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A Markov Chain Approximation for ATS Modeling for the Variable Sampling Interval CCC Control Charts
Abstract:The cumulative conformance count (CCC) charts are widespread in process monitoring of high-yield manufacturing. Recently, it is found the use of variable sampling interval (VSI) scheme could further enhance the efficiency of the standard CCC charts. The average time to signal (ATS) a shift in defect rate has become traditional measure of efficiency of a chart with the VSI scheme. Determining the ATS is frequently a difficult and tedious task. A simple method based on a finite Markov Chain approach for modeling the ATS is developed. In addition, numerical results are given.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080738Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1210
 T. N. Goh, "A control chart for very high yield processes," Quality Assurance, vol. 13, pp. 18-22, 1987.
 P. D. Bourke, "Detecting a shift in fraction nonconforming using run-length control charts with 100% inspection," Journal of Quality Technology, vol. 23, pp. 225-238, 1991.
 F. C. Kaminsky, J. C. Benneyan, R. D. Davis, and R. J. Burke, "Statistical control charts based on a geometric distribution," Journal of Quality Technology, vol. 24, pp. 63-69, 1992.
 E. A. Glushkovsky, "On-line G-control chart for attribute data," Quality & Reliability Engineering International, vol. 10, pp. 217-227, 1994.
 M. Xie and T. N. Goh, "Some procedures for decision making in controlling high yield processes," Quality & Reliability Engineering International, vol. 8, pp. 355-360, 1995.
 R. Noorossana, A. Saghaei, K.Paynabar, and Y. Samimi, "On the conditional decision procedure for high yield processes," Computers & Industrial Engineering, vol. 53, pp. 469-477, 2007.
 V. Kuralmani, M. Xie, T. N. Goh, and F. F. Gan, "A conditional decision procedure for high yield processes," IIE Transactions, vol. 34, pp. 1021-1030, 2002.
 J. Y. Liu, M. Xie, T. N. Goh, Q. H. Liu, and Z. H. Yang, "Cumulative count of conforming chart with variable sampling intervals," International Journal of Production Economics, vol. 101, pp. 286-297, 2006.
 M. R. Reynolds, Jr., R. W. Amin, J. C. Arnold, and J. A. Nachlas, " X charts with variable sampling intervals," Technometrics, vol. 30, pp. 181-192, 1988.
 M. R. Reynolds, Jr., and J. C. Arnold, "Optimal one-sided Shewhart control charts with variable sampling intervals," Sequential Analysis, vol. 8, pp. 51-77, 1989.
 G. C. Runger and J. J. Pignatiello, Jr., "Adaptive sampling for process control," Journal of Quality Technology, vol. 23, pp. 133-155, 1991.
 M. S. Saccucci, R. W. Amin, J. M. Lucas, "Exponentially weighted moving average control schemes with variable sampling intervals," Communications in Statistics-Simulation and Computation, vol. 21, pp. 627-657, 1992.
 T. S. Vaughan, "Variable sampling interval np process control chart," Communications in Statistics-Theory and Method, vol. 22, pp. 147-167, 1993.
 K. T. Lee, D. S. Bai, "Variable sampling interval X control charts with run rules," International Journal of Industrial Engineering-Theory, Application, & Practice, vol. 7, pp. 147-158, 2000.
 E. K. Epprecht and A. F. B. Costa, "Adaptive sample size control charts for attributes," Quality Engineering, vol. 13, pp. 465-473, 2001.
 D. S. Bai and K. T. Lee, "Variable sampling interval X control chart with improved switching rule," International Journal of Production Economics, vol. 76, pp. 189-199, 2002.
 J. R. Villalobos, L. Mu├▒oz, and M. A. Gutierrez, "Using fixed and adaptive multivariate SPC charts for on-line SMD assembly monitoring," International Journal of Production Economics, vol. 95, pp. 109-121, 2005.
 E. ├çinlar, Introduction to Stochastic Processes, Prentice Hall, Englewood Cliffs, NJ, 1975.