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Implementation of Markov Chain: Review and New Application
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 Title & Authors
Implementation of Markov Chain: Review and New Application
Park, Chang-Soon;
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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.
Process control;transient region;absorbing region;transition probability;average number of visits;reset chart;
 Cited by
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. crossref(new window)

Park, C., Lee. J. and Kim. Y. (2004). Economic design of a variable sampling rate EWMA chart, IIE Transactions, 36, 387-399. crossref(new window)

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. crossref(new window)

Reynolds, M. R. (1996). Variable-sampling-interval control charts with sampling at xed time, IIE Trans-actions, 29, 497-510.

Reynolds, M. R. and Arnolds, J. C. (2001). EWMA control charts with variable sample sizes and variable sampling intervals, IIE Transactions, 33, 511-530.

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.