Is average run length to false alarm always an informative criterion?

Sequential Analysis

Volumn 27, Issue 4, 2008, Pages 354-376

  Mei, Yajun ^a,b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b Georgia Institute of Technology   (United States)

Author keywords

Average run length; CUSUM; Expected false alarm rate; Quantile run length; Statistical process control; Surveillance

Indexed keywords

AVERAGE RUN LENGTHS; BAYESIAN APPROACHES; CHANGE-POINT PROBLEM; CUSUM; DETECTION SCHEME; FALSE ALARM RATE; PERFORMANCE CRITERION; RUN LENGTH;

ALARM SYSTEMS; BAYESIAN NETWORKS; HIDDEN MARKOV MODELS; SPACE SURVEILLANCE; STATISTICAL PROCESS CONTROL;

ERRORS;

EID: 55349142870     PISSN: 07474946     EISSN: 15324176     Source Type: Journal    
DOI: 10.1080/07474940802445790     Document Type: Article

References (44)

1. Bansal, R. K. and Papantoni-Kazakos, P. (1986). An Algorithm for Detecting a Change in a Stochastic Process, IEEE Transactions on Information Theory 32: 227-235.
2. Barnard, G. A. (1959). Control Charts and Stochastic Processes, Journal of Royal Statistical Society, Series B 21: 239-271.
3. Baron, M. and Tartakovsky, A. (2006). Asymptotic Bayesian Change-Point Detection Theory for General Continuous-Time Models, Sequential Analysis 25: 257-296.
4. Basseville, M. and Nikiforov, I. (1993). Detection of Abrupt Changes: Theory and Applications, Englewood Cliffs: Prentice-Hall.
5. Beibel, M. (1997). Sequential Change-Point Detection in Continuous Time When the Post-Change Drift Is Unknown, Bernoulli 3: 457-478.
6. Berk, R. H. (1970). Stopping Times of SPRTs Based on Exchangeable Models, Annals of Mathematical Statistics 41: 979-990.
7. Blackwell, D. (1946). On an Equation of Wald, Annals of Mathematical Statistics 17: 84-87.
8. Brodsky, B. E. and Darkhovsky, B. S. (1993). Non-Parametric Methods in Change-Point Problems, Netherlands: Kluwer.
9. Brodsky, B. E. and Darkhovsky, B. S. (2000). Non-Parametric Statistical Diagnosis: Problems and Methods, Netherlands: Kluwer.
10. Fienberg, S. E. and Shmueli, G. (2005). Statistical Issues and Challenges Associated with Rapid Detection of Bio-terrorist Attacks, Statistics in Medicine 24: 513-529.
11. Fuh, C.-D. (2003). SPRT and CUSUM in Hidden Markov Models, Annals of Statistics 31: 942-977.
12. Fuh, C.-D. (2004). Asymptotic Operating Characteristics of an Optimal Change Point Detection in Hidden Markov Models, Annals of Statistics 32: 2305-2339.
13. Hewitt, E. and Savage, L. J. (1955). Symmetric Measures on Cartesian Products, Transactions of American Mathematical Society 80: 470-501.
14. Jensen, W., Jones-Farmer, L. A., Champ, C. W., and Woodall, W. H. (2006). Effects of Parameter Estimation on Control Chart Properties: A Literature Review, Journal of Quality Control 38: 349-364.
15. Kenett, R. S. and Zacks, S. (1998). Modern Industrial Statistics: Design and Control of Quality and Reliability, Pacific Grove: Duxbury.
16. Kiefer, J. and Sacks, J. (1963). Asymptotically Optimum Sequential Inference and Design, Annals of Mathematical Statistics 34: 705-750.
17. Krieger, A. M., Pollak, M., and Yakir, B. (2003). Surveillance of a Simple Linear Regression, Journal of American Statistical Association 98: 456-469.
18. Kulldorff, M. (2001). Prospective Time-Periodic Geographic Disease Surveillance Using a Scan Statistic, Journal of Royal Statistical Society, Series A 164: 61-72.
