Methods and systems for detecting a fault in a data set from an industrial process are disclosed. One method includes forming a first data matrix at a data processing framework from time-series training data, and performing a principal component pursuit on the first data matrix to form an uncorrupted, unscaled matrix and a sparse matrix in the memory, and scaling the uncorrupted, unscaled matrix to form an uncorrupted scaled matrix. The method also includes performing a dynamic principal component analysis (DPCA) on the uncorrupted scaled matrix to form a DPCA model, and determining a squared prediction error from the DPCA model. Based on the squared prediction error, faults are detected in a different data set from operation of the industrial process. At least one of (1) correcting the one or more faults in the different data set or (2) performing a repair operation on a sensor is performed.