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Detecting shifts in Conway–Maxwell–Poisson profile with deviance residual-based CUSUM and EWMA charts under multicollinearity

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Abstract

Monitoring profiles with count responses is a common situation in industrial processes and for a count distributed process, the Conway–Maxwell–Poisson (COM-Poisson) regression model yields better outcomes for under- and overdispersed count variables. In this study, we propose CUSUM and EWMA charts based on the deviance residuals obtained from the COM-Poisson model, which are fitted by the PCR and r–k class estimators. We conducted a simulation study to evaluate the effect of additive and multiplicative types shifts in various shift sizes, the number of predictor, and several dispersion levels and to compare the performance of the proposed control charts with control charts in the literature in terms of average run length and standard deviation of run length. Moreover, a real data set is also analyzed to see the performance of the newly proposed control charts. The results show the superiority of the newly proposed control charts against some competitors, including CUSUM and EWMA control charts based on ML, PCR, and ridge deviance residuals in the presence of multicollinearity.

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Notes

  1. \({\hat{W}}\) represents the estimated from of W where \(\mu \) is replaced by its estimator obtained by the indexed name.

  2. The tuning parameter value of the ridge estimator in COM-Poisson regression can be computed by the method given by Sami et al. (2022b), whereas many methods can be found in linear regression.

  3. Multicollinearity degree of about 0.95 is targeted to support the simulation study.

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Acknowledgements

This work was supported by the Research Fund of Çukurova University, Turkey under Project Number FDK-2019-11935.

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Authors and Affiliations

  1. Faculty of Science and Letters, Department of Statistics, Çukurova University, Adana, Turkey

    Ulduz Mammadova & M. Revan Özkale

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  1. Ulduz Mammadova
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  2. M. Revan Özkale
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Correspondence to Ulduz Mammadova.

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Appendix: Simulation study results

Appendix: Simulation study results

Table 14 ARL\(_1\) results when additive shift is present
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Table 15 \(ARL_1\) results when multiplicative shift is present
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Table 16 SDRL results when additive shift is present
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Table 17 SDRL results when multiplicative shift is present
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Mammadova, U., Özkale, M.R. Detecting shifts in Conway–Maxwell–Poisson profile with deviance residual-based CUSUM and EWMA charts under multicollinearity. Stat Papers 65, 597–643 (2024). https://doi.org/10.1007/s00362-023-01399-z

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