Models and modeling of interconnected critical infrastructures are on the rise. A different framework is provided here for analyzing and distinguishing interconnected operations in real time and over time. Our framework treats interconnected operations as the unit and level of analysis rather than as methodologically distinct operations of conceptually separate infrastructures. We focus on interconnectivity configurations, shifts, connected system control variables, and changing performance standards across important shifts. Implications of the conceptual and methodological refocusing are drawn for policy and management. Our framework allows for a new understanding of reliability in relation to interconnectivity management, including the identification of potential errors in assessing and acting upon interconnectivity shifts. These include failing to recognize when changes in communication patterns need to follow from interconnectivity shifts and neglecting the operational importance of improvisations where system control variables (like electricity frequency or water pressure) overlap or are shared. Larger implications for interinfrastructural and societal safety are drawn throughout.