A Markov Chain Model for the Multivariate Exponentially Weighted Moving Averages Control Chart

Journal of the American Statistical Association

Volumn 91, Issue 436, 1996, Pages 1701-1706

  Runger, George C ^a   Prabhu, Sharad S ^b  

^a ARIZONA STATE UNIVERSITY   (United States)

^b SAS INSTITUTE INC   (United States)

Author keywords

Average run length; Exponentially weighted moving averages; Multivariate control chart; Statistical process control

Indexed keywords

EID: 0030335354     PISSN: 01621459     EISSN: 1537274X     Source Type: Journal    
DOI: 10.1080/01621459.1996.10476741     Document Type: Article

References (19)

1. Brook, D., and Evans, D. A. (1972), "An Approach to the Probability Distribution of CUSUM Run Lengths," Biometrika, 59, 539-549.
2. Champ, C. w., and Rigdon, S. E. (l991), "A Comparison of the Markov Chain and the Integral Equation Approaches for Evaluating the Run Length Distribution of Quality Control Charts," Communications in Statistics, Part Be-Simulation and Computation, 20, 191-204.
3. Crosier, R. B. (1988), "Multivariate Generalizations of Cumulative Sum Quality Control Schemes," Technometrics, 30,291-303.
4. Crowder, S. V. (1987), "A Simple Method for Studying Run-Length Distribution of Exponentially Weighted Moving Average Control Charts," Technometrics, 29, 401-407.
5. Eaton, M. L. (1983), Multivariate Statistics, New York: Wiley.
6. Hawkins, D. M. (1992), "Evaluation of Average Run Length of Cumulative Sum Charts for an Arbitrary Data Distribution," Communications in Statistics, Part B-Simulation and Computation, 21, 1004-1020.
7. Hawkins, D. M. (1991), "Multivariate Quality Control Using Regression-Adjusted Variables," Technometrics, 33, 61-75.
8. Healy, J. D. (1987), "A Note on Multivariate CUSUM Procedures," Technometrics, 29, 409-412.
9. Hotelling, H. H. (1947), "Multivariate Quality Controllllustrated by the Air Testing of Sample Bombsights," in Techniques of Statistical Analysis, eds. C. Eisenhart, M. W. Hastay, and W. A. Wallis, New York: McGraw-Hill, pp. 111-184.
10. Jackson, J. E. (1991), A User's Guide to Prinicpal Components, New York: Wiley.
11. Lowry, C. A., Woodall, W. H., Champ, C. w., and Rigdon, S. E. (1992), "A Multivariate Exponentially Weighted Moving Average Control Chart," Technometrics, 34, 46-53.
12. Lucas, J. M., and Saccucci, M. S. (1990), "Exponentially Weighted Moving Journal of the American Statistical Association, December 1996 Average Control Schemes: Properties and Enhancements," Technometrics, 32, 1-12.
13. Mardia, K. V., Kent, J. T., and Bibby, J. M. (1979), Multivariate Analysis, New York: Academic Press.
14. Pignatiello, J. J., and Runger, G. C. (1990), "Comparisons of Multivariate CUSUM Charts," Journal of Quality Technology, 22,173-186.
15. Prabhu, S. S., and Runger, G. C. (1995), "Analysis of a Two-Dimensional Markov Chain," Communications in Statistics-Simulation and Computation, 25, 75-80.
16. Rigdon, S. E. (1995a), "A Double-Integral Equation for the Average Run Length of a Multivariate Exponentially Weighted Moving Average Control Chart," Statistics and Probability Letters, 24, 365-373.
17. Rigdon, S. E. (1995b), "An Integral Equation for the In-Control Average Run Length of a Multivariate Exponentially Weighted Moving Average Control Chart," Journal ofStatistical Computation and Simulation, 52, 351-365.
18. Roberts, S. W. (1959), "Control Chart Tests Based on Geometric Moving Averages," Technometrics, 1,239-250.
19. Woodall, W. H., and Ncube, M. M. (1985), "Multivariate CUSUM QualityControl Procedures," Technometrics, 27, 285-292.