A Decision-based Perspective on Assessing System Robustness

Abstract

Although robustness often is cited as a desirable property of a system, a widely-accepted approach for quantifying it remains elusive. Informally, a system is robust if it avoids the downside consequences associated with uncertainty or perturbations. Prior approaches to quantifying robustness rely on the standard deviation of system responses or the expected ratio of performance under perturbation to nominal performance. Because the principal usefulness of any system metric is to inform decisions about the design of that system, we turn to rigorous decision theory for guidance on how to deal with the concept of robustness. We find that existing proposals for robustness quantification are inconsistent with accepted theory for rational decision making. Rather than propose an alternative quantification scheme, we argue that fundamentally there is no need to quantify robustness as an independent figure of merit. Instead, systems engineers can make decisions that favor system robustness using established methods based on expected utility theory. A key to this is formulating the decision problem in terms of fundamental objectives rather than means objectives. One's preference to favor robustness is associated with being risk averse over the fundamental objectives and is captured by using a concave utility function.