% Generated by roxygen2: do not edit by hand
% Please edit documentation in R/FORM.R
\name{FORM}
\alias{FORM}
\title{First-Order Reliability Method (FORM)}
\usage{
FORM(
  lsf,
  lDistr,
  n_optim = 10,
  loctol = 0.01,
  optim_type = "rackfies",
  debug.level = 0
)
}
\arguments{
\item{lsf}{Objective function representing the limit-state, e.g. \code{function(R,E){R-E}}.
Supplied automatically by a SYS_ object - do not provide manually.}

\item{lDistr}{List of distribution objects created by TesiproV. Supplied automatically by
a SYS_ object - do not provide manually.}

\item{n_optim}{Number of optimization cycles (not required for Lagrangian algorithms).}

\item{loctol}{Local tolerance for convergence of the solver algorithm.}

\item{optim_type}{Optimization type: `"auglag"` (Augmented Lagrangian) or `"rackfies"`
(Rackwitz-Fiessler iterative scheme).}

\item{debug.level}{Verbosity level: 0 = silent, 1 = basic info, 2 = detailed output.}
}
\value{
A list containing:
  * `beta` - Hasofer-Lind reliability index
  * `pf` - probability of failure
  * `x_points` - design point in physical space
  * `dy` - gradient vector at design point
}
\description{
First-Order Reliability Method (FORM) for the approximation
of failure probabilities in structