  Reliable, risk-averse design of complex engineering systems with optimized
performance requires dealing with uncertainties. A conventional approach is to
add safety margins to a design that was obtained from deterministic
optimization. Safer engineering designs require appropriate cost and constraint
function definitions that capture the risk associated with unwanted system
behavior in the presence of uncertainties. The paper proposes two notions of
certifiability. The first is based on accounting for the magnitude of failure
to ensure data-informed conservativeness. The second is the ability to provide
optimization convergence guarantees by preserving convexity. Satisfying these
notions leads to certifiable risk-based design optimization (CRiBDO). In the
context of CRiBDO, risk measures based on superquantile (a.k.a. conditional
value-at-risk) and buffered probability of failure are analyzed. CRiBDO is
contrasted with reliability-based design optimization (RBDO), where
uncertainties are accounted for via the probability of failure, through a
structural and a thermal design problem. A reformulation of the short column
structural design problem leading to a convex CRiBDO problem is presented. The
CRiBDO formulations capture more information about the problem to assign the
appropriate conservativeness, exhibit superior optimization convergence by
preserving properties of underlying functions, and alleviate the adverse
effects of choosing hard failure thresholds required in RBDO.
