A change point approach for phase I analysis in multistage processes

Technometrics

Volumn 50, Issue 3, 2008, Pages 344-356

  Zou, Changliang ^a   Tsung, Fugee ^b   Liu, Yukun ^a  

^a NANKAI UNIVERSITY   (China)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

Author keywords

Binary Segmentation; Directional Information; Generalized Likelihood Ratio Test; Statistical Process Control

Indexed keywords

CONTROL THEORY; MAXIMUM LIKELIHOOD ESTIMATION; NUMERICAL ANALYSIS; TELECOMMUNICATION NETWORKS; VECTORS;

BINARY SEGMENTATION; BINARY SEGMENTATIONS; CHANGE POINTS; CURRENT PROCESSES; DIRECTIONAL INFORMATION; DIRECTIONAL INFORMATIONS; EXISTING METHODS; FOCUS DETECTIONS; GENERALIZED LIKELIHOOD RATIO TEST; HISTORICAL DATUMS; MULTISTAGE PROCESSES; PHASE I; SIMULATION RESULTS; SINGLE STEPS; SINGLE VECTORS; SPACE MODELS; SUB SPACES; UNIVARIATE;

STATISTICAL PROCESS CONTROL;

EID: 48949109127     PISSN: 00401706     EISSN: None     Source Type: Journal    
DOI: 10.1198/004017008000000307     Document Type: Article

References (36)

