Multivariate Gamma-Poisson Model and Parameter Estimation for Polytomous Data : Application to Defective Pixels of LCD

다가자료에 적합한 다변수 감마-포아송 모델과 파라미터 추정방법 : LCD 화소불량 응용

  • Ha, Jung-Hoon (School of Information and Computer Engineering, Hongik University)
  • 하정훈 (홍익대학교 정보컴퓨터공학부 산업공학)
  • Received : 2011.01.14
  • Accepted : 2011.03.14
  • Published : 2011.03.31

Abstract

Poisson model and Gamma-Poisson model are popularly used to analyze statistical behavior from defective data. The methods are based on binary criteria, that is, good or failure. However, manufacturing industries prefer polytomous criteria for classifying manufactured products due to flexibility of marketing. In this paper, I introduce two multivariate Gamma-Poisson(MGP) models and estimation methods of the parameters in the models, which are able to handle polytomous data. The models and estimators are verified on defective pixels of LCD manufacturing. Experimental results show that both the independent MGP model and the multinomial MGP model have excellent performance in terms of mean absolute deviation and the choice of method depends on the purpose of use.

Keywords

References

  1. Shiau, J. H., Chen, C-R., and Feltz, C. J.; "An empirical Bayes process monitoring technique for polytomous data," Quality and Reliability Engineering International, 21 : 13-28, 2005. https://doi.org/10.1002/qre.604
  2. International Organization for Standardization; ISO 13406-2 : 2001(F) Ch 7.20, ISO, 2001.
  3. Dai, X. L., Hunt, M. A., and Schulze, M. A.; in : Machine Vision Applications in Industrial Inspection XI, Proceedings of SPIE, 5011, Santa Clara, CA, 23-24, 2003.
  4. Shankar, N. G. and Zhong, Z. W.; "Defect Detection on Semiconductor Wafer Surfaces," Microelectronic Engineering, 77(3-4) : 337-346, 2005. https://doi.org/10.1016/j.mee.2004.12.003
  5. Ha, C.; "Relationship Between Yield and Cost Considering Repair and Rework for LCD Manufacturing System," Journal of the Korean Institute of Industrial Engineers, 33(3) : 364-372, 2007.
  6. ICE; Yield and Yield Management, Chapter 3 in Cost Effective IC Manufacturing 1998-1999, Integrated Circuit Engineering Corporation, 1997.
  7. Shindo, W., Nurani, R. K., and Strojwas, A. J.; "Effects of defect propagation/growth on inline defect-based yield prediction," IEEE Transactions on Semiconductor Manufacturing, 11(4) : 546-551, 1998. https://doi.org/10.1109/66.728550
  8. Stapper, C. H. and Rosner, R. J.; "Integrated circuit yield management and yield analysis : development and implementation," IEEE Transactions on Semiconductor Manufacturing, 8(2) : 95-102, 1995.
  9. Stapper, C. H.; "Modeling of defects in integrated circuit photolitho graphic patterns," IBM Journal of Research and Development, 28(4) : 461-475, 1984.
  10. Milor, L. S.; "Yield modeling based on in-line scanner defect sizing and a circuit's critical area," IEEE Transactions on Semiconductor Manufacturing, 12(1) : 26-35, 1999. https://doi.org/10.1109/66.744517
  11. Ha, C.; "Effective construction method of defect size distribution using AOI data : application for semiconductor and LCD manufacturing," IE Interfaces, 21(2) : 151-160, 2008.
  12. Ghosh, S. K., Mukhopadhyay, P., and Lu, J. C.; "Bayesian analysis of zero-inflated regression models," Journal of Statistical Planning and Inference, 136 : 1360-1375, 2006. https://doi.org/10.1016/j.jspi.2004.10.008
  13. Ha, C., Chang, J. H., and Kim, J. H.; "Estimation of Defect Clustering Parameter Using Markov Chain Monte Carlo," Journal of the Society of Korea Industrial and Systems Engineering, 32(3) : 99-109, 2009.
  14. Nelson, J. F.; "Multivariate Gamma-Poisson Models," Journal of the American Statistical Association, 80(392) : 828-834, 1985. https://doi.org/10.1080/01621459.1985.10478190
  15. Piegorsch, W. W.; "Maximum Likelihood Estimation for the Negative Binomial Dispersion Parameter," Biometrics, 46 : 863-867, 1990. https://doi.org/10.2307/2532104