In order to monitor patients in the Intensive Care Unit, healthcare practitioners set threshold alarms on each of many individual vital sign monitors. The current alarm algorithms elicit numerous false positive alarms producing an inefficient healthcare system, where nurses habitually ignore low level alarms due to their overabundance. In this paper, we describe an algorithm that considers multiple vital signs when monitoring a post coronary artery bypass graft (post-CABG) surgery patient. The algorithm employs a Fuzzy Expert System to mimic the decision processes of nurses. In addition, it includes a Clinical Decision Support tool that uses Bayesian theory to display the possible CABG-related complications the patient might be undergoing at any point in time, as well as the most relevant risk factors. As a result, this multivariate approach decreases clinical alarms by an average of 59% with a standard deviation of 17% (Sample of 32 patients, 1,451 hours of vital sign data). Interviews comparing our proposed system with the approach currently used in hospitals have also confirmed the potential efficiency gains from this approach.