Reliability is an important aspect of operatingsafety-critical applications of networked systems, such as inavionics. In order to ensure sufficient reliability, one approachis to apply redundancy. However, redundancy may be costlyif the degree of redundancy is too high. This paper proposesan optimization-based framework for guaranteeing the desiredreliability of any graph-based networked system. It focuses onintegrated modular avionics architecture, based on the use ofminimally redundant components. This framework consists oftwo steps. The first is to compute the minimum number ofcomponents within the architecture, using a geometric program.The second is to determine the topology with the minimal numberof connections between these components, using a signomialprogram. Finally, the method is illustrated on a small examplenetwork and a larger network of the A350 avionics architecture.