Conventional risk analysis and assessment tools rely on the use of probability to represent and quantify uncertainties. Modeling complex engineering problems with pure probabilistic approach can encounter challenges, particularly in cases where contextual knowledge and information are needed to define probability distributions or models. For the study and assessment of risks associated with complex engineering systems, researchers have been exploring augmentation of pure probabilistic techniques with alternative, non-fully, or imprecise probabilistic techniques to represent uncertainties. This exploratory research applies an alternative probability theory, quantum probability and the associated tools of quantum mechanics, to investigate their usefulness as a risk analysis and assessment tool for engineering problems. In particular, we investigate the application of the quantum framework to study complex engineering systems where the tracking of states and contextual knowledge can be a challenge. This study attempts to gain insights into the treatment of uncertainty, to explore the theoretical implication of an integrated framework for the treatment of aleatory and epistemic uncertainties, and to evaluate the use of quantum probability to improve the fidelity and robustness of risk system models and risk analysis techniques.