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A Markov Chain Approximation for ATS Modeling for the Variable Sampling Interval CCC Control Charts

Authors: Y. K. Chen, K. C. Chiou, C. Y. Chen

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.

Keywords: Cumulative conformance count, variable sampling interval, Markov Chain, average time to signal, control chart.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1080738

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References:


[1] T. N. Goh, "A control chart for very high yield processes," Quality Assurance, vol. 13, pp. 18-22, 1987.
[2] 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.
[3] 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.
[4] E. A. Glushkovsky, "On-line G-control chart for attribute data," Quality & Reliability Engineering International, vol. 10, pp. 217-227, 1994.
[5] 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.
[6] 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.
[7] 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.
[8] 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.
[9] 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.
[10] 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.
[11] G. C. Runger and J. J. Pignatiello, Jr., "Adaptive sampling for process control," Journal of Quality Technology, vol. 23, pp. 133-155, 1991.
[12] 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.
[13] T. S. Vaughan, "Variable sampling interval np process control chart," Communications in Statistics-Theory and Method, vol. 22, pp. 147-167, 1993.
[14] 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.
[15] E. K. Epprecht and A. F. B. Costa, "Adaptive sample size control charts for attributes," Quality Engineering, vol. 13, pp. 465-473, 2001.
[16] 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.
[17] 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.
[18] E. Çinlar, Introduction to Stochastic Processes, Prentice Hall, Englewood Cliffs, NJ, 1975.