A system for the representation, editing, evaluation, and inference of graphical models is disclosed which can be used to construct and evaluate a graphical model or graphical network and to calculate inference values. An efficient method of updating graphical models is demonstrated, and provides the basis for an improved system for manipulation and evaluation of probabilistic models. The graphical network editor is useful in the construction of graphical modes such as Bayesian Networks. The graphical network and network graphical user interface (GUI) are used in conjunction with each other to model a system wherein failure probabilities and the current state of components are taken into account to monitor the health and progress of a system for an engineer or engineering software to evaluate and monitor. The evaluation is useful in the monitoring of assets and other real systems having multiple, dependent, and independently operating components such as a pump, a manufacturing plant, a production line, an assembly line, where asset health and quality control is a concern. The asset components each influencing some overall outcome of a system or situation. Success or failure or probability of success, probability of failure and health of the system can be monitored and manipulated by altering the values of prior probability and posterior probability values. Failure correlation between components can be evaluated wherein failure rates of asset is unknown. Production and quality can be monitored and altered.