CHAPTER 2
LITERATURE SURVEY: 1VETHODS FOR RELIABILITY ANALYSIS AND
RELIABILITY-BASED DESIGN OPTIMIZATION
The basic conceptual structure of the reliability-based design optimization (RBDO)
problem, called RBDO framework, can be formulated as
minimize F = F(d)
such that
P3 () <;Pf ,j = n(2-1)
where F is the obj ective function, d is a vector of design variables, Pj is the probability of
failure of the jth failure mode, P,' is the allowable probability of failure of the jth failure
mode, n, is the total number of failure modes, and x is a vector of random variables.
To perform RBDO, reliability analyses must be performed to evaluate the
probability of failure, which requires multiple evaluations of system performance (such
as stresses in a structure). Depending on the specific reliability analysis method, the
computational cost of a single reliability analysis is usually comparable to or higher than
the cost of performing a deterministic local optimization. Furthermore, RBDO requires
multiple reliability analyses, thus the computational cost of performing RBDO by directly
coupling design optimization with reliability analysis is at least an order of magnitude
higher than deterministic optimization. Efficient frameworks must be developed to
overcome this computational burden.
This chapter presents a literature review of state-of-the-art reliability analysis
methods and RBDO frameworks, and concludes with the motivation to develop the
methodologies in Chapters 3, 6, and 7 for solving the problems.