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Enhanced Cumulative Sum Charts for Monitoring Process Dispersion

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  • Mu’azu Ramat Abujiya
  • Muhammad Riaz
  • Muhammad Hisyam Lee

Abstract

The cumulative sum (CUSUM) control chart is widely used in industry for the detection of small and moderate shifts in process location and dispersion. For efficient monitoring of process variability, we present several CUSUM control charts for monitoring changes in standard deviation of a normal process. The newly developed control charts based on well-structured sampling techniques - extreme ranked set sampling, extreme double ranked set sampling and double extreme ranked set sampling, have significantly enhanced CUSUM chart ability to detect a wide range of shifts in process variability. The relative performances of the proposed CUSUM scale charts are evaluated in terms of the average run length (ARL) and standard deviation of run length, for point shift in variability. Moreover, for overall performance, we implore the use of the average ratio ARL and average extra quadratic loss. A comparison of the proposed CUSUM control charts with the classical CUSUM R chart, the classical CUSUM S chart, the fast initial response (FIR) CUSUM R chart, the FIR CUSUM S chart, the ranked set sampling (RSS) based CUSUM R chart and the RSS based CUSUM S chart, among others, are presented. An illustrative example using real dataset is given to demonstrate the practicability of the application of the proposed schemes.

Suggested Citation

  • Mu’azu Ramat Abujiya & Muhammad Riaz & Muhammad Hisyam Lee, 2015. "Enhanced Cumulative Sum Charts for Monitoring Process Dispersion," PLOS ONE, Public Library of Science, vol. 10(4), pages 1-22, April.
    • Handle: RePEc:plo:pone00:0124520
    DOI: 10.1371/journal.pone.0124520
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    References listed on IDEAS

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    1. Knoth, Sven, 2006. "Computation of the ARL for CUSUM-S2 schemes," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 499-512, November.
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    Cited by:

    1. Nasir Abbas & Mu’azu Ramat Abujiya & Muhammad Riaz & Tahir Mahmood, 2020. "Cumulative Sum Chart Modeled under the Presence of Outliers," Mathematics, MDPI, vol. 8(2), pages 1-30, February.

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