The Run Length Distribution of the CUSUM with Estimated Parameters

References

• Bagshaw, M. and Johnson, R. A. (1975). “The Influence of Reference Values and Estimated Variance on the ARL of CUSUM Tests”. Journal of the Royal Statistical Society B 37, pp. 413–420.
   Google Scholar
• Brook, D. and Evans, D. A. (1972). “An Approach to the Probability Distribution of CUSUM Run Length”. Biometrika 59, pp. 539–549.
   Web of Science ®Google Scholar
• Burroughs, T. E.; Rigdon, S. E.; and Champ, C. W. (1993). “An Analysis of Shewhart Charts with Runs Rules When No Standards Are Given”. Proceedings of the Quality and Productivity Section of the American Statistical Association August 8–12, San Francisco, CA, pp. 16–19.
   Google Scholar
• Burroughs, T. E.; Rigdon, S. E.; and Champ, C. W. (1995). “Analysis of the Shewhart S-Chart with Runs Rules When No Standards Are Given”. Proceedings of the Twenty-Sixth Annual Meeting of the Midwest Decision Sciences Institute May 4–6, St. Louis. MO, pp. 268–270.
   Google Scholar
• Champ, C. W.; Rigdon, S. E.; and Scharnagl, K. A. (2001). “A Method for Deriving Integral Equations Useful in Control Chart Performance Analysis”. Nonlinear Analysis 47, pp. 2089–2101.
   Web of Science ®Google Scholar
• Chakrabortl, S. (2000). “Run Length, Average Run Length, and False Alarm Rate of Shewhart X-bar Chart: Exact Derivations by Conditioning”. Communications in Statistics: Simulation and Computation 29, pp. 61–81.
   Web of Science ®Google Scholar
• Chen, G. (1997). “The Mean and Standard Deviation of the Run Length Distribution of X-bar Charts when Control Limits are Estimated”. Statistica Sinica 7, pp. 789–798.
   Web of Science ®Google Scholar
• Del Castillo, E. (1996a). “Run Length Distributions and Economic Design of Charts with Unknown Process Variance”. Metrika 43, pp. 189–201.
   Web of Science ®Google Scholar
• Del Castillo, E. (1996b). “Evaluation of Run Length Distribution for Charts with Unknown Variance”. Journal of Quality Technology 28, pp. 116–122.
   Web of Science ®Google Scholar
• Derman, C. and Ross, S. (1995). “An Improved Estimator of σ in Quality Control”. Probability in the Engineering and Informational Sciences 9. pp. 411–415.
   Google Scholar
• Fellner, W. H. (1990). “Algorithm AS 258: Average Run Lengths for Cumulative Sum Schemes”. Applied Statistics 39. pp. 402–412.
   Google Scholar
• Gan, F. F. (1991). “An Optimal Design of CUSUM Quality Control Charts”. Journal of Quality Technology 23, pp. 279–286.
   Web of Science ®Google Scholar
• Gan, F. F. (1993). “The Run Length Distribution of a Cumulative Sum Control Chart”. Journal of Quality Technology 25, pp. 205–215.
   Web of Science ®Google Scholar
• Ghosh, B. K.; Reynolds, M. R., Jr. and Hui, Y. V. (1981). “Shewhart -Charts with Estimated Process Variance”. Communications in Statistics—Theory and Methods 18, pp.1797–1822.
   Web of Science ®Google Scholar
• Goel, A. L. and Wu, S. M. (1971). “Determination of ARL and a Contour Nomogram for CUSUM Charts to Control Normal Mean”. Technometrics 13, pp. 221–230.
   Web of Science ®Google Scholar
• Gold, M. S. (1989). “The Geometric Approximation to the CUSUM Run Length Distribution”. Biometrika 76. pp. 725–733.
   Web of Science ®Google Scholar
• Hawkins, D. M. and Olwell, D. H. (1998). Cumulative Sum Charts and Charting for Quality Improvement. Springer, New York. NY.
   Google Scholar
• Jones, L. A. (2002). “The Statistical Design of EWMA Control Charts with Estimated Parameters”. Journal of Quality Technology 34, pp. 277–288.
   Web of Science ®Google Scholar
• Jones, L. A.; Champ, C. W.; and Rigdon, S. E. (2001). “The Performance of Exponentially Weighted Moving Average Charts with Estimated Parameters”. Technometrics 43, pp. 156–167.
   Web of Science ®Google Scholar
• Kemp, K. W. (1961). “The Average Run Length of the Cumulative Sum Chart when a V-Mask is Used”. Journal of the Royal Statistical Society B 23, pp. 149–153.
   Google Scholar
• Lu, C. W. and Reynolds, M. R., Jr. (1999). “EWMA Control Charts for Monitoring the Mean of Autocorrelated Processes”. Journal of Quality Technology 31, pp. 166–188.
   Web of Science ®Google Scholar
• Luceño, A. and Puig-Pey, J. (2000). “Evaluation of the Run-Length Probability Distribution for CUSUM Charts: Assessing Chart Performance”. Technometrics 42, pp. 411–416.
   Web of Science ®Google Scholar
• Luceno, A. and Puig-Pey, J. (2002). “Computing the Run Length Probability Distribution for CUSUM Charts”. Journal of Quality Technology 34, pp. 209–215.
   Web of Science ®Google Scholar
• Ng, C. H. and Case, K. E. (1992). “Control Limits and the ARL: Some Surprises”. First Industrial Engineering Research Conference Proceedings, pp. 127–129.
   Google Scholar
• Page, E. S. (1954). “Continuous Inspection Schemes”. Biometrika 41, pp. 100–114.
   Web of Science ®Google Scholar
• Quesenberry, C. P. (1993). “The Effect of Sample Size on Estimated Limits for and Control Charts”. Journal of Quality Technology 25, pp. 237–247.
   Web of Science ®Google Scholar
• van Dobben de Bruyn, C. S. (1968). Cumulative Sum Tests: Theory and Practice, Griffin, London, UK.
   Google Scholar
• Woodall, W. H. (1983). “The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables”. Technometrics 25, pp. 295–301.
   Web of Science ®Google Scholar
• Woodall, W. H. (1986). “The Design of CUSUM Quality Control Charts”. Journal of Quality Technology 18, pp. 99–102.
   Web of Science ®Google Scholar
• Yang, M. C. K. (1990). “Properties of the CUSUM Chart When There is No Standard Value (in Chinese)”. Journal of Chinese Statistical Association 28, pp. 57–77.
   Google Scholar
• Yang, Z.; Xie, M.; Kuralmani, V.; and Tsui, K. (2002). “On the Performance of Geometric Charts with Estimated Control Limits”. Journal of Quality Technology 34, pp. 448–458.
   Web of Science ®Google Scholar