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The phrase "System of Systems" (SoS) has been in use for at least the past ten years. As customers of the aerospace and defense industries began asking for broad capabilities rather than for single systems to meet specific requirements, the notion of a system comprised of multiple, independently operating systems has become more important as the way to meet the desired set of capabilities. Recently, systems of systems have been identified in many other domains, such as health care, energy, logistics, and transportation. Because individual systems can operate independently within an SoS, many engineering methods and tools used to design large-scale, but monolithic, systems do not appear to work for designing systems of systems. This paper presents a three-axis taxonomy that can guide design method development and use for systems of systems. Based on this perspective, two experimental methods applications are presented for SoS problems.

The complex, multidisciplinary nature of aerospace design problems, as well as the requirement to examine life-cycle characteristics, have exposed a need to model and manage uncertainty. In this paper, a formal approach for modeling uncertainty in such design problems is presented. The approach includes uncertainties associated with mathematical models, operation environment, response measurement, and input requirements. In addition, a new method for propagating this uncertainty (in an efficient manner) to find robust design solutions is developed and described. The uncertainty model combined with the probabilistic robust design technique is a critical advancement in multidisciplinary system design, in that it identifies solutions that have a maximum probability of success. Continued research in both uncertainty modeling and efficient robust design methods appears essential. Both the uncertainty model and robust design technique are demonstrated on an example problem involving the design of a supersonic transport aircraft using the relaxed static stability technology. At each step, validation studies are performed and initial results indicate that the robust design method represents an accurate depiction of the problem. This depiction provides critical insight into where and why uncertainty affects the family of design solutions.

Within the context of multi-disciplinary aircraft analysis and design, a new approach has been formulated and described which allows for the rapid technical feasibility and economic viability assessment of multiattribute, multi-constrained designs. The approach, referred to here as Virtual Stochastic Life Cycle Design, facilitates the multi-disciplinary consideration of a system, accounting for life-cycle issues in a stochastic fashion. The life-cycle consideration is deemed essential in order to evaluate the emerging, all encompassing system objective of affordability. The stochastic treatment is employed to account for the knowledge variation/uncertainty that occurs in time through the various phases of design. Variability found in the treatment of assumptions, ambiguous requirements, code fidelity (imprecision), economic uncertainty, and technological risk are all examples of categories of uncertainty that the proposed probabilistic approach can assess. For cases where the problem is over-constrained and a feasible solution is not possible, the proposed method facilitates the identification and provides guidance in the determination of potential barriers which will have to be overcome via the infusion of new technologies. The specific task of examining system feasibility and viability is encapsulated and outlined in a series of easy to follow steps. Finally, the method concludes with a brief description and discussion of proposed decision making techniques to achieve optimal designs with reduced variability. This decision making is achieved through a combined utility theory and Robust Design Simulation approach.