A CUSUM Control Chart to Monitor Wafer Quality
C-control chart assumes that process nonconformities follow a Poisson distribution. In actuality, however, this Poisson distribution does not always occur. A process control for semiconductor based on a Poisson distribution always underestimates the true average amount of nonconformities and the process variance. Quality is described more accurately if a compound Poisson process is used for process control at this time. A cumulative sum (CUSUM) control chart is much better than a C control chart when a small shift will be detected. This study calculates one-sided CUSUM ARLs using a Markov chain approach to construct a CUSUM control chart with an underlying Poisson-Gamma compound distribution for the failure mechanism. Moreover, an actual data set from a wafer plant is used to demonstrate the operation of the proposed model. The results show that a CUSUM control chart realizes significantly better performance than EWMA.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1328390Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 2410
 S. F. Liu and F. L. Chen, "A data clustering model for wafer yield loss in semiconductor manufacturing." Journal of the Chinese Institute of Industrial Engineers, 21(4), pp. 328-338, 2004.
 S. H. Tong and B. J. Yum, "A dual burn-in policy for detect-tolerant memory products using the number of repairs as a quality indicator." Microelectronic Reliability, 48, pp. 471-480, 2008.
 C. H. Stapper, "The effects of wafer to wafer defect density variations on integrated circuit defect and fault distributions." IBM Journal of Research Development, 29(1), pp. 87- 97, 1985.
 S.L. Albin and D. J. Friedman, "Clustered defect in IC fabrication: Impact on process control charts." IEEE Transactions on Semiconductor Manufacturing, 14(1), pp. 36-42, 1991.
 L. I. Tong and L. C. Chao, "Novel yield model for integrated circuits with clustered defects." Expert System with Applications, 34, pp. 2334-2341, 2008.
 J. A. Cunningham, "The use and evaluation of yield models integrated circuit manufacturing." IEEE Transactions on Semiconductor Manufacturing, 3(2), pp. 60-71, 1990.
 K. L. Hsieh, L. I. Tong and M. C. Wang, "The application of control chart for defects and defect clustering in IC manufacturing based on fuzzy theory." Expert System with Applications, 32, pp. 765-776, 2007.
 C. W. Chen, Y. S. Wu, and K. W. Su, "A study on detecting small shifts in quality levels with the geometric Poisson process using EWMA control schemes." Journal of Quality. 13(1), pp. 85-97, 2006.
 D. C. Montgomery, "Introduction to statistical quality control." 3rd ed. John Wiley and Sons, New York, NY. 2005.
 F. J. Yu, Y. Y. Yang, M. J. Wang and Z. Wu, "Using EWMA control schemes for monitoring wafer quality in negative binomial process." Microelectronic Reliability, 51, pp. 400-405, 2011.
 G. V. Moustakides, "Optimal stopping times for detecting changes in distributions." Annals of Statistics, 14, pp. 1379-1387, 1986.
 B. T. Murphy, "Cost-size optimum of monolithic integrated circuits." Proceeding of the IEEE, 52, pp. 1537-1545, 1964.
 C. H. Stapper, "Defect density distribution for LSI yield calculations." IEEE Transactions on Electron Devices, 20, pp. 655-657, 1973.
 R. Winkelmann, "Econometric analysis of count data." 5th ed. Springer-Verlag, Heidelberg, 2008.
 C. H. Stapper, "LSI yield modeling and process monitoring." IBM Journal of Research Development, 40(1/2), pp. 112-118, 2000.
 D. Brook, and D. A. Evans, " An approach to the probability distribution of CUSUM run length. Biometrika," 59(3), pp. 539-549, 1972.
 J. M. Lucas, and R. B. Crosier, "Fast Initial Response for CUSUM Quality Control Schemes: Give You CUSUM a Head Start." Technometrics, 24, 199-205, 1982.
 J. C. Chang, and F. F. Gan, "Cumulative sum charts for high yield processes." Statistica Sinica, 11, pp. 791-805, 2001.
 J. C. Fu, F. A. Spiring, and H. Xie, "On the average run lengths of quality control schemes using a Markov chain approach." Statistics and Probability Letters, 56, pp. 369-380, 2002.
 L. C. Chao, "The yield prediction model with neural network for integrated circuit-based on Poisson model," Master-s thesis, Department of Industrial Engineering and Management, National Chiao Tung University, Taiwan. 1997.