Key performance indicator (KPI)-relevant fault detection method has been raised for decades to hugely increase the economic interest of modern industries. However, the typical data-driven approaches like the kernel principal component analysis (KPCA) and the kernel entropy analysis (KECA) are inefficient to consider the influence taken by the fault factor on the KPI. Thus, in this work, an algorithm called the kernel entropy regression (KECR) is proposed to enhance the interpretability between the fault and the KPI. The proposed algorithm captures the information relevant to the KPI state in the subspace and rewords the decomposition of the KECA method. The angular structure of the KECR method achieves an accurate partition for process variables to hugely decrease false detection results. In the end, an industrial case is utilized to demonstrate the effectiveness of the KECR method.