The synthetic control chart based on two sample variances for monitoring the covariance matrix

Quality and Reliability Engineering International

Volumn 25, Issue 5, 2009, Pages 595-606

  Machado, M A G ^a   Costa, A F B ^a   Rahim, M A ^b  

^a SÃO PAULO STATE UNIVERSITY UNESP   (Brazil)

^b UNIVERSITY OF NEW BRUNSWICK   (Canada)

Author keywords

Control charts; Covariance matrix; Generalized variance; Synthetic

Indexed keywords

BIVARIATE; CONTROL CHARTS; DIAGNOSTIC FEATURES; GENERALIZED VARIANCE; OUT-OF-CONTROL; PROCESS CHANGE; QUALITY CHARACTERISTIC; SAMPLE VARIANCE; SYNTHETIC; SYNTHETIC CONTROL CHART;

FLOWCHARTING; STATISTICS;

COVARIANCE MATRIX;

EID: 67749106171     PISSN: 07488017     EISSN: 10991638     Source Type: Journal    
DOI: 10.1002/qre.992     Document Type: Article

References (38)

1. Page ES. Continuous inspection schemes. Biometrika 1954;41:100-115.
2. Reynolds MR Jr, Stoumbos ZG. Should exponentially weighted moving average and cumulative sum charts be used with Shewhart limits. Technometrics 2005;47:409-424.
3. Lucas JM, Saccucci MS. Exponentially weighted moving average control schemes: Properties and enhancements. Technometrics 1990;32:1-16.
4. Costa AFB, Rahim MA. A single EWMA chart for monitoring process mean and process variance. Quality Technology and Quantitative Management 2006;3:295-305.
5. Costa AFB. X̄ charts with variable sample size. Journal of Quality Technology 1994;26:155-163.
6. Costa AFB. Joint X̄ and R charts with variable sample sizes and sampling intervals. Journal of Quality Technology 1999;31:387-397.
7. De Magalhães MS, Costa AFB, Moura Neto FD. Adaptive control charts: A Markovian approach for processes subject to independent out-of-control disturbances. International Journal of Production Economics 2006;99:236-246.
8. Daudin JJ. Double sampling X̄ charts. Journal of Quality Technology 1992;24:78-87.
9. Wu Z, Spedding TA. A synthetic control chart for detecting small shifts in the process mean. Journal of Quality Technology 2000;32:32-38.
10. Wu Z, Spedding TA. Implementing synthetic control charts. Journal of Quality Technology 2000;32:75-78.
11. Wu Z, Yeo SH, Spedding TA. A synthetic control chart for detecting fraction nonconforming increases. Journal of Quality Technology 2001;33:104-111.
12. Wu Z, Yeo SH. Implementing synthetic control charts for attributes. Journal of Quality Technology 2001;33:112-114.
13. Calzada ME, Scariano SM. The robustness of the synthetic control chart to non-normality. Communications in Statistics: Simulation and Computation 2001;30:311-326.
14. Davis RB, Woodall WH. Evaluating improving the synthetic control chart. Journal of Quality Technology 2002;34:200-208.
15. Scariano SM, Calzada ME. A note on the lower-sided synthetic chart for exponentials. Quality Engineering 2003;15:677-680.
16. Gadre MP, Rattihalli RN. Unit group-runs chart to identify increases in fraction nonconforming. Journal of Quality Technology 2005;37:199-209.
17. Chen FL, Huang HJ. A synthetic control chart for monitoring process dispersion with sample range. International Journal of Advanced Manufacturing Technology 2005;26:842-851.
18. Huang HJ, Chen FL. A synthetic control chart for monitoring process dispersion with sample standard deviation. Computers and Industrial Engineering 2005;49:221-240.
19. Hotelling H. Multivariate quality control, illustrated by the air testing of sample bombsights. Techniques of Statistical Analysis. McGraw-Hill: New York, 1947; 111-184.
20. Woodall WH, Ncube MM. Multivariate CUSUM quality control procedures. Technometrics 1985;27:285-292.
21. Crosier RB. Multivariate generalizations of cumulative sum quality control schemes. Technometrics 1988;30:291-303.
22. Prabhu SS, Runger GC. Designing a multivariate EWMA control chart. Journal of Quality Technology 1997;29:8-15.
23. Runge GC, Keats B, Montgomery DC, Scraton RD. Improving the performance of the multivariate exponentially weighted moving average control chart. Quality and Reliability Engineering International 1999;15:161-166.
24. Molnau WE, Runger GC, Montgomery DC, Skinner KR, Loredo EN, Prabhu SS. A program for ARL calculation for multivariate EWMA charts. Journal of Quality Technology 2001;33:515-521.
25. Lee MH, Khoo MBC. Optimal statistical design of a multivariate EWMA chart based on ARL and MRL. Communications in Statistics-Simulation and Computation 2006;35:831-847.
26. 2 control charts with variable sampling schemes as opposed to MEWMA chart. International Journal of Production Research 2003;41:2169-2182.
27. He D, Grigoryan A. Multivariate multiple sampling charts. IIE Transactions 2005;37:509-521.
28. 2 charts. Quality and Reliability Engineering International 2008;24:153-166.
29. Alt FB. Multivariate quality control. Encyclopedia of Statistical Sciences, Kotz S, Johnson NL (eds.). Wiley: New York, 1985.
30. Aparisi F, Jabaloyes J, Carrión A. Statistical properties of the |S| multivariate control chart. Communication in Statistics-Theory and Methods 1999;28:2671-2686.
31. Aparisi F, Jabaloyes J, Carrión A. Generalized variance chart design with adaptive sample sizes. The bivariate case. Communication in Statistics-Simulation and Computation 2001;30:931-948.
32. Grigoryan A, He D. Multivariate double sampling |S| charts for controlling process variability. International Journal of Production Research 2005;43:715-730.
33. Yeh AB, Huwang L, Wu CW. A multivariate EWMA control chart for monitoring process variability with individual observations. IIE Transactions 2005;37:1023-1035.
34. Bourke PD. Detecting a shift in fraction nonconforming using run-length control charts with 100% inspection. Journal of Quality Technology 1991;23:225-238.
35. Serel DA, Moskowitz H, Tang J. Univariate X̄ control charts for individual characteristics in a multinormal model. IIE Transactions 2000;32:1115-1125.
36. Montgomery DC. Introduction to Statistical Quality Control. Wiley: New York, 2004.
37. Surtihadi J, Raghavachari M, Runger G. Multivariate control charts for process dispersion. International Journal of Production Research 2004;42:2993-3009.
38. Microsoft Fortran Power Station 4.0. Professional Edition with Microsoft IMSL Mathematical and Statistical Libraries, Microsoft Corporation, 1995.