approximated to different levels of accuracy in optimization. Even combined with above
approaches, nested MPP approach still suffers the problems of high computational cost
and convergence. Several RBDO approaches are being developed to solve these
problems.
Inverse Reliability Approach
Recently, there has been interest in using alternative measures of safety in RBDO.
These measures are based on margin of safety or safety factors that are commonly used
as measures of safety in deterministic design. The safety factor is generally expressed as
the quotient of allowable over response, such as the commonly used central safety factor
that is defined as the ratio of the mean value of allowable over the mean value of the
response. The selection of safety factor for a given problem involves both objective
knowledge (such as data on the scatter of material properties) and subjective knowledge
(such as expert opinion). Given a safety factor, the reliability of the design is generally
unknown, which may lead to unsafe or inefficient design. Therefore, using safety factor
in reliability-based design optimization seems to be counter productive.
Freudenthal (1962) showed that reliability can be expressed in terms of the
probability distribution function of the safety factor. Elishakoff (2001) surveyed the
relationship between safety factor and reliability, and showed that in some cases the
safety factor can be expressed explicitly in terms of reliability. The standard safety factor
is defined with respect to the response obtained with the mean values of the random
variables. Thus a safety factor of 1.5 implies that with the mean values of the random
variables, we have a 50% margin between the response (e.g., stress) and the capacity
(e.g., failure stress). However, the value of the safety factor does not tell us what the
reliability is. Birger (1970), as reported by Elishakoff (2001), introduced a factor, which