  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 \textit{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 \textit{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.