1. Anderson, T. W. (1984), An Introduction to Multivariate Statistical Analysis (2nd ed.), New York: Wiley.
2. Basseville, M., and Nikiforov, I. V. (1993), Detection of Abrupt Changes: Theory and Application, Englewood Cliffs, NJ: Prentice-Hall.
3. Bhattacharya, P. K. (1987), "Maximum Likelihood Estimation of a Change Point in the Distribution of Independent Random Variables: General Multiparameter Case," Journal of Multivariate Analysis, 23, 183-208.
4. Camelio, J., Hu, S. J., and Ceglarek, D. (2003), "Modeling Variation Propagation of Multi-Station Assembly Systems With Compliant Parts," Journal of Mechanical Design, 125, 673-681.
5. Chen, J., and Gupta, A. K. (2000), Parametric Statistical Change Point Analysis, Berlin: Birkhauser.
6. Csorgo, M., and Horvath, L. (1997), Limit Theorems in Change-Point Analysis, New York: Wiley.
7. Ding, Y., Ceglarek, D., and Shi, J. (2002a), "Fault Diagnosis of Multistage Manufacturing Processes by Using a State-Space Approach," ASME Transactions, Journal of Manufacturing Science and Engineering, 124, 313-322.
8. Ding, Y., Jin, J., Ceglarek, D., and Shi, J. (2005), "Process- Oriented Tolerancing for Multi-Station Assembly Systems," IIE Transactions, 37, 493-508.
9. Ding, Y., Shi, J., and Ceglarek, D. (2002b), "Diagnosability Analysis of Multistage Manufacturing Processes," ASME Transactions, Journal of Dynamic Systems, Measurement and Control, 124, 1-33.
10. Djurdjanovic, D., and Ni, J. (2001), "Linear State-Space Modeling of Dimensional Machining Errors," Transactions of NAMRI/SME, XXIX, 541-548.
11. Durbin, J., and Koopman, S. J. (2001), Time Series Analysis by State-Space Methods, New York: Oxford University Press.
12. Gombay, E., and Horvath, L. (1996), "Approximations for the Time and Change and the Power Function in Change Point Models," Journal of Statistical Planning and Inference, 52, 43-66.
13. Hawkins, D. M. (1977), "Testing a Sequence of Observations for a Shift in Location," Journal of the American Statistical Association, 72, 180-186.
14. Huang, Q., Zhou, S., and Shi, J. (2002), "Diagnosis of Multi-Operational Machining Processes Through Variation Propagation Analysis," Robotics and CIM Journal, 18, 233-239.
15. James, B., James, K. L., and Siegmund, D. (1987), "Tests for a Change Point," Biometrika, 74, 71-84.
16. - (1992), "Asymptotic Approximations for Likelihood Ratio Tests and Confidence Regions for a Change Point in the Mean of a Multivariate Normal Distribution," Statistica Sinica, 2, 69-90.
17. Jin, J., and Shi, J. (1999), "State-Space Modeling of Sheet Metal Assembly for Dimensional Control," ASME Transactions, Journal of Manufacturing Science and Engineering, 121, 756-762.
18. Kim, T. S., and May, G. S. (1999), "Sequential Modeling of via Formation in Photosensitive Dielectric Materials for MCM-D Applications," IEEE Transactions on Semiconductor Manufacturing, 12, 345-352.
19. Lehmann, E. L. (1986), Testing Statistical Hypotheses (2nd ed.), New York: Wiley.
20. Rao, C. R., and Kleffe, J. (1988), Estimation of Variance Components and Applications, Amsterdam: North-Holland.
21. Rao, P. S. R. S. (1997), Variance Components Estimation: Mixed Models, Methodologies and Applications, London: Chapman & Hall.
22. Roy, S. N. (1953), "On a Heuristic Method of Test Construction and Its Use in Multivariate Analysis," The Annals of Mathematical Statistics, 24, 220-238.
23. Samuel-Cahn, E. (1996), "Is the Simes Improved Bonferroni Procedure Conservative?" Biometrika, 83, 928-933.
24. 2 Random Variables: A Proof of Simes's Conjecture," The Annals of Statistics, 26, 494-504.
25. Sarkar, S. K., and Chang, C. K. (1997), "The Simes Method for Multiple Hypotheses Testing With Positively Dependent Test Statistics," Journal of the American Statistical Association, 92, 1601-1608.
26. Shi, J. (2006), Stream of Variation Modeling and Analysis for Multistage Manufacturing, Boca Raton, FL: CRC Press.
27. Simes, R. J. (1986), "An Improved Bonferroni Procedure for Multiple Tests of Significance," Biometrika, 73, 751-754.
28. Srivastava, M. S., and Worsley, K. J. (1986), "Likelihood Ratio Tests for a Change in the Multivariate Normal Mean," Journal of the American Statistical Association, 81, 199-204.
29. Sullivan, J. H., and Woodall, W. H. (2000), "Change Point Detection of Mean Vector or Covariance Matrix Shifts Using Multivariate Individual Observations," IIE Transactions, 32, 537-549.
30. Vostrikova, L. J. (1981), "Detecting Disorder in Multidimensional Random Processes," Soviet Mathematics Doklady, 24, 55-59.
31. Xiang, L., and Tsung, F. (2008), "Statistical Monitoring of Multistage Processes Based on Engineering Models," IIE Transactions, 40, 957-970.
32. Yao, Y. (1988), "Estimating the Number of Change-Points via the Schwarz Criterion," Statistics and Probability Letters, 6, 181-189.
33. Zantek, P. F., Gordon, P. W., and Robert, D. P. (2006), "A Self-Starting Procedure for Monitoring Process Quality in Multistage Manufacturing Systems," IIE Transactions, 38, 293-308.
34. Zhou, S., Chen, Y., and Shi, J. (2004), "Statistical Estimation and Testing for Variation Root-Cause Identification of Multistage Manufacturing Processes," IEEE Transactions on Automation Science and Engineering, 1, 73-83.
35. Zhou, S., Ding, Y., Chen, Y., and Shi, J. (2003a), "Diagnosability Study of Multistage Manufacturing Processes Based on Linear Mixed-Effects Models," Technometrics, 45, 312-325.
36. Zhou, S., Huang, Q., and Shi, J. (2003b), "State-Space Modeling of Dimensional Variation Propagation in Multistage Machining Process Using Differential Motion Vector," IEEE Transactions on Robotics and Automation, 19, 296-309.