Multivariate statistical monitoring charts are efficient tools for assessing the quality of a process by identifying abnormalities. Most commonly used multivariate monitoring charts, such as the Hotelling T2 rule, however, assume the availability of uncorrelated Gaussian observations. Unfortunately, very often, real data do not satisfy these assumptions, and thus limit the usefulness of these techniques in practice. Furthermore, in many real applications, changes can occur in the shape of the multivariate distribution of the process while its mean or variance remains the same. Conventional process monitoring charts, such as the T2 chart, fail to detect such changes in the distribution. In this article, we develop new copula-based multivariate monitoring techniques for possibly autocorrelated, non-Gaussian data that can detect changes in the shape of a multivariate distribution that are usually overlooked by conventional monitoring charts. Using synthetic data, we demonstrate the effectiveness of the developed charts over a conventional monitoring chart. Results indicate that the proposed charts are very promising because copula-based charts are, in practice, designed to monitor the entire distribution of a process instead of the individual components. The developed monitoring charts are validated through practical application on data from a decentralized wastewater treatment plant in Golden, CO, United States.