Right-censored failure time data is a common data type in manufacturing industry and healthcare applications. Some control charting procedures were previously proposed to monitor the right-censored failure time data under some specific distributional assumptions for the observed failure times and censoring times. But these assumptions may not be always satisfied in the real-world data. Therefore, a more generalized control chart technique, which can handle different types of distributions of the data, is highly needed. Considering the limitations of existing methodologies for detecting changes of hazard rate, this paper develops a generalized statistical procedure to monitor the failure time data in the presence of random right censoring when abundant historical failure times are available. The developed method makes use of the one-sample nonparametric rank tests without any specific assumptions of the data distribution. The operating characteristic functions of the control chart are derived on the basis of the asymptotic properties of the rank statistics. Case studies are presented to show the effectiveness of the proposed control chart technique, and its performance is investigated and compared with some Shewhart-type control charts based on the conditional expected value weight.