Synthetic c charts with known and estimated process parameters based on median run length and expected median run length

Ming Ha Lee, Michael Boon Chong Khoo, Abdul Haq, M. L. Dennis Wong, Xin Ying Chew

    Research output: Contribution to journalArticlepeer-review

    1 Citation (Scopus)
    8 Downloads (Pure)


    In statistical process control, the total number of nonconformities per unit of a process is monitored by using the c chart. In this study, the run length performance of the synthetic c chart with known process parameter (denoted as the KP-Syn-c chart) and the synthetic c chart with estimated process parameter (denoted as the EP-Syn-c chart) are evaluated in terms of the median run length (MRL). The results show that the sensitivity of the MRL-based EP-Syn-c chart is dependent on the number of preliminary samples used in the Phase-I analysis. Furthermore, percentiles of the run length distribution are used to provide a better understanding for the run length performance of the EP-Syn-c chart. The numerical analysis shows that the required minimum number of preliminary samples can be very large for the MRL-based EP-Syn-c chart to perform similar as the KP-Syn-c chart. An optimization procedure is suggested to compute the design parameters of the EP-Syn-c chart by minimizing the out-of-control MRL. Furthermore, the optimal design procedure of the EP-Syn-c chart is also provided through minimizing the out-of-control expected MRL for the unknown process shift size. An example is provided to illustrate the design and implementation of the MRL-based EP-Syn-c chart.
    Original languageEnglish
    Pages (from-to)168-183
    Number of pages16
    JournalQuality Technology and Quantitative Management
    Issue number2
    Early online date10 Aug 2022
    Publication statusPublished - 4 Mar 2023


    • Estimated process parameter
    • expected median run length
    • median run length
    • synthetic c chart

    ASJC Scopus subject areas

    • Business and International Management
    • Industrial relations
    • Management Science and Operations Research
    • Information Systems and Management
    • Management of Technology and Innovation


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