A CUSUM Chart for Monitoring a Proportion When Inspecting Continuously

References

• Bourke, P. D. (1991). “Detecting a Shift in Fraction Nonconforming Using Run-Length Control Charts with 100% Inspection”. Journal of Quality Technology 23, pp. 225–238.
   Web of Science ®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
• Burden, R. L. and Faires, J. D. (1993). Numerical Analysis, 5th ed. PWS Publishing, Boston, MA.
   Google Scholar
• Cheney, W. and Kincaid, D. (1985). Numerical Mathematics and Computing, 2nd ed. Brooks/Cole Publishing, Pacific Grove, CA.
   Google Scholar
• Gan, F. F. (1993). “An Optimal Design of CUSUM Control Charts for Binomial Counts”. Journal of Applied Statistics 20, pp. 445–460.
   Google Scholar
• Ghosh, B. K. (1970). Sequential Tests of Statistical Hypotheses. Addison-Wesley/Longman Publishing, Boston, MA.
   Google Scholar
• Hawkins, D. M. (1992). “Evaluation of Average Run Lengths of Cumulative Sum Charts for an Arbitrary Data Distribution”. Communications in Statistics—Simulation and Computation 21, pp. 1001–1020.
   Web of Science ®Google Scholar
• Hawkins, D. M. and Olwell, D. H. (1998). Cumulative Sum Charts and Charting for Quality Improvement. Springer-Verlag, New York, NY.
   Google Scholar
• Lucas, J. M. (1989). “Control Schemes for Low Count Levels”. Journal of Quality Technology 21, pp. 199–201.
   Web of Science ®Google Scholar
• Lucas, J. M. and Crosier, R. B. (1982). “Fast Initial Response for CUSUM Quality Control Schemes: Give Your CUSUM a Head Start”. Technometrics 24, pp. 199–205.
   Web of Science ®Google Scholar
• Page, E. S. (1954). “Continuous Inspection Schemes”. Biometrika 41, pp. 100–114.
   Web of Science ®Google Scholar
• Rendtel, U. (1990). “CUSUM-Schemes With Variable Sampling Intervals and Sample Sizes”. Statistical Papers 31, pp. 103–118.
   Google Scholar
• Reynolds, M. R., Jr. (1996). “Variable Sampling Interval Control Charts with Sampling at Fixed Times”. IIIE Transactions 28, pp. 497–510.
   Web of Science ®Google Scholar
• Reynolds, M. R., Jr.; Amin, R. W.; and Arnold, J. C. (1990). “CUSUM Charts with Variable Sampling Intervals”. Technometrics 32, pp. 371–384.
   Web of Science ®Google Scholar
• Reynolds, M. R., Jr. and Stoumbos, Z. G. (1998a). “Some Recent Developments in Control Charts for Monitoring a Proportion” in Statistical Process Monitoring and Optimization edited by S. H. Park and G. G. Vining. Marcel Dekker, New York, NY (to appear).
   Google Scholar
• Reynolds, M. R., Jr. and Stoumbos, Z. G. (1998b). “The SPRT Chart for Monitoring a Proportion”. IIIE Transactions on Quality and Reliability 30, pp. 545–561.
   Web of Science ®Google Scholar
• Runger, G. C. and Willemain, T. R. (1995). “Model-Based and Model-Free Control of Autocorrelated Processes”. Journal of Quality Technology 27, pp. 283–292.
   Web of Science ®Google Scholar
• Ryan, T. P. and Schwertman, N. C. (1997). “Optimal Limits for Attributes Control Charts”. Journal of Quality Technology 29, pp. 86–98.
   Web of Science ®Google Scholar
• Siegmund, D. (1979). “Corrected Diffusion Approximations in Certain Random Walk Problems”. Advances in Applied Probability 11, pp. 701–719.
   Web of Science ®Google Scholar
• Siegmund, D. (1985). Sequential Analysis. Springer-Verlag, New York, NY.
   Google Scholar
• Stoumbos, Z. G. and Reynolds, M. R., Jr. (1997a). “Control Charts Applying a Sequential Test at Fixed Sampling Intervals”. Journal of Quality Technology 29, pp. 21–40.
   Web of Science ®Google Scholar
• Stoumbos, Z. G. and Reynolds, M. R., Jr. (1997b). “Corrected Diffusion Theory Approximations in Evaluating Properties of SPRT Charts for Monitoring a Process Mean”. Nonlinear Analysis 30, pp. 3987–3996.
   Web of Science ®Google Scholar
• Wald, A. (1947). Sequential Analysis. Dover Publications, New York, NY.
   Google Scholar
• Woodall, W. H. (1997). “Control Charts Based on Attribute Data: Bibliography and Review”. Journal of Quality Technology 29, pp. 172–183.
   Web of Science ®Google Scholar
• Woodall, W. H. and Adams, B. M. (1993). “The Statistical Design of CUSUM Charts”. Quality Engineering 5, pp. 559–570.
   Google Scholar
• Yashchin, E. (1985). “On a Unified Approach to the Analysis of Two-Sided Cumulative Sum Control Schemes with Head-starts”. Advances in Applied Probability 17, pp. 562–593.
   Web of Science ®Google Scholar
• Zacks, S. (1981). “The Probability Distribution and the Expected Value of a Stopping Variable Associated with Onesided CUSUM Procedures for Non-Negative Integer Valued Random Variables”. Communications in Statistics—Theory and Methods 10, pp. 2245–2258.
   Web of Science ®Google Scholar