A bayesian scheme to detect changes in the mean of a short-run process

Technometrics

Volumn 47, Issue 4, 2005, Pages 446-456

  Tsiamyrtzis, Panagiotis ^a   Hawkins, Douglas M ^b  

^a ATHENS UNIVERSITY OF ECONOMICS AND BUSINESS   (Greece)

^b UNIVERSITY OF MINNESOTA   (United States)

Author keywords

Bayesian statistical process control; Kalman filter; Normal mixture; Tool wear

Indexed keywords

BAYESIAN STATISTICAL PROCESS CONTROL; NORMAL MIXTURE; TOOL WEAR;

KALMAN FILTERING; MATHEMATICAL MODELS; NORMAL DISTRIBUTION; PROBLEM SOLVING;

STATISTICAL PROCESS CONTROL;

EID: 27844464414     PISSN: 00401706     EISSN: None     Source Type: Trade Journal    
DOI: 10.1198/004017005000000346     Document Type: Article

References (24)

1. Bothe, D. R. (1989), "A Powerful New Control Chart for Job Shops," in 43rd Annual Quality Congress Transactions, Milwaukee, WI: American Society for Quality, pp. 265-270.
2. Burr, J. T. (1989), "SPC in the Short Run," in 43rd Annual Quality Congress Transactions, Milwaukee, WI: American Society for Quality, pp. 776-780.
3. Casella, G., and Berger, R. L. (1990), Statistical Inference, Pacific Grove, CA: Wadsworth/Brooks-Cole.
4. Chang, J. T., and Fricker, R. D. (1999), "Detecting When a Monotonically Increasing Mean Has Crossed a Threshold," Journal of Quality Technology, 31, 217-234.
5. Chernoff, H., and Zacks, S. (1964), "Estimating the Current Mean of a Normal Distribution Which Is Subjected to Changes in Time," The Annals of Mathematical Statistics, 40, 999-1018.
6. Crowder, S., and Eshleman, L. (2001), "Small Sample Properties of an Adaptive Filter Applied to Low Volume SPC," Journal of Quality Technology, 33, 29-46.
7. Del Castillo, E., and Montgomery, D. C. (1992), "Average Run Length Properties of Q-Charts for Short-Run Statistical Control: Enhancements and Alternative Method," Publication 92-30, Quality and Reliability Group, Arizona State University.
8. Duncan, D. B., and Horn, S. D. (1972), "Linear Dynamic Recursive Estimation From the Viewpoint of Regression Analysis," Journal of the American Statistical Association, 67, 815-821.
9. Geisser, S. (1993), Predictive Inference: An Introduction, London: Chapman & Hall.
10. Hawkins, D. M. (1987), "Self-Starting Cusum Charts for Location and Scale," The Statistician, 36, 299-315.
11. Jeffreys, H. (1948), Theory of Probability (2nd ed.), Oxford, U.K.: Oxford University Press.
12. Kalman, R. E. (1960), "A New Approach to Linear Filtering and Prediction Problems," Journal of Basic Engineering, 82, 35-45.
13. Meinhold, R. J., and Singpurwalla, N. D. (1983), "Understanding the Kalman Filter," The American Statistician, 37, 123-127.
14. Montgomery, C. D. (1997), Introduction to Statistical Quality Control, New York: Wiley.
15. Montgomery, C. D., and Mastrangelo, C. M. (1991), "Some Statistical Process Control Methods for Autocorrelated Data" (with discussion), Journal of Quality Technology, 23, 179-204.
16. Quesenberry, C. P. (1990), "SPC Variables Q-Charts for Short Runs," in Quality Concepts'90 Conference Proceedings, pp. 223-236.
17. _ (1991), "SPC Q Charts for Start-up Processes and Short or Long Runs," Journal of Quality Technology, 23, 213-224.
18. Roberts, S. W. (1959), "Control Chart Tests Based on Geometric Moving Average," Technometrics, 1, 239-250.
19. Tsiamyrtzis, P. (2000), "A Bayesian Approach to Quality Control Problems," unpublished doctoral dissertation, University of Minnesota, School of Statistics.
20. Wasserman, G. S., and Sudjianto, A. (1993), "Short-Run SPC Based Upon the Second Order Dynamic Linear Model for Trend Detection," Communication in Statistics, Part A - Theory and Methods, 22, 1011-1036.
21. West, M., and Harrison, J. (1996), Bayesian Forecasting and Dynamic Models (2nd ed.), New York: Springer-Verlag.
22. Wheeler, D. J. (1992), Short Run SPC, Knoxville, TN: SPC Press.
23. Woodward, P. W., and Naylor, J. C. (1993), "An Application of Bayesian Methods in SPC," The Statistician, 42, 461-469.
24. Wright, C. M., Booth, D. E., and Hu, M. Y. (2001), "Joint Estimation: SPC Method for Short-Run Autocorellated Data," Journal of Quality Technology, 33, 365-378.