The GLR Chart for Poisson Process with Individual Observations

Abstract:

A GLR (generalized likelihood ratio) chart for Poisson distributed process with individual observations is proposed and the design procedure of the GLR chart is discussed. The performance of the GLR charts is compared to the exponentially weighted moving average (EWMA) chart and the GWMA chart. The numerical experiments show that the GLR chart has comparable performance as the other two charts. However, the GLR chart is much easier to design and implement since there are more design parameters in these two charts.

• Periodical: Advanced Materials Research (Volumes 542-543)
• Pages: 42-46
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.542-543.42
• Online since: June 2012
• Authors: Li Li
• Keywords: GLR Chart, Individual Observations, Moving Window, Poisson Process

References

[1] J. M. Lucas, Counted Data CUSUM's, Technometrics, vol. 27, no. 2(1985), pp.129-144.

[2] C. M. Borror, C. W. Champ, and S. E. Rigdon, Poisson EWMA control charts, Journal of Quality Technology, vol. 30, no. 4(1998), pp.352-361.

DOI: 10.1080/00224065.1998.11979871

[3] J. M. Lucas, Combined Shewhart-CUSUM Quality Control Schemes: A Robustness Study for CUSUM Quality Control Schemes, Journal of Quality Technology, vol. 14(1982), pp.51-59.

DOI: 10.1080/00224065.1982.11978790

[4] Z. Wu, M. Yang, W. Jiang, and M. Khoo, Optimization Designs of the Combined Shewhart-CUSUM Control Charts, Computational Statistics & Data Analysis, vol. 53(2008), pp.496-506.

DOI: 10.1016/j.csda.2008.08.032

[5] Y. Zhao, F. Tsung, and Z. Wang, Dual CUSUM Control Schemes for Detecting a Range of Mean Shifts, IIE Transactions, vol. 37(2005), pp.1047-1057.

DOI: 10.1080/07408170500232321

[6] R. S. Sparks, CUSUM Charts for Signalling Varying Location Shifts, Journal of Quality Technology, vol. 32, no. 2(2000), pp.157-171.

DOI: 10.1080/00224065.2000.11979987

[7] D. Han, F. Tsung, X. Hu, and K. Wang, CUSUM and EWMA Multi-charts for Detecting a Range of Mean Shifts, Statistica Sinica, vol. 17(2007), pp.1139-1164.

[8] L. Shu and W. Jiang, A Markov Chain Model for the Adaptive CUSUM Control Chart, Journal of Quality Technology, vol. 38, no. 2(2006), pp.135-147.

DOI: 10.1080/00224065.2006.11918601

[9] W. Jiang, L. Shu, and D. Apley, Adaptive CUSUM Procedures with EWMA-based Shift Estimators, IIE Transactions, vol. 40(2008), pp.992-1003.

DOI: 10.1080/07408170801961412

[10] Z. Wu, J. Jiao, M. Yang, Y. Liu, and Z. Wang, An Enhanced Adaptive CUSUM Control Chart, IIE Transactions, vol. 41(2009), pp.642-653.

DOI: 10.1080/07408170802712582

[11] A. Willsky and H. Jones, A Generalized Likelihood Ratio Approach to the Detection and Estimation of Jumps in Linear Systems, IEEE Transactions on Automatic Control, vol. 21, no. 1(1976), pp.108-112.

DOI: 10.1109/tac.1976.1101146

[12] T. L. Lai, Sequential Analysis:Some Classical Problems and New Challenges, Statistica Sinica, vol. 11(2001), pp.303-408.

[13] M. R. Reynolds and J. Lou, An Evaluation of a GLR Control Chart for Monitoring the Process Mean, Journal of Quality Technology, vol. 42, no. 3(2010), pp.287-310.

DOI: 10.1080/00224065.2010.11917825

[14] D. W. Apley and J. Shi, The GLRT for Statistical Process Control of Autocorrelated Processes, IIE Transactions, vol. 31(1999), pp.1123-1134.

DOI: 10.1080/07408179908969913

[15] D. M. Hawkins and P. Qiu, The Change-point Model for Statistical Process Control, Journal of Quality Technology, vol. 35, no. 4(2003), pp.355-366.

[16] D. M. Hawkins and K. D. Zamba, Statistical Process Control for Shifts in Mean or Variance Using a Changepoint Formulation, Technometrics, vol. 47, no. 2(2005), pp.164-173.

DOI: 10.1198/004017004000000644

[17] E. Gombay, Sequential Change-point Detection with Likelihood Ratios, Statistics & Probability Letters, vol. 49, no. 2(2000), pp.195-204.

DOI: 10.1016/s0167-7152(00)00048-1

[18] S. H. Sheu and W. C. Chiu. Poisson GWMA Control Chart. Communication in Statistics-Simulation and Computation, vol. 36, no. 5(2007), pp.1099-1114

DOI: 10.1080/03610910701540037