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A parameter-tuned genetic algorithm for statistically constrained economic design of multivariate CUSUM control charts: a Taguchi loss approach

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  • Seyed Niaki
  • Mohammad Ershadi

Abstract

In this research, the main parameters of the multivariate cumulative sum (CUSUM) control chart (the reference value k, the control limit H, the sample size n and the sampling interval h) are determined by minimising the Lorenzen–Vance cost function [Lorenzen, T.J., and Vance, L.C. (1986), ‘The Economic Design of Control Charts: A Unified Approach’, Technometrics, 28, 3–10], in which the external costs of employing the chart are added. In addition, the model is statistically constrained to achieve desired in-control and out-of-control average run lengths. The Taguchi loss approach is used to model the problem and a genetic algorithm, for which its main parameters are tuned using the response surface methodology (RSM), is proposed to solve it. At the end, sensitivity analyses on the main parameters of the cost function are presented and their practical conclusions are drawn. The results show that RSM significantly improves the performance of the proposed algorithm and the external costs of applying the chart, which are due to real-world constraints, do not increase the average total loss very much.

Suggested Citation

  • Seyed Niaki & Mohammad Ershadi, 2012. "A parameter-tuned genetic algorithm for statistically constrained economic design of multivariate CUSUM control charts: a Taguchi loss approach," International Journal of Systems Science, Taylor & Francis Journals, vol. 43(12), pages 2275-2287.
    • Handle: RePEc:taf:tsysxx:v:43:y:2012:i:12:p:2275-2287
    DOI: 10.1080/00207721.2011.570878
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    Cited by:

    1. M.J. Ershadi & R. Noorossana & S.T.A Niaki, 2016. "Economic-statistical design of simple linear profiles with variable sampling interval," Journal of Applied Statistics, Taylor & Francis Journals, vol. 43(8), pages 1400-1418, June.
    2. Jose Jorge Muñoz & Manuel J. Campuzano & Jaime Mosquera, 2022. "Optimized np Attribute Control Chart Using Triple Sampling," Mathematics, MDPI, vol. 10(20), pages 1-21, October.
    3. Amir Ahmadi-Javid & Mohsen Ebadi, 2021. "Economic design of memory-type control charts: The fallacy of the formula proposed by Lorenzen and Vance (1986)," Computational Statistics, Springer, vol. 36(1), pages 661-690, March.

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