Inactivating pathogens is essential to eradicate waterborne diseases. However, disinfection forms undesirable disinfection by-products (DBPs) in the presence of natural organic matter. Many regulations and guidelines exist to limit DBP exposure for eliminating possible health impacts such as bladder cancer, reproductive effects, and child development effects. In this paper, an index named non-compliance potential (NCP) index is proposed to evaluate regulatory violations by DBPs. The index can serve to evaluate water quality in distribution networks using the Bayesian Belief Network (BBN). BBN is a graphical model to represent contributing variables and their probabilistic relationships. Total trihalomethanes (TTHM), haloacetic acids (HAA5), and free residual chlorine (FRC) are selected as the variables to predict the NCP index. A methodology has been proposed to implement the index using either monitored data, empirical model results (e.g., multiple linear regression), and disinfectant kinetics through EPANET simulations. The index's usefulness is demonstrated through two case studies on municipal distribution systems using both full-scale monitoring and modeled data. The proposed approach can be implemented for data-sparse conditions, making it especially useful for smaller municipal drinking water systems.