관리도에서 Markov연쇄의 적용: 복습 및 새로운 응용

• 박창순 (중앙대학교 응용통계학과)
• Accepted : 20110600
• Published : 2011.08.31

Abstract

Properties of statistical process control procedures may not be derived analytically in many cases; however, the application of a Markov chain can solve such problems. This article shows how to derive the properties of the process control procedures using the generated Markov chains when the control statistic satisfies the Markov property. Markov chain approaches that appear in the literature (such as the statistical design and economic design of the control chart as well as the variable sampling rate design) are reviewed along with the introduction of research results for application to a new control procedure and reset chart. The joint application of a Markov chain approach and analytical solutions (when available) can guarantee the correct derivation of the properties. A Markov chain approach is recommended over simulation studies due to its precise derivation of properties and short calculation times.

Acknowledgement

Supported by : 한국학술진흥재단

References

1. Park, C. (2007). An algorithm for the properties of the integrated process control with bounded adjustments and EWMA monitoring, International Journal of Production Research, 45, 5571-5587. https://doi.org/10.1080/00207540701325397
2. Park, C., Lee. J. and Kim. Y. (2004). Economic design of a variable sampling rate EWMA chart, IIE Transactions, 36, 387-399. https://doi.org/10.1080/07408170490426116
3. Park, C. S. and Reynolds, M. R. (2008). Economic design of an integrated process control procedure with repeated adjustments and EWMA monitoring, Journal of the Korean Statistical Society, 37, 155-174. https://doi.org/10.1016/j.jkss.2007.10.005
4. Reynolds, M. R. (1996). Variable-sampling-interval control charts with sampling at xed time, IIE Trans-actions, 29, 497-510.
5. Reynolds, M. R. and Arnolds, J. C. (2001). EWMA control charts with variable sample sizes and variable sampling intervals, IIE Transactions, 33, 511-530.
6. Woodall, W. H. and Reynolds, M. R. (1983). A discrete Markov chain representation of the sequential probability ratio test, Sequential Analysis: Design Methods and Applications, 2, 27-44.