  Design and operation of complex engineering systems rely on reliability
optimization. Such optimization requires us to account for uncertainties
expressed in terms of compli-cated, high-dimensional probability distributions,
for which only samples or data might be available. However, using data or
samples often degrades the computational efficiency, particularly as the
conventional failure probability is estimated using the indicator function
whose gradient is not defined at zero. To address this issue, by leveraging the
buffered failure probability, the paper develops the buffered optimization and
reliability method (BORM) for efficient, data-driven optimization of
reliability. The proposed formulations, algo-rithms, and strategies greatly
improve the computational efficiency of the optimization and thereby address
the needs of high-dimensional and nonlinear problems. In addition, an
analytical formula is developed to estimate the reliability sensitivity, a
subject fraught with difficulty when using the conventional failure
probability. The buffered failure probability is thoroughly investigated in the
context of many different distributions, leading to a novel measure of
tail-heaviness called the buffered tail index. The efficiency and accuracy of
the proposed optimization methodology are demonstrated by three numerical
examples, which underline the unique advantages of the buffered failure
probability for data-driven reliability analysis.
