This paper presents a statistical monitoring methodology to identify and diagnose intermittent stochastic faults occurring in a nonlinear dynamic chemical process. This methodology addresses three important aspects in model-based fault detection and diagnosis (FDD): model simplicity, interpretability, and calibration. The goal is to generate a surrogate model that can be easily interpreted while maintaining model flexibility and efficiency. The key feature is the use of an active set optimization in combination with a Gaussian process (GP) model for fault detection and classification. To optimally select measured variables for inferring faults, an active set optimization with l1-norm regularization is combined with statistical analysis. This can provide a trade-off between model dimensionality and model prediction error. To ensure sufficient data for the calibration of GP models, an improvement in a probability-based model adjustment algorithm is developed. The performance of the developed FDD scheme is illustrated with two examples: (i) a chemical process consisting of two continuous, stirred tank reactors (CSTRs) and a flash tank separator, and (ii) the Tennessee Eastman benchmark problem. In addition, to deal with multiple-root-cause faults, the GP model based classification was investigated. The summary of the results show that the methodology in this work can cope with both individual and simultaneous occurrences of multiple-root-cause faults in the presence of uncertainty.