In the manufacturing industry, it is crucial to identify process variables that strongly affect product quality so that high product quality is maintained. Conventional methods based on variable importance have not necessarily shown good results. In the present work, we propose a new method to estimate variable importance. First, we construct a regression model for predicting product quality from process variables by using support vector regression or gaussian process regression, then we compute variable importance from the sensitivity of the model. It is demonstrated through a numerical example and an industrial case study that the proposed method outperforms conventional methods such as partial least squares and random forest.