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Run-sum control charts for monitoring the coefficient of variation

Author

Listed:
  • Teoh, W.L.
  • Khoo, Michael B.C.
  • Castagliola, Philippe
  • Yeong, W.C.
  • Teh, S.Y.

Abstract

The coefficient of variation (CV) is a unit-free and effective normalized measure of dispersion. Monitoring the CV is a crucial approach in Statistical Process Control when the quality characteristic has a distinct mean value and its variance is a function of the mean. This setting is common in many scientific areas, such as in the fields of engineering, medicine and various societal applications. Therefore, this paper develops a simple yet efficient procedure to monitor the CV using run-sum control charts. The run-length properties of the run-sum CV (RS-γ) charts are characterized by the Markov chain approach. This paper proposes two optimization algorithms for the RS-γ charts, i.e. by minimizing (i) the average run length (ARL) for a deterministic shift size and (ii) the expected ARL over a process shift domain. Performance comparisons under both the zero- and steady-state modes are made with the Shewhart-γ, Run-rules-γ and EWMA-γ charts. The results show that the proposed RS-γ charts outperform their existing counterparts for all or certain ranges of shifts in the CV. The application of the optimal RS-γ charts is illustrated with real data collected from a casting process.

Suggested Citation

  • Teoh, W.L. & Khoo, Michael B.C. & Castagliola, Philippe & Yeong, W.C. & Teh, S.Y., 2017. "Run-sum control charts for monitoring the coefficient of variation," European Journal of Operational Research, Elsevier, vol. 257(1), pages 144-158.
    • Handle: RePEc:eee:ejores:v:257:y:2017:i:1:p:144-158
    DOI: 10.1016/j.ejor.2016.08.067
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    References listed on IDEAS

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    1. Leoni, Roberto Campos & Costa, Antonio Fernando Branco & Machado, Marcela Aparecida Guerreiro, 2015. "The effect of the autocorrelation on the performance of the T2 chart," European Journal of Operational Research, Elsevier, vol. 247(1), pages 155-165.
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    7. Haridy, Salah & Wu, Zhang & Lee, Ka Man & Bhuiyan, Nadia, 2013. "Optimal average sample number of the SPRT chart for monitoring fraction nonconforming," European Journal of Operational Research, Elsevier, vol. 229(2), pages 411-421.
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    Cited by:

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    4. Nguyen, H.D. & Tran, K.P. & Tran, K.D., 2021. "The effect of measurement errors on the performance of the Exponentially Weighted Moving Average control charts for the Ratio of Two Normally Distributed Variables," European Journal of Operational Research, Elsevier, vol. 293(1), pages 203-218.
    5. Pablo Bonilla-Escribano & David Ramírez & Alejandro Porras-Segovia & Antonio Artés-Rodríguez, 2020. "Assessment of Variability in Irregularly Sampled Time Series: Applications to Mental Healthcare," Mathematics, MDPI, vol. 9(1), pages 1-18, December.

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