  This paper presents three new computational methods for calculating design
sensitivities of statistical moments and reliability of high-dimensional
complex systems subject to random input. The first method represents a novel
integration of polynomial dimensional decomposition (PDD) of a multivariate
stochastic response function and score functions. Applied to the statistical
moments, the method provides mean-square convergent analytical expressions of
design sensitivities of the first two moments of a stochastic response. The
second and third methods, relevant to probability distribution or reliability
analysis, exploit two distinct combinations built on PDD: the PDD-SPA method,
entailing the saddlepoint approximation (SPA) and score functions; and the
PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the PDD
approximation and score functions. For all three methods developed, the
statistical moments or failure probabilities and their design sensitivities are
both determined concurrently from a single stochastic analysis or simulation.
Numerical examples, including a 100-dimensional mathematical problem, indicate
that the new methods developed provide not only theoretically convergent or
accurate design sensitivities, but also computationally efficient solutions. A
practical example involving robust design optimization of a three-hole bracket
illustrates the usefulness of the proposed methods.
