factor value of 0.9 means that we need to multiply the response by 0.9 or increase the

capacity by 1/0.9 to achieve the target reliability.

 Tu et al. (2000) used probabilistic performance measure, which is closely related to

Birger's safety factor, for RBDO using most probable point (MPP) methods (e.g., first

order reliability method). They showed that the search for the optimum design converged

faster by driving the safety margin to zero than by driving the probability of failure to its

target value. Wu et al. (1998, 2001) used probabilistic sufficiency factors in order to

replace the RBDO with a series of deterministic optimizations by converting reliability

constraints to equivalent deterministic constraints.

 The use of the probabilistic sufficiency factor gives a designer more quantitative

measure of the resources needed to satisfy the safety requirements. For example, if the

requirement is that the probability of failure is below 10-6 and the designer Einds that the

actual probability is 10-4, he or she cannot tell how much change is required to satisfy the

requirement. If instead the designer Einds that a probability of 10-6 is achieved with a

probabilistic sufficiency factor of 0.9, it is easier to estimate the required resources. For a

stress-dominated linear problem, raising the probabilistic sufficiency factor from 0.9 to 1

typically requires a weight increase of about 10 percent of weight of the overstressed

components .

 Reliability analysis of systems with multiple failure modes often employs Monte

Carlo simulation, which generates numerical noise due to limited sample size. Noise in

the probability of failure or safety index may cause reliability-based design optimization

(RBDO) to converge to a spurious optimum. The accuracy of MCS with a given number

of samples deteriorates with decreasing probability of failure. For RBDO problems with