This article proposes a new combination of a correlative statistical analysis and the sliding window technique to detect incipient faults. Compared with the existing monitoring methods based on principal component and transformed component analyses, the combination fully uses the information from the process and quality variables. The sliding window, however, inevitably increases the computational burden due to the repeated window calculations. Therefore, a recursive algorithm is proposed in this article, which has been shown to have less calculation complexity. Furthermore, a randomized algorithm is proposed to determine the width of the sliding window. A numerical example and the thermal power plant process are presented to show the effectiveness and advantages of the proposed method.