Minimizing a general loss function in off‐line quality control

We consider in the present paper the analysis of parameter designs in off‐line quality control. The main objective is to seek levels of the production factors that would minimize the expected loss. Unlike classical analyses which focus on the analysis of the mean and variance in minimizing a quadratic loss function, the proposed method is applicable to a general loss function. An appropriate transformation is first sought to eliminate the dependency of the variance on the mean (to achieve ‘separation’ in the terminology of Box). This is accomplished through a preliminary analysis using a recently proposed parametric heteroscedastic regression model. With the dependency of the variance on the mean eliminated, methods with established properties can be applied to estimate simultaneously the mean and the variance functions in the new metric. The expected loss function is then estimated and minimized based on a distributional free procedure using the empirical distribution of the standardized residuals. This alleviates the need for a full parametric model, which, if incorrectly specified, may lead to biased results. Although a transformation is employed as an intermediate step of analysis, the loss function is minimized in its original metric. Copyright © 2002 John Wiley & Sons, Ltd.