Traditional multivariate control charts assume that measurement from manufacturing processes follows a multivariate normal distribution. However, this assumption may not hold or may be difficult to verify because not all the measurement from manufacturing processes are normal distributed in practice. This study develops a new multivariate control chart for monitoring the processes with non-normal data. We propose a mechanism based on integrating the one-class classification method and the adaptive technique. The adaptive technique is used to improve the sensitivity to small shift on one-class classification in statistical process control. In addition, this design provides an easy way to allocate the value of type I error so it is easier to be implemented. Finally, the simulation study and the real data from industry are used to demonstrate the effectiveness of the propose control charts.
[1] S. Bersimis, S. Psarakis, and J. Panaretos, "Multivariate statistical process
control charts: an overview,” Quality and Reliability Engineering
International, vol. 23, no.5, pp. 517-543. Aug 2007.W.-K. Chen, Linear
Networks and Systems (Book style). Belmont, CA: Wadsworth, 1993,
pp. 123–135.
[2] H. Hotelling, "Multivariate quality control-illustrated by the air testing of
sample bombsight,"Techniques of Statistical Analysis, McGraw-Hill:
New York, 1947, pp. 111-184.
[3] R.B. Crosier, "Multivariate generalizations of cumulative sum
quality-control schemes,” Technometrics, vol. 30, no. 3, pp. 291-303,
Aug 1988.
[4] C. A.Lowry, W.H. Woodall, C.W. Champ, and S.E. Rigdon, "A
multivariate exponentially weighted moving average control
chart,”Technometrics, vol. 34, no. 1, pp. 46-53,Feb 1992.
[5] R.Y.Liu, "Control chart for multivariate process,” Journal of the
American Statistical Association, vol. 90, no. 432, pp. 1380-1387, Dec
1995.
[6] R.Y.Liu and J. Tang, "Control charts for dependent and independent
measurements based on bootstrap methods,”Journal of the American
Statistical Association, vol. 91, no. 436, pp. 1694-1700,Dec 1996.
[7] G.Z. Stoumbos and L. A. Jones, "On the properties and design of
individuals control charts based on simplicial depth,” Nonlinear Studies,
vol. 7, no. 2, pp. 147-178, June2000.
[8] P. QiuandD. Hawkins, "A rank based multivariate CUSUM procedure,”
Technometrics, vol. 43, no. 2, pp. 120-132,May 2001.
[9] P. QiuandD. Hawkins, "A nonparametric multivariate CUSUM procedure
for detecting shifts in all directions,” Journal of the Royal Statistical
Society-D, vol. 52,pp. 151-164, 2003.
[10] C. Zou and F. Tsung, "A multivariate sign EWMA control chart,”
Technometrics, vol. 53, no. 1, pp. 84-97,Feb 2011.
[11] P. Qiu, "Distribution-free multivariate process control based on log-linear
modeling,” IIE Transactions, vol. 40, no. 7, pp. 664-677, 2008.
[12] G.Z. Stoumbos and J.H. Sullivan, "Robustness to non-normality of the
multivariate EWMA control chart.” Journal of Quality Technology, vol.
34, no. 3,pp. 260-276,Jul2002.
[13] C.Zou, Z. Wang and F. Tsung, "A spatial rank-based multivariate EWMA
control chart,” Naval Research Logistics, vol. 59, pp. 91-110. Mar 2012.
[14] R. Sun and F. Tsung, "A kernel distance-based multivariate control chart
using support vector methods,” InternationalJournal of Production
Research, vol. 41, no. 13, pp. 2975-2989. Sep 2003.
[15] S.Kumar, A.K.Choudhary, M.Kumar, R. Shankar and M.K. Tiwari,
"Kernel distance-based robust support vector methods and its application
in developing a robust K-chart,” InternationalJournal of Production
Research, vol. 44, no. 1,pp. 77-96,Jan 2006.
[16] F. Camci, R.B. Chinnam and R.D. Ellis, "Robust kernel distance
multivariate control chart using support vector principles,”
InternationalJournal of Production Research, vol. 46, no. 18, pp.
5075-5095, 2008.
