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One-sided variable sampling interval EWMA control charts for monitoring the multivariate coefficient of variation in the presence of measurement errors

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Abstract

Online monitoring of the multivariate coefficient of variation (MCV) can be of interest in many real situations in which the dispersion of a multivariate process is meant to remain constant with regard to its position. To this aim, several control charts have been recently proposed in the literature. In this paper, the new one-sided adaptive charts to monitor the MCV are proposed. The chart applies a variable sampling interval (VSI) strategy on an exponentially weighted moving average (EWMA) scheme, aiming at benefiting from the known advantages of both approaches. Formulas to optimally determine the parameters of the chart are derived and presented. The proposed chart is shown to outperform competing charts under most circumstances. The presence of the measurement errors is considered to understand their effects on the charts. An illustrative example is also included.

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Funding

VGB’s research work was supported by the Ministerio de Ciencia e Innovación of Spain under grant no. PID2019-110442GB-I00.

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Authors and Affiliations

  1. Institute of Artificial Intelligence and Data Science, Dong A University, Da Nang, Vietnam

    Quoc-Thông Nguyen & Kim Duc Tran

  2. HEC Management School, University of Liège, Liège, 4000, Belgium

    Quoc-Thông Nguyen & Cédric Heuchenne

  3. Université de Lille, ENSAIT, GEMTEX, F-59000, Lille, France

    Quoc-Thông Nguyen & Kim Phuc Tran

  4. Centre for Quality and Change Management, Universitat Politècnica de València, València, Spain

    Vicent Giner-Bosch

Authors
  1. Quoc-Thông Nguyen
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  2. Vicent Giner-Bosch
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  3. Kim Duc Tran
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  4. Cédric Heuchenne
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  5. Kim Phuc Tran
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Correspondence to Cédric Heuchenne.

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Appendix

Appendix

Fig. 10
figure 10

ATS curves of the downward (left) and upward (right) VSI EWMA MCV charts for p = 2,γ0 = 0.1,n = 5 with measurement parameters B = 1,m = 1, and 𝜃2 ∈{0,0.3,0.5,1}

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Fig. 11
figure 11

ATS curves of the downward (left) and upward (right) VSI EWMA MCV charts for p = 2,γ0 = 0.2,n = 5 with measurement parameters B = 1,m = 1, and 𝜃2 ∈{0,0.3,0.5,1}

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Fig. 12
figure 12

ATS curves of the downward (left) and upward (right) VSI EWMA MCV charts for p = 2,γ0 = 0.3,n = 5 with measurement parameters B = 1,m = 1, and 𝜃2 ∈{0,0.3,0.5,1}

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Fig. 13
figure 13

ATS curves of the downward (left) and upward (right) VSI EWMA MCV charts for p = 2,γ0 = 0.1,n = 5 with measurement parameters 𝜃2 = 0.3,m = 1, and B ∈{1,5}

Full size image
Fig. 14
figure 14

ATS curves of the downward (left) and upward (right) VSI EWMA MCV charts for p = 2,γ0 = 0.2,n = 5 with measurement parameters 𝜃2 = 0.3,m = 1, and B ∈{1,5}

Full size image
Fig. 15
figure 15

ATS curves of the downward (left) and upward (right) VSI EWMA MCV charts for p = 2,γ0 = 0.3,n = 5 with measurement parameters 𝜃2 = 0.3,m = 1, and B ∈{1,5}

Full size image

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Nguyen, QT., Giner-Bosch, V., Tran, K.D. et al. One-sided variable sampling interval EWMA control charts for monitoring the multivariate coefficient of variation in the presence of measurement errors. Int J Adv Manuf Technol 115, 1821–1851 (2021). https://doi.org/10.1007/s00170-021-07138-8

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