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Synthetic-Type Control Charts for Time-Between-Events Monitoring

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  • Fang Yen Yen
  • Khoo Michael Boon Chong
  • Lee Ming Ha

Abstract

This paper proposes three synthetic-type control charts to monitor the mean time-between-events of a homogenous Poisson process. The first proposed chart combines an Erlang (cumulative time between events, Tr) chart and a conforming run length (CRL) chart, denoted as Synth-Tr chart. The second proposed chart combines an exponential (or T) chart and a group conforming run length (GCRL) chart, denoted as GR-T chart. The third proposed chart combines an Erlang chart and a GCRL chart, denoted as GR-Tr chart. By using a Markov chain approach, the zero- and steady-state average number of observations to signal (ANOS) of the proposed charts are obtained, in order to evaluate the performance of the three charts. The optimal design of the proposed charts is shown in this paper. The proposed charts are superior to the existing T chart, Tr chart, and Synth-T chart. As compared to the EWMA-T chart, the GR-T chart performs better in detecting large shifts, in terms of the zero- and steady-state performances. The zero-state Synth-T4 and GR-Tr (r = 3 or 4) charts outperform the EWMA-T chart for all shifts, whereas the Synth-Tr (r = 2 or 3) and GR-T2 charts perform better for moderate to large shifts. For the steady-state process, the Synth-Tr and GR-Tr charts are more efficient than the EWMA-T chart in detecting small to moderate shifts.

Suggested Citation

  • Fang Yen Yen & Khoo Michael Boon Chong & Lee Ming Ha, 2013. "Synthetic-Type Control Charts for Time-Between-Events Monitoring," PLOS ONE, Public Library of Science, vol. 8(6), pages 1-13, June.
    • Handle: RePEc:plo:pone00:0065440
    DOI: 10.1371/journal.pone.0065440
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    References listed on IDEAS

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    1. Patrick Bourke, 2001. "The geometric CUSUM chart with sampling inspection for monitoring fraction defective," Journal of Applied Statistics, Taylor & Francis Journals, vol. 28(8), pages 951-972.
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    Cited by:

    1. Shamstabar, Yousof & Shahriari, Hamid & Samimi, Yaser, 2021. "Reliability monitoring of systems with cumulative shock-based deterioration process," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. XueLong Hu & AnAn Tang & YuLong Qiao & JinSheng Sun & BaoCai Guo, 2020. "On the conditional performance of the synthetic chart with unknown process parameters using the exceedance probability criterion," PLOS ONE, Public Library of Science, vol. 15(10), pages 1-20, October.

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