[17] C.S. Cheng and H.P. Cheng, "Identifying the source of variance shifts in
the multivariate process using neural networks and support vector
machines,” Expert Systems with Applications, vol. 35, no.1-2, pp.
198-206, Jul-Aug 2008.
[18] W.Gani, H. Taleb and M. Limam,"An assessment of the
kernel-distance-based multivariate control chart through an industrial
application,” Quality and Reliability Engineering International, vol. 27,
no. 4, pp. 391-401,Jun 2011.
[19] X. Ning and F. Tsung, "Improved design of kernel distance-based charts
using support vector method,” IIE Transactions, vol. 45, no. 4, pp.
467-476,Apr2013.
[20] T.Sukchotrat, S.B. Kim and F. Tsung, "One-class classification-based
control charts for multivariate process monitoring,” IIE Transactions, vol.
42, no. 2, pp. 107-120. 2009.
[21] X. Ning and F. Tsung, "A density-based statistical process control scheme
for high-dimensional and mixed-type observations,” IIE Transactions,
vol. 44, no. 4,pp. 301-311. 2012.
[22] D. M. J. Tax and R. P. W. Duin, "Data domain description using support
vectors,” European Symposium on Aritficial Neural Networks, pp.
251-256. 1999.
[23] C. Cortes and V. Vapnik, "Support-vector networks,” Machine Learning,
vol. 20, no. 3, pp. 273-297,Sep 1995.
[24] F. Aparisi, "Hotelling’s T2 control chart with adaptive sample size,”
InternationalJournal of Production Research, vol. 34, no. 10, pp.
2853-2862,Oct 1996.
[25] F. Aparisi and C.L. Haro, "Hotelling’s T2 control chart with sampling
intervals,”InternationalJournal of Production Research, vol. 39, no. 14,
pp. 3127-3140,Sep 2001.
[26] F. Aparisi and C.L. Haro, "A comparison of T2 control chart with
variable sampling schemes as opposed to MEWMA chart,”
InternationalJournal of Production Research, vol. 41, no. 10, pp.
2169-2182,Jul 2003.
[27] Y.K. Chen and K.C. Chiou, "Adaptive sampling enhancement for
Hotelling’s T2 charts,” In: The 2005 International Conference in
Management Sciences and Decision Marking, Tamkang University, pp.
281-296. 2005.
[28] D. M. J. Tax and R. P. W. Duin, "Uniform object generation for
optimizing one-class classifiers,” Journal of Machine Learning
Research,vol. 2, pp. 251-256, 2002.
[29] Y.K. Chen and K.L. Hsieh, "Hotelling’s T2 charts with variable sample
size and control limit,” European Journal of Operational Research, vol.
182, no. 3,pp. 1251-1262,Nov 2007.
[30] D. He and A. Grigoryan, "Construction of double sampling S-control
charts for agile manufacturing,” Quality and Reliability Engineering
International, vol. 18, no. 4, pp. 343-355,Jul-Aug 2002.
[31] D. He and A. Grigoryan, "Multivariate multiple sampling charts,” IIE
Transactions, vol. 37, no. 6, pp. 509-521, 2005.
[32] D. He and A. Grigoryan, "Statistical design of joint double sampling X ̅
and s charts,” European Journal of Operational Research, vol. 168, no. 1,
pp. 122-142,Jan 2006.
[33] D.He, A. Grigoryan and M. Sigh, "Design of double and triple sampling X ̅ control charts using genetic algorithms,” InternationalJournal of
Production Research, vol. 40, no. 6, pp. 1387-1404,Apr 2002.
[34] Y.K. Chen, "Economic design of X ̅ control charts for non-normal data
using variable sampling policy,” InternationalJournal of Production
Research, vol. 92, no. 1, pp. 61-74,Nov2004.
[35] D.E.Goldberg, Genetic Algorithms on Search Optimization and Machine
Learning Reading. Addison-Wesley, MA, 1989.
