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,