The Korean Journal of Applied Statistics (응용통계연구)

The Korean Statistical Society (한국통계학회)
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A GLR Chart for Monitoring a Zero-Inflated Poisson Process

ZIP 공정을 관리하는 GLR 관리도

  • Choi, Mi Lim (Department of Applied Statistics, Chung-Ang University) ;
  • Lee, Jaeheon (Department of Applied Statistics, Chung-Ang University)
  • 최미림 (중앙대학교 응용통계학과) ;
  • 이재헌 (중앙대학교 응용통계학과)
  • Received : 2014.01.09
  • Accepted : 2014.03.06
  • Published : 2014.04.30
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Abstract

The number of nonconformities in a unit is commonly modeled by a Poisson distribution. As an extension of a Poisson distribution, a zero-inflated Poisson(ZIP) process can be used to fit count data with an excessive number of zeroes. In this paper, we propose a generalized likelihood ratio(GLR) chart to monitor shifts in the two parameters of the ZIP process. We also compare the proposed GLR chart with the combined cumulative sum(CUSUM) chart and the single CUSUM chart. It is shown that the overall performance of the GLR chart is comparable with CUSUM charts and is significantly better in some cases where the actual directions of the shifts are different from the pre-specified directions in CUSUM charts.

단위 영역의 결점수는 일반적으로 Poisson 분포를 가정한다. 이 Poisson 분포의 확장된 형태로 ZIP(zero-inflated Poisson) 분포를 고려할 수 있는데, 이 모형은 데이터에 0이 많이 관측되는 경우 잘 적합된다고 알려져 있다. 이 논문에서는 ZIP 분포를 따르는 공정을 관리하는 GLR(generalized likelihood ratio) 관리도 절차를 제안하고 있다. 또한 제안된 GLR 관리도의 효율을 기존에 제안된 CUSUM 관리도들과 비교하였다. 그 결과 제안된 GLR 관리도는 모수의 다양한 변화에 대해 효율이 좋거나 또는 효율이 크게 떨어지지 않았고, 특히 CUSUM 관리도에서 모수가 미리 설정한 방향과 다르게 변화했을 때 효율이 크게 나빠지는 문제를 해결할 수 있는 대안이라는 결론을 얻을 수 있었다.

Keywords

References

  1. Borror, C. M., Champ, C. W. and Rigdon, S. E. (1998). Poisson EWMA control charts, Journal of Quality Technology, 30, 352-361.
  2. Chen, N., Zhou, S., Chang, T.-S. and Huang, H. (2008). Attribute control charts using generalized zeroinflated Poisson distribution, Quality and Reliability Engineering International, 24, 793-806. https://doi.org/10.1002/qre.928
  3. Choi, M. L. and Lee, J. (2014). GLR charts for simultaneously monitoring a sustained shift and a linear drift in the process mean, Communications for Statistical Applications and Methods, to appear.
  4. He, B., Xie, M., Goh, T. N. and Ranjan, P. (2003). On the estimation error in zero-inflated Poisson model for process control, International journal of Reliability, Quality, and Safety Engineering, 10, 159-169. https://doi.org/10.1142/S0218539303001068
  5. He, S., Huang, W. and Woodall, W. H. (2012). CUSUM charts for monitoring a zero-inflated Poisson process, Quality and Reliability Engineering International, 28, 181-192. https://doi.org/10.1002/qre.1228
  6. Lai, T. L. (1995). Sequential changepoint detection in quality-control and dynamical-systems, Journal of the Royal Statistical Society: Series B-Statistical Methodology, 57, 613-658.
  7. Lucas, J. M. (1985). Counted data CUSUM's, Technometrics, 27, 129-144. https://doi.org/10.1080/00401706.1985.10488030
  8. Reynolds, M. R. Jr., 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.
  9. Sim, C. H. and Lim, M. H. (2008). Attribute charts for zero-inflated processes, Communications in Statistics- Simulation and Computation, 37, 1440-1452. https://doi.org/10.1080/03610910801983145
  10. Xie, M. and Goh, T. N. (1993). SPC of a near zero-defect process subject to random shock, Quality and Reliability Engineering International, 9, 89-93. https://doi.org/10.1002/qre.4680090205
  11. Xie, M., He, B. and Goh, T. N. (2001). Zero-inflated Poisson model in statistical process control, Computational Statistics and Data Analysis, 38, 191-201. https://doi.org/10.1016/S0167-9473(01)00033-0

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  1. Poisson GLR Control Charts vol.27, pp.5, 2014, https://doi.org/10.5351/KJAS.2014.27.5.787