A cubic quality loss function and its applications

Abstract

AbstractThe traditional quality evaluation method believed that when the product quality characteristic was within the specification limit, no loss was produced. Taguchi proposed that even if the characteristic was within the range of users' demand, the fluctuation of quality characteristic would still cause loss to users and society. Therefore, he proposed a quadratic quality loss function to describe this loss. The function was established based on the Taylor expansion. It neglected terms with powers higher than 2, which would cause a certain deviation between the calculated and true value. Moreover, the tolerance and loss in the quadratic loss function must satisfied specific relationship, which limited its use. In this paper, the Taylor expansion items are raised to third order. The quality loss coefficients are discussed and analyzed so that the cubic quality loss function is established. In addition, the method of calculating hidden quality cost is given by using the cubic loss function. The hidden quality cost is affected by the quality loss coefficients and should be a range. The cubic quality loss function studies the inapplicability of quadratic loss function, so it widens the scope of application of quality loss function.