Multi-parameter monitoring systems in Intensive Care Units (ICUs) monitor the clinical condition of critical state patients. These Systems of Systems (SoS) comprise a set of Constituent Systems (CS) to measure parameters such as heart rate, respiratory frequency, and temperature. Due to the critical nature and relevance of ICUs, such SoS shall be as reliable as possible. That is especially true in emergencies, as the COVID-19 outbreak that resulted in the burden of health care systems. We developed a modular and parametric model to perform reliability analysis and to provide insights to assist the management of multi-parameter monitoring systems used in ICUs, also considering maintenance. First, we modeled a multi-parameter monitoring system for ICUs using the CHESS methodology and modeling language. Afterward, we performed a reliability analysis using the CHESS state-based analysis plugin for different scenarios. We identified that the main power supply and the battery are the CS that present the most negative impacts on reliability. In emergencies, reduced time ranges of planned maintenance, when applied during a short period, showed to be promising strategies.