Currently, the safety studies of the system (which are also collectively known as the safety case) cease or reduce in their utility after system certification, and with that, a vast amount of knowledge about the failure (or safe) behaviour of the system is usually rendered useless. In this thesis, we argue that this knowledge could be usefully exploited in the context of an appropriate on-line safety monitoring scheme. As a practical application of our approach, we propose a safety monitor that operates on safety cases to support the on-line detection and control of hazardous failures in safety critical systems. Firstly,