Hidden quality cost function of a product based on the cubic approximation of the Taylor expansion

The-Nominal-The-Best (N-type) loss function is established based on the Taylor expansion. Results become more accurate as more Taylor expansion items are retained. N-type loss function neglects terms with powers higher than two, which inevitably leads to a certain deviation between the calculated result and the true value. In this paper, Taylor expansion is retained to the third-order, and the quality loss function is extended to three items. The quality loss coefficients of each item are determined, and the asymmetric piecewise cubic quality loss function is established. The deviation between the cubic and quadratic functions is evaluated. The formula for calculating the hidden quality cost of a product is derived by choosing an appropriate density distribution function and using process capability. Two cases are utilised to analyse and discuss the quality loss and hidden quality cost of a product using the cubic quality loss and quadratic quality loss functions. This paper provides a more accurate approach for the study of product quality management.