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, the use of safety factor in reliability-based design optimization seems
to be counter productive.
Freudenthal (1962) showed that reliability can be expressed in term 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. Therefore, Birger (1970), as reported by Elishakoff (2001), introduced a factor, which
we call here the probabilistic sufficiency factor that is more closely related to the target
reliability. A probabilistic sufficiency factor of 1.0 implies that the reliability is equal to
the target reliability, a probabilistic sufficiency factor larger than one means that the
reliability exceeds the target reliability, and probabilistic sufficiency factor less than one
means that the system is not as safe as we wish. Specifically, a probabilistic sufficiency