With the rapid development of sensor technology, the data of modern industrial processes are collected and stored. Data-driven approaches have been widely used for status monitoring, most of which assume that the measurement data are accurate and reliable. However, in reality, the data obtained from sensors are usually contaminated with measurement errors, high noises and uncertainties. In this paper, vertices independent component analysis (V-ICA) is proposed to monitor the status of non-Gaussian processes with the above problems. First, kernel density estimation (KDE)-based measurement data transformation strategy is developed for uniformly transforming the measurement data into interval format. Then, the proposed method extracts independent components by constructing hypercubes based on all the possible combinations between the bounds of interval data. Furthermore, two monitoring statistics are introduced to analyze process status, both of which have multiple values to describe process uncertainties at a time. By taking the errors, high noises and uncertainties into consideration and giving all possible combinations between the bounds of interval data, the proposed method can extract correlation structure reliably and carry out effective fault detection. The simulation results in the six-variable system and the continuous stirred tank reactor system reveal that the V-ICA-based monitoring strategy outperforms PCA and ICA.