A Study on EWMA charts with runs rules—the Markov chain approach

Michael Boon Chong Khoo, Philippe Castagliola, J. Y. Liew, Wei Lin Teoh, Petros E. Maravelakis

Research output: Contribution to journalArticlepeer-review

21 Citations (Scopus)


Runs rules are usually used with Shewhart-type charts to enhance the charts' sensitivities toward small and moderate shifts. Abbas et al. in 2011 took it a step further by proposing two runs rules schemes, applied to the exponentially weighted moving average (EWMA) chart and evaluated their average run length (ARL) performances using simulation. They showed that the proposed schemes are superior to the classical EWMA chart and other schemes being investigated. Besides pointing out some erroneous ARL and standard deviation of the run length (SDRL) computations in Abbas et al., this paper presents a Markov chain approach for computing the ARL, percentiles of the run length (RL) distribution and SDRL, for the two runs rules schemes of Abbas et al. Using Markov chain, we also propose two combined runs rules EWMA schemes to quicken the two schemes of Abbas et al. in responding to large shifts. The runs rules (basic and combined rules) EWMA schemes will be compared with some existing control charting methods, where the former charts are shown to prevail.

Original languageEnglish
Pages (from-to)4156-4180
Number of pages25
JournalCommunications in Statistics - Theory and Methods
Issue number14
Publication statusPublished - 2016


  • Average run length (ARL)
  • EWMA chart
  • Markov chain
  • Percentiles of the run length (RL) distribution
  • Runs rules
  • Standard deviation of the run length (SDRL)

ASJC Scopus subject areas

  • Statistics and Probability


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