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Survivability is receiving increasing attention as a key property of critical systems. Survivability is the capability of a system to fulfill its mission, in a timely manner, in the presence of attacks, failures, or accidents. We present a method for analyzing survivability of distributed network systems and an example of its application. Survivability requires system capabilities for intrusion resistance, recognition, and recovery. The Survivable Network Analysis (SNA) method permits assessment of survivability at the architecture level. Steps in the method include system mission and architecture definition, essential capability definition, compromisable capability definition, and survivability analysis of architectural softspots that are both essential and compromisable. Intrusion scenarios play a key role in the analysis. SNA results are summarized in a Survivability Map that links recommended survivability strategies to the system architecture. The case study summarizes application of the SNA method to a subsystem of a large-scale, distributed healthcare system.