Review of Methods for Reliability Analysis
The most common techniques for reliability analysis are Monte Carlo simulation,
approaches based on most probable point (MPP), and decoupledd" Monte Carlo sampling
of a response surface approximation fit to samples from some experimental design.
Different techniques are preferable under different circumstances.
Problem Definition
The limit state function of the reliability analysis problem is defined as G(x), where
G(x) represents a performance criterion and x is a random variable vector. Failure occurs
when G(x)<0. Thus the failure surface or limit state of interest can be described as
G(x)=0. The probability of failure can be calculated as
P, = fx (x)dx (2-2)
G(x) 0
where fx(x) is the joint probability distribution function (JPDF). This integral is hard to
evaluate because the integration domain defined by G(x)<0 is usually unknown and
integration in high dimension is very difficult.
Commonly used probabilistic analysis methods are based on either simulation
techniques such as Monte Carlo simulation or moment-based methods such as the first-
order-reliability-method (FORM) or second-order-reliability-method (SORM) (Melchers
1999).
Monte Carlo Simulation
Monte Carlo simulation (MCS) (e.g., Rubinstein 1981) generates a number of
samples of the random variables x by using a random number generator. The number of
samples required is usually determined by confidence interval analysis. Simulations (e.g.,
structural analyses) are then performed for each of these samples. Statistics such as mean,