Structural reliability or structural reliability is the application of reliability engineering theories to buildings, homes, bridges and other types of construction. Reliability is also used as a probabilistic measure of structural safety.[1]​[2]​ The reliability of a structure is defined as the complement probability of failure (Reliability = 1 - Probability of failure). Failure occurs when the total load is greater than the total strength of the structure. Structural reliability has become a well-known design philosophy in the 20th century, and could replace traditional deterministic ways of design[3]​ and maintenance.[1]​.

Both structural loads and resistances are probabilistically modeled as random variables. With this approach the probability of failure of a structure is calculated. When the loads and resistances are explicit and statistically independent, the probability of failure can be calculated as follows.[1]​[2]​.

where is the probability of failure, is the cumulative distribution function of the resistance and is the probability density of the load, the variable is the value of the load or request. An alternative way would be to write the probability of failure as:.

where 𝑋 is the vector of the basic variables, and G(X) which is called the limit state function could be a line, surface or volume that takes the integral on its surface.

Analytical solutions

When the load and resistance are expressed explicitly (such as equation (1) above), and their distributions are normal, the integral of equation (1) has a closed-form solution as follows.

Monte Carlo method

In most cases, load and resistance are not normally distributed. Therefore, it is impossible to analytically solve the integrals of equations (1) and (2). The use of Monte Carlo simulation is one approach that could be used in such cases.[1][2][4]​.