and less accurate DRS. Then the Pyf can re-calibrated by a single expensive MCS. This

is a variable-fidelity technique, with a large number of inexpensive MCS combined with

a small number of expensive MCS.

 A compromise between the deterministic optimization and the full probabilistic

optimization is afforded by the probabilistic sufficiency factor Pyf by using an

intermediate target probability PI, which is higher than the required probability Pr and

can be estimated via a less expensive MCS and less accurate DRS. Then the Pyf can re-

calibrated by a single expensive MCS. This is a variable-fidelity technique, with a large

number of inexpensive MC S combined with a small number of expensive MC S.

 For the beam example we illustrate the process by setting a low required

probability of 0.0000135, and using as intermediate probability 0.00135, the value used

as required probability for the previous examples. We start by finding an initial optimum

design with the intermediate probability as the required probability. This involves the

generation of a response surface approximation of~s Pyl forthe in~termidiate probability as

well as finding the optimum based on this response surface. We then perform an

expensive MCS which is adequate for estimating the required probability. Here we use

MCS with 107 samples. We now calculate the Psf from this accurate MCS, and denote it

Psf. At that design the Psf predictled by uthe response: surfacet approximation is about 1,

because the initial optimization was performed with a lower limit of 1 on the Psf. In

contrast, uthe ac~curalte P/ will in general be different for several reasons. These include

the higher accuracy of the MCS, the response surface errors, and most important the

lower probability requirements. For example, with 107 samples, at this initial design we

may get P/=1.0I1 for the intlltermedate probabIiliy (based on Lthe 13500 lowest safety