The discipline of Asset Management (AM), which focuses on the management of physical assets in an integrated and holistic way along their life cycle, can be adopted by companies to promote sustainability since it enhances asset reliability and availability for the whole duration of its usage. Within the manufacturing industry, a relevant AM-related performance indicator is the Overall Equipment Effectiveness (OEE), which measures the efficiency of equipment. However, traditionally OEE measures the performance of individual equipment only, while neglecting the system perspective, which is core in AM. Only few contributions propose an extension towards a system-level performance indicator. After the OEE-related system-level indicators from the scientific literature are reviewed, an application of one of them in an industrial case is presented, selected as the indicator best fitting the characteristics of the industrial case itself, which is a disconnected flow manufacturing line. The application of the system-level indicator allows comparing it with the traditional OEE. Results show that a system approach better supports AM since the information carried out by the indicator is more complete and adherent with the actual asset and system characteristics. In turn, the system-level perspective is assumed just as a first step towards a holistic performance improvement as it is required by AM. A step forward to fulfill the sustainable performance is the integration of measurements of other sustainability-related impacts leading to effective asset-related decisions.