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Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information

Author

Listed:
  • Muhammad Arslan
  • Muhammad Azeem Ashraf
  • Syed Masroor Anwar
  • Zahid Rasheed
  • Xuelong Hu
  • Saddam Akbar Abbasi
  • Thomas Hanne

Abstract

The classical cumulative SUM (CUSUM) chart is commonly used to monitor a particular size of the mean shift. In many real processes, it is assumed that the shift level varies within a range, and the exact level of the shift size is mostly unknown. For detecting a range of shift size, the dual-CUSUM (DC) and dual-Crosier CUSUM (DCC) charts are used to provide better detection ability as compared to the CUSUM and Crosier CUSUM (CC) charts, respectively. This paper introduces a new mixed exponentially weighted moving average (EWMA)-DCC (EDCC) chart to monitor process mean. In addition, AIB-based EWMA-DC (EDC) and EDCC charts (namely, AIB-EDC and AIB-EDCC charts) are suggested to detect shifts in the process mean level. Monte Carlo simulations are used to compute the run length (RL) characteristics of the proposed charts. A detailed comparison of the proposed schemes with other competing charts is also provided. It turns out that the proposed chart provides better performance than the counterparts when detecting a range of mean shift sizes. A real-life application is also presented to illustrate the implementation of the existing and proposed charts.

Suggested Citation

  • Muhammad Arslan & Muhammad Azeem Ashraf & Syed Masroor Anwar & Zahid Rasheed & Xuelong Hu & Saddam Akbar Abbasi & Thomas Hanne, 2022. "Novel Mixed EWMA Dual-Crosier CUSUM Mean Charts without and with Auxiliary Information," Mathematical Problems in Engineering, Hindawi, vol. 2022, pages 1-15, March.
    • Handle: RePEc:hin:jnlmpe:1362193
    DOI: 10.1155/2022/1362193
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