19. Lai, T. L. (1995). Sequential Change-Point Detection in Quality Control and Dynamical Systems (with discussions), Journal of Royal Statistical Society, Series B 57: 613-658.
20. Lai, T. L. (1998). Information Bounds and Quick Detection of Parameter Changes in Stochastic Systems, IEEE Transactions on Information Theory 44: 2917-2929.
21. Lai, T. L. (2001). Sequential Analysis: Some Classical Problems and New Challenges, Statistica Sinica 11: 303-408.
22. Lorden, G. (1971). Procedures for Reacting to a Change in Distribution, Annals of Mathematical Statistics 42: 1897-1908.
23. Mei, Y. (2006a). Sequential Change-Point Detection When Unknown Parameters Are Present in the Pre-Change Distribution, Annals of Statistics 34: 92-122.
24. Mei, Y. (2006b). Suboptimal Properties of Page's CUSUM and Shiryayev-Roberts Procedures in Change-Point Problems with Dependent Observations, Statistica Sinica 16: 883-897.
25. Moustakides, G. V. (1986). Optimal Stopping Times for Detecting Changes in Distributions, Annals of Statistics 14: 1379-1387.
26. Page, E. S. (1954). Continuous Inspection Schemes, Biometrika 41: 100-115.
27. Pollak, M. (1985). Optimal Detection of a Change in Distribution, Annals of Statistics 13: 206-227.
28. Pollak, M. (1987). Average Run Lengths of an Optimal Method of Detecting a Change in Distribution, Annals of Statistics 15: 749-779.
29. Pollak, M. and Siegmund, D. (1991). Sequential Detection of a Change in a Normal Mean When the Initial Value Is Unknown, Annals of Statistics 19: 394-416.
30. Poor, H. V. (1998). Quickest Detection with Exponential Penalty for Delay, Annals of Statistics 26: 2179-2205.
31. Ritov, Y. (1990). Decision Theoretic Optimality of the CUSUM Procedure, Annals of Statistics 18: 1464-1469.
32. Roberts, S. W. (1966). A Comparison of Some Control Chart Procedures, Technometrics 8: 411-430.
33. Shewhart, W. A. (1931). Economic Control of Quality of Manufactured Product, New York: Van Nostrand.
34. Shiryayev, A. N. (1963). On Optimum Methods in Quickest Detection Problems, Theory of Probability and Its Applications 8: 22-46.
35. Shiryayev, A. N. (1978). Optimal Stopping Rules, New York: Springer.
36. Siegmund, D. (1985). Sequential Analysis: Tests and Confidence Intervals, New York: Springer.
37. Stoumbos, Z., Reynolds, M. R., Jr., Ryan, T. P., and Woodall, W. H. (2000). The State of Statistical Process Control as We Proceed into the 21st Century, Journal of American Statistical Association 95: 992-998.
38. Tartakovsky, A., Rozovskii, B., Blazek, R., and Kim, H. (2006). Detection of Intrusion in Information Systems by Sequential Change-Point Methods (with discussions), Statistical Methodology 3: 252-340.
39. Wald, A. (1947). Sequential Analysis, New York: Wiley.
40. Woodall, W. H. (1983). The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables, Technometrics 25: 295-301.
41. Woodall, W. H. (2006). The Use of Control Charts in Health-Care and Public-Health Surveillance (with discussions), Journal of Quality Technology 38: 89-134.
42. Woodroofe, M. (1982). Nonlinear Renewal Theory in Sequential Analysis, Philadelphia: SIAM.
43. Yakir, B. (1994). Optimal Detection of a Change in Distribution When the Observations Form a Markov Chain with a Finite State Space, in Change-Point Problems, Carlstein, E., Muller, H., and Siegmund, D. eds., pp. 346-358, Hayward: Institute of Mathematical Statistics.
44. Yakir, B., Krieger, A. M., and Pollak, M. (1999). Detecting a Change in Regression: First Order Optimality, Annals of Statistics 27: 1896-1913.