Risk-Based Design Optimization Via Probability of Failure, Conditional Value-at-Risk, and Buffered Probability of Failure

When designing systems, uncertainties must be dealt with at various levels. The designer must define appropriate cost and constraint functions that account for such uncertainties and capture the risk associated with unwanted system behavior. The choice of these cost and constraint functions additionally plays an important role in the convergence behavior of the optimization and, among other things, the final design. This paper studies different types of risk-based optimization problem formulations that can aid in efficient and robust design of complex engineering systems. In tutorial form, the paper describes risk-based optimization problem formulations, specifically, reliability-based design optimization, conditional-value-at-risk-based optimization, and buffered-failure-probability-based optimization. The properties of each formulation are analyzed and general guidelines for the appropriate choice of the optimization problem are provided for a given application setup. An in-depth understanding of the different optimization problems should facilitate development of future methods for designing safe engineering systems.