In time-sensitive applications within industry 4.0, e.g. anomaly detection and human-in-the-loop, the data generated by multiple sources should be quickly separated to give the applications more time to make decisions and ultimately improve production performance. In this paper, we propose a Component-dependent Independent Component Analysis (CdICA) method that can separate multiple randomly mixed signals into independent source signals faster, for further data analysis in time-sensitive applications. Based on the Independent Component Analysis (ICA) algorithm, we first generate an initial separation matrix relying on the known mixture components, so that the separation speed of the traditional ICA can be increased. Our simulative results show that the CdICA method reduces the separation time by 55% to 83% compared to the most notable related work called FastICA and meanwhile it does not diminish the accuracy of the separation.