Monitoring systems play a crucial role in improving system failure resilience and preventing tragic consequences brought by unexpected system failure and saving the consequential high cost. Continuous monitoring systems have been applied to diversified systems for well-informed operations. Although plenty research has devoted to predicting system states using the continuous data flow, there still lacks a systematic decision-making framework for system designers and engineering system owners to maximize their benefits on adopting monitoring systems. This paper constructs such a decision-making framework, with which system owners can evaluate the operation cost change under specific operation modes considering the effectiveness of continuous monitoring systems in predicting system failures. Two case studies have been conducted to illustrate the value evaluation of the monitoring information and the system maintenance process with the aid of different prognostic results based on the monitoring data. The first case study considers a health-state prediction with fixed accuracy while the second one incorporates the accuracy improvement as the monitoring data accumulates. Results show that the value of monitoring systems will be influenced by the deviation among the equipment group, the accuracy of system-state prediction, and different types of cost involved in the operating process. And the adjustment of maintenance actions based on monitoring and prognosis information will help improve the value of monitoring systems.