Monitoring techniques play an important role in ensuring consistent product quality and safe operation in the process industry. Data-based models such Principal Component Analysis (PCA) are utilized as they are computationally efficient, and can handle high dimensional data. Most conventional techniques assume that process data generally follow a Gaussian distribution, are decorrelated, and contain a moderate level of noise. When practical data violate these assumptions, wavelet-based models such as multiscale principal component analysis (MSPCA) can be utilized in order to address these violations. Statistical hypothesis testing methods, such as the generalized likelihood ratio (GLR) technique, have been incorporated with different models in order to enhance fault detection performance. As literature has seen limited integration of multiscale multivariate models with hypothesis testing methods, an objective of this work is to develop and evaluate the performance of different multiscale multivariate fault algorithms, to determine and establish the proper method of integration of both techniques. Two illustrative examples will be utilized: one using simulated synthetic data, and the other using the benchmark Tennessee Eastman Process. The results demonstrate that the improved MSPCA-based GLR technique that was developed in this work is able to provide better detection results, with lower missed detection rates, and ARL1 values than the other techniques.