[1] S. Bersimis, S. Psarakis, and J. Panaretos, "Multivariate statistical process
control charts: an overview,” Quality and Reliability Engineering
International, vol. 23, no.5, pp. 517-543. Aug 2007.W.-K. Chen, Linear
Networks and Systems (Book style). Belmont, CA: Wadsworth, 1993,
pp. 123–135.
[2] H. Hotelling, "Multivariate quality control-illustrated by the air testing of
sample bombsight,"Techniques of Statistical Analysis, McGraw-Hill:
New York, 1947, pp. 111-184.
[3] R.B. Crosier, "Multivariate generalizations of cumulative sum
quality-control schemes,” Technometrics, vol. 30, no. 3, pp. 291-303,
Aug 1988.
[4] C. A.Lowry, W.H. Woodall, C.W. Champ, and S.E. Rigdon, "A
multivariate exponentially weighted moving average control
chart,”Technometrics, vol. 34, no. 1, pp. 46-53,Feb 1992.
[5] R.Y.Liu, "Control chart for multivariate process,” Journal of the
American Statistical Association, vol. 90, no. 432, pp. 1380-1387, Dec
1995.
[6] R.Y.Liu and J. Tang, "Control charts for dependent and independent
measurements based on bootstrap methods,”Journal of the American
Statistical Association, vol. 91, no. 436, pp. 1694-1700,Dec 1996.
[7] G.Z. Stoumbos and L. A. Jones, "On the properties and design of
individuals control charts based on simplicial depth,” Nonlinear Studies,
vol. 7, no. 2, pp. 147-178, June2000.
[8] P. QiuandD. Hawkins, "A rank based multivariate CUSUM procedure,”
Technometrics, vol. 43, no. 2, pp. 120-132,May 2001.
[9] P. QiuandD. Hawkins, "A nonparametric multivariate CUSUM procedure
for detecting shifts in all directions,” Journal of the Royal Statistical
Society-D, vol. 52,pp. 151-164, 2003.
[10] C. Zou and F. Tsung, "A multivariate sign EWMA control chart,”
Technometrics, vol. 53, no. 1, pp. 84-97,Feb 2011.
[11] P. Qiu, "Distribution-free multivariate process control based on log-linear
modeling,” IIE Transactions, vol. 40, no. 7, pp. 664-677, 2008.
[12] G.Z. Stoumbos and J.H. Sullivan, "Robustness to non-normality of the
multivariate EWMA control chart.” Journal of Quality Technology, vol.
34, no. 3,pp. 260-276,Jul2002.
[13] C.Zou, Z. Wang and F. Tsung, "A spatial rank-based multivariate EWMA
control chart,” Naval Research Logistics, vol. 59, pp. 91-110. Mar 2012.
[14] R. Sun and F. Tsung, "A kernel distance-based multivariate control chart
using support vector methods,” InternationalJournal of Production
Research, vol. 41, no. 13, pp. 2975-2989. Sep 2003.
[15] S.Kumar, A.K.Choudhary, M.Kumar, R. Shankar and M.K. Tiwari,
"Kernel distance-based robust support vector methods and its application
in developing a robust K-chart,” InternationalJournal of Production
Research, vol. 44, no. 1,pp. 77-96,Jan 2006.
[16] F. Camci, R.B. Chinnam and R.D. Ellis, "Robust kernel distance
multivariate control chart using support vector principles,”
InternationalJournal of Production Research, vol. 46, no. 18, pp.
5075-5095, 2008.
[17] C.S. Cheng and H.P. Cheng, "Identifying the source of variance shifts in
the multivariate process using neural networks and support vector
machines,” Expert Systems with Applications, vol. 35, no.1-2, pp.
198-206, Jul-Aug 2008.
[18] W.Gani, H. Taleb and M. Limam,"An assessment of the
kernel-distance-based multivariate control chart through an industrial
application,” Quality and Reliability Engineering International, vol. 27,
no. 4, pp. 391-401,Jun 2011.
[19] X. Ning and F. Tsung, "Improved design of kernel distance-based charts
using support vector method,” IIE Transactions, vol. 45, no. 4, pp.
467-476,Apr2013.
[20] T.Sukchotrat, S.B. Kim and F. Tsung, "One-class classification-based
control charts for multivariate process monitoring,” IIE Transactions, vol.
