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.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] J. A. Cunningham, "The use and evaluation of yield models integrated
circuit manufacturing." IEEE Transactions on Semiconductor
Manufacturing, 3(2), pp. 60-71, 1990.
[7] 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.
[8] 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.
[9] D. C. Montgomery, "Introduction to statistical quality control." 3rd ed.
John Wiley and Sons, New York, NY. 2005.
[10] 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.
[11] G. V. Moustakides, "Optimal stopping times for detecting changes in
distributions." Annals of Statistics, 14, pp. 1379-1387, 1986.
[12] B. T. Murphy, "Cost-size optimum of monolithic integrated circuits."
Proceeding of the IEEE, 52, pp. 1537-1545, 1964.
[13] C. H. Stapper, "Defect density distribution for LSI yield calculations."
IEEE Transactions on Electron Devices, 20, pp. 655-657, 1973.
[14] R. Winkelmann, "Econometric analysis of count data." 5th ed.
Springer-Verlag, Heidelberg, 2008.
[15] C. H. Stapper, "LSI yield modeling and process monitoring." IBM
Journal of Research Development, 40(1/2), pp. 112-118, 2000.
[16] D. Brook, and D. A. Evans, " An approach to the probability distribution
of CUSUM run length. Biometrika," 59(3), pp. 539-549, 1972.
[17] 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.
[18] J. C. Chang, and F. F. Gan, "Cumulative sum charts for high yield
processes." Statistica Sinica, 11, pp. 791-805, 2001.
[19] 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.
[20] 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.
[1] 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.
[2] 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.
[3] 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.
[4] 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.
[5] 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.
[6] J. A. Cunningham, "The use and evaluation of yield models integrated
circuit manufacturing." IEEE Transactions on Semiconductor
Manufacturing, 3(2), pp. 60-71, 1990.
[7] 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.
[8] 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.
[9] D. C. Montgomery, "Introduction to statistical quality control." 3rd ed.
John Wiley and Sons, New York, NY. 2005.
[10] 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.
[11] G. V. Moustakides, "Optimal stopping times for detecting changes in
distributions." Annals of Statistics, 14, pp. 1379-1387, 1986.
[12] B. T. Murphy, "Cost-size optimum of monolithic integrated circuits."
Proceeding of the IEEE, 52, pp. 1537-1545, 1964.
[13] C. H. Stapper, "Defect density distribution for LSI yield calculations."
IEEE Transactions on Electron Devices, 20, pp. 655-657, 1973.
[14] R. Winkelmann, "Econometric analysis of count data." 5th ed.
Springer-Verlag, Heidelberg, 2008.
[15] C. H. Stapper, "LSI yield modeling and process monitoring." IBM
Journal of Research Development, 40(1/2), pp. 112-118, 2000.
[16] D. Brook, and D. A. Evans, " An approach to the probability distribution
of CUSUM run length. Biometrika," 59(3), pp. 539-549, 1972.
[17] 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.
[18] J. C. Chang, and F. F. Gan, "Cumulative sum charts for high yield
processes." Statistica Sinica, 11, pp. 791-805, 2001.
[19] 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.
[20] 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.
@article{"International Journal of Mechanical, Industrial and Aerospace Sciences:49556", author = "Sheng-Shu Cheng and Fong-Jung Yu", title = "A CUSUM Control Chart to Monitor Wafer Quality", abstract = "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.
", keywords = "Nonconformities, Compound Poisson distribution, CUSUM control chart.", volume = "7", number = "6", pages = "968-6", }
