart. To evaluate the effect of selecting the value of γ, we use the out-of-control average run length and relative mean index as the performance measure for the combined ${\bar{X}}-S^2$ chart.

키워드

참고문헌

  1. Faraz, A., Saniga, E., and Montgomery, D. (2019). Percentile-based control chart design with an application to Shewhart $\bar{X}$and $S^2$ control charts, Quality and Reliability Engineering International, 35, 116-126. https://doi.org/10.1002/qre.2384
  2. McCracken, A. K. and Chakraborti, S. (2013). Control charts for joint monitoring of mean and variance: an overview, Quality Technology and Quantitative Management, 10, 17-36. https://doi.org/10.1080/16843703.2013.11673306
  3. McCracken, A. K., Chakraborti, S., and Mukherjee, A. (2013). Control charts for simultaneous monitoring of unknown mean and variance of normally distributed processes, Journal of Quality Technology, 45, 360-376. https://doi.org/10.1080/00224065.2013.11917944
  4. McWilliams, T. , Saniga, E., and Davis, D. (2001). Economic-statistical design of $\bar{X}$ and R or $\bar{X}$ and S charts, Journal of Quality Technology, 33, 234-241. https://doi.org/10.1080/00224065.2001.11980070
  5. Montgomery, D. C. (2013). Statistical Quality Control: A Modern Introduction (7th ed.), John Wiley & Sons, Singapore.
  6. Quinino, R. C., Cruz, F. R. B., and Ho, L. L. (2020). Attribute inspection control charts for the joint monitoring of mean and variance, Computers & Industrial Engineering, 139, 106131. https://doi.org/10.1016/j.cie.2019.106131
  7. Saniga, E. (1991). Joint statistical design of $\bar{X}$ and R control charts, Journal of Quality Technology, 23, 156-162. https://doi.org/10.1080/00224065.1991.11979305
  8. Sanusi, R. A., Mukherjee, A., and Xie, M. (2019). A comparative study of some EWMA schemes for simultaneous monitoring of mean and variance of a Gaussian process, Computers & Industrial Engineering, 135, 426-439. https://doi.org/10.1016/j.cie.2019.06.021
  9. Zhang, C, Tsung, F., and Xiang, D. (2016). Monitoring censored lifetime data with a weighted-likelihood scheme, Naval Research Logistics, 63, 631-646. https://doi.org/10.1002/nav.21724