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On-board processing systems are often deployed in hostile environments and must therefore adhere to stringent constraints such as low power, small size, and high dependability in the presence of faults. Since it is challenging for designers to simultaneously consider the many design tradeoffs and meet the numerous and unique demands and constraints of various on-board systems, designers typically rely on a limited set of familiar devices and design strategies that may not be optimal for a particular system's operating situation. In this paper, we present a framework to ease these system design challenges and aid designers in considering a broad range of devices and strategies for on-board processing, highlighting the most promising options early in the design process. Our framework considers the interactions between four key system properties - device, mission, fault-tolerant strategy, and application - which allows the framework to evaluate how well a design will meet mission constraints based on design evaluation metrics to identify tradeoffs between varying devices and fault-tolerant strategies. This paper focuses on the power and dependability evaluation metrics, which our framework calculates and leverages to evaluate the effectiveness of varying system designs. Finally, we use our framework to evaluate system designs for two case studies on hyperspectral-imaging (HSI) missions.