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Design of Quality Gain-Loss Function with the Cubic Term Consideration for Larger-the-Better Characteristic and Smaller-the-Better Characteristic

Author

Listed:
  • Bo Wang

    (School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450016, China)

  • Ruiyu Yang

    (School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450016, China)

  • Pengyuan Li

    (School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450016, China
    Central China Regional Headquarters of Powerchina Road-Bridge Co., Ltd., Zhengzhou 450016, China)

  • Qikai Li

    (School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450016, China)

  • Hui Yu

    (School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450016, China)

  • Zhiyong Li

    (School of Water Conservancy, North China University of Water Resources and Electric Power, Zhengzhou 450016, China)

Abstract

This research was based on the loss relationship diagrams of the linear term, quadratic term, and the cubic term losses in the quality gain–loss function (QGLF) for the larger-the-better characteristic (LBC) and the smaller-the-better characteristic (SBC). Limitations of ignoring the cubic term loss in the QGLF for the LBC and the SBC were analyzed. A QGLF model for LBC and SBC was proposed when considering the cubic term loss, using the threshold set at the ratio of the quadratic term loss to the cubic term loss. The calculation formulas for the coefficients of the linear term loss and the quadratic and cubic term losses in the QGLF for LBC and SBC when considering the cubic term were analyzed. By calculating and comparing the QGLF and the percentage discrepancy value of the continuous curing time of the concrete construction of dams and the temperature of the concrete pouring outlet, it was proved that directly ignoring the cubic term loss led to a discrepancy between the estimated quality loss value and the actual loss.

Suggested Citation

  • Bo Wang & Ruiyu Yang & Pengyuan Li & Qikai Li & Hui Yu & Zhiyong Li, 2025. "Design of Quality Gain-Loss Function with the Cubic Term Consideration for Larger-the-Better Characteristic and Smaller-the-Better Characteristic," Mathematics, MDPI, vol. 13(5), pages 1-20, February.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:5:p:777-:d:1600607
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    References listed on IDEAS

    as
    1. Yen-chang Chang & Wen-liang Hung, 2007. "LINEX Loss Functions with Applications to Determining the Optimum Process Parameters," Quality & Quantity: International Journal of Methodology, Springer, vol. 41(2), pages 291-301, April.
    2. Shuangshuang Li & Xintian Liu & Yansong Wang & Xiaolan Wang, 2018. "Hidden quality cost function of a product based on the cubic approximation of the Taylor expansion," International Journal of Production Research, Taylor & Francis Journals, vol. 56(14), pages 4762-4780, July.
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