42, no. 2, pp. 107-120. 2009.
[21] X. Ning and F. Tsung, "A density-based statistical process control scheme
for high-dimensional and mixed-type observations,” IIE Transactions,
vol. 44, no. 4,pp. 301-311. 2012.
[22] D. M. J. Tax and R. P. W. Duin, "Data domain description using support
vectors,” European Symposium on Aritficial Neural Networks, pp.
251-256. 1999.
[23] C. Cortes and V. Vapnik, "Support-vector networks,” Machine Learning,
vol. 20, no. 3, pp. 273-297,Sep 1995.
[24] F. Aparisi, "Hotelling’s T2 control chart with adaptive sample size,”
InternationalJournal of Production Research, vol. 34, no. 10, pp.
2853-2862,Oct 1996.
[25] F. Aparisi and C.L. Haro, "Hotelling’s T2 control chart with sampling
intervals,”InternationalJournal of Production Research, vol. 39, no. 14,
pp. 3127-3140,Sep 2001.
[26] F. Aparisi and C.L. Haro, "A comparison of T2 control chart with
variable sampling schemes as opposed to MEWMA chart,”
InternationalJournal of Production Research, vol. 41, no. 10, pp.
2169-2182,Jul 2003.
[27] Y.K. Chen and K.C. Chiou, "Adaptive sampling enhancement for
Hotelling’s T2 charts,” In: The 2005 International Conference in
Management Sciences and Decision Marking, Tamkang University, pp.
281-296. 2005.
[28] D. M. J. Tax and R. P. W. Duin, "Uniform object generation for
optimizing one-class classifiers,” Journal of Machine Learning
Research,vol. 2, pp. 251-256, 2002.
[29] Y.K. Chen and K.L. Hsieh, "Hotelling’s T2 charts with variable sample
size and control limit,” European Journal of Operational Research, vol.
182, no. 3,pp. 1251-1262,Nov 2007.
[30] D. He and A. Grigoryan, "Construction of double sampling S-control
charts for agile manufacturing,” Quality and Reliability Engineering
International, vol. 18, no. 4, pp. 343-355,Jul-Aug 2002.
[31] D. He and A. Grigoryan, "Multivariate multiple sampling charts,” IIE
Transactions, vol. 37, no. 6, pp. 509-521, 2005.
[32] D. He and A. Grigoryan, "Statistical design of joint double sampling X ̅
and s charts,” European Journal of Operational Research, vol. 168, no. 1,
pp. 122-142,Jan 2006.
[33] D.He, A. Grigoryan and M. Sigh, "Design of double and triple sampling X ̅ control charts using genetic algorithms,” InternationalJournal of
Production Research, vol. 40, no. 6, pp. 1387-1404,Apr 2002.
[34] Y.K. Chen, "Economic design of X ̅ control charts for non-normal data
using variable sampling policy,” InternationalJournal of Production
Research, vol. 92, no. 1, pp. 61-74,Nov2004.
[35] D.E.Goldberg, Genetic Algorithms on Search Optimization and Machine
Learning Reading. Addison-Wesley, MA, 1989.
@article{"International Journal of Information, Control and Computer Sciences:53792", author = "Chia-Hau Liu and Tai-Yue Wang", title = "An AK-Chart for the Non-Normal Data", abstract = "Traditional multivariate control charts assume that measurement from manufacturing processes follows a multivariate normal distribution. However, this assumption may not hold or may be difficult to verify because not all the measurement from manufacturing processes are normal distributed in practice. This study develops a new multivariate control chart for monitoring the processes with non-normal data. We propose a mechanism based on integrating the one-class classification method and the adaptive technique. The adaptive technique is used to improve the sensitivity to small shift on one-class classification in statistical process control. In addition, this design provides an easy way to allocate the value of type I error so it is easier to be implemented. Finally, the simulation study and the real data from industry are used to demonstrate the effectiveness of the propose control charts.
", keywords = "Multivariate control chart, statistical process control, one-class classification method.", volume = "8", number = "7", pages = "1080-6", }
