Determining the Optimum Process Parameters by Asymmetric Quality Loss Function

Huang presented a trade-off problem, taking both product quality and process adjustment cost into account, to determine the optimum parameters (i.e., the process mean and process variance) of the input characteristic in the transformation model. In Huang's transformation model, the input characteristic, x, is assumed to be normally distributed and the output characteristic, y, is nominal-the-best with a target value. The relationship between x and y can be either linear or quadratic. When formulating the cost function in the transformation model, Huang used the symmetric quadratic loss function to measure the loss of profit. In this paper, we extend Huang's quadratic transformation model to a more general case by respectively using asymmetric quadratic and asymmetric linear loss functions in the cost function. The modified cost functions using asymmetric quadratic and asymmetric linear loss functions are developed. A numerical example is provided for illustration.