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

Bo Wang, Ruiyu Yang, Pengyuan Li, Qikai Li, Hui Yu and Zhiyong Li ()
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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
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

Mathematics, 2025, vol. 13, issue 5, 1-20

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.

Keywords: the larger-the-better characteristic; the smaller-the-better characteristic; quality gain-loss function; loss coefficient; compensation amount (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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