Partial least squares (PLS) and linear regression methods have been widely utilized for qualityrelated fault detection in industrial processes recently. Since these traditional approaches assume that process variables follow Gaussian distribution approximately, their effectiveness will be challenged when facing non-Gaussian processes. To deal with this difficulty, a new quality relevant process monitoring approach based on improved independent component regression (IICR) is presented in this article. Taking high-order statistical information into account, ICA is performed onto process data to produce independent components (ICs). In order to remove irrelevant variation orthogonal to quality variable and keep as much quality-related fault information as possible, a new quality-related independent components selection method is applied to these ICs. Then the regression relationship between filtered ICs and the product quality is built. QR decomposition for regression coefficient matrix is able to give out quality-related and quality-unrelated projectors. After the measured variable matrix is divided into quality relevant and quality irrelevant parts, novel monitoring indices are designed for fault detection. finally, applications to two simulation cases testify the effectiveness of our proposed quality-related fault detection method for non-Gaussian processes. INDEX TERMS Quality-related fault detection, independent component regression, orthogonal signal correction, non-Gaussian process, QR decomposition.