응용통계연구 (The Korean Journal of Applied Statistics)

  • 제27권5호
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  • Pages.787-796
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  • 2014
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  • 1225-066X(pISSN)
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  • 2383-5818(eISSN)
한국통계학회 (The Korean Statistical Society)
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Poisson GLR 관리도

Poisson GLR Control Charts

  • 이재헌 (중앙대학교 응용통계학과) ;
  • 박종태 (평택대학교 디지털응용정보학과)
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University) ;
  • Park, Jongtae (Department of Digital Information and Statistics, Pyeongtaek University)
  • 투고 : 2014.08.13
  • 심사 : 2014.09.12
  • 발행 : 2014.10.31
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초록

Poisson 분포를 따르는 결점수를 관측하여 공정을 관리할 때 표본 크기를 동일하게 유지하기가 힘든 경우가 많다. 이 논문은 표본 크기가 동일하지 않은 경우 Poisson 공정모수의 변화를 탐지하는 GLR(generalized likelihood ratio) 관리도 절차를 제안하고 있다. 또한 제안된 GLR 관리도의 효율을 모의실험을 통하여 기존에 연구된 CUSUM 관리도들과 비교하였다. 모의실험 결과, 제안된 GLR 관리도는 공정모수의 다양한 변화에 대해 효율이 대체적으로 양호했으며, CUSUM 관리도에서 실제 공정모수의 변화값이 미리 지정한 값과 차이가 많이 날 경우 CUSUM 관리도에 비해 효율이 월등히 좋음을 알 수 있었다.

Situations where sample size is not constant are common when monitoring a process with Poisson count data. In this paper, we propose a generalized likelihood ratio(GLR) control chart to detect shifts in the Poisson rate when the sample size varies. The performance of the proposed GLR chart is compared with the performance of several cumulative sum(CUSUM) type charts. It is shown that the overall performance of the GLR chart is comparable with CUSUM type charts and is significantly better in cases where the actual value of the shift is different from the pre-specified value in CUSUM type charts.

키워드

참고문헌

  1. Choi, M. L. and Lee, J. (2014a). GLR charts for simultaneously monitoring a sustained shift and a linear drift in the process mean, Communications for Statistical Applications and Methods, 21, 69-80. https://doi.org/10.5351/CSAM.2014.21.1.069
  2. Choi, M. L. and Lee, J. (2014b). A GLR chart for monitoring a zero-inflated Poisson process, The Korean Journal of Applied Statistics, 27, 345-355. https://doi.org/10.5351/KJAS.2014.27.2.345
  3. Dong, Y., Hedayat, A. S. and Sinha, B. K. (2008). Surveillance strategies for detecting changepoint in incidence rate based on exponentially weighted moving average methods, Journal of the American Statistical Association, 103, 843-853. https://doi.org/10.1198/016214508000000166
  4. Hawkins, D. M. and Olwell, D. H. (1998). Cumulative Sum Charts and Charting for Quality Improvement, New York, NY: Springer.
  5. Mei, Y., Han, S. W. and Tsui, K. L. (2011). Early detection of a change in Poisson rate after accounting for population size effects, Statistica Sinica, 21, 597-624. https://doi.org/10.5705/ss.2011.027a
  6. Reynolds, M. R. J. and Lou, J. (2010). An evaluation of a GLR control chart for monitoring the process mean, Journal of Quality Technology, 42, 287-310. https://doi.org/10.1080/00224065.2010.11917825
  7. Reynolds, M. R. J., Lou, J., Lee, J. and Wang, S. (2013). The design of GLR control charts for monitoring the process mean and variance, Journal of Quality Technology, 45, 34-60. https://doi.org/10.1080/00224065.2013.11917914
  8. Rossi, G., Lampugnani, L. and Marchi, M. (1999). An approximate CUSUM procedure for surveillance of health events, Statistics in Medicine, 18, 2111-2122. https://doi.org/10.1002/(SICI)1097-0258(19990830)18:16<2111::AID-SIM171>3.0.CO;2-Q
  9. Ryan, A. G. and Woodall, W. H. (2010). Control charts for Poisson count data with varying sample sizes, Journal of Quality Technology, 42, 260-275. https://doi.org/10.1080/00224065.2010.11917823
  10. Yashchin, E. (1989). Weighted cumulative sum technique, Technometrics, 31, 321-338. https://doi.org/10.1080/00401706.1989.10488555

피인용 문헌

  1. A note on GLR charts for monitoring count processes vol.34, pp.6, 2018, https://doi.org/10.1002/qre.2306