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.