Summary
This chapter presented a probabilistic sufficiency factor as a measure of the safety
level relative to a target safety level, which can be obtained from the results of Monte
Carlo simulation with little extra computation. It was shown that a design response
surface approximation can be more accurately fitted to the probabilistic sufficiency factor
than to the probability of failure or the safety index. Using the beam design example with
single or system reliability constraints, it was demonstrated that the design response
surface approximation based on probabilistic sufficiency factor has superior accuracy and
accelerates the convergence of reliability-based design optimization. The probabilistic
sufficiency factor also provides more information in regions of such low probability that
the probability of failure or safety index cannot be estimated by Monte Carlo simulation
with a given sample size, which is helpful in guiding the optimizer. Finally it was shown
that the probabilistic sufficiency factor can be employed by the designer to estimate the
required additional weight to achieve a target safety level, which might be difficult with
probability of failure or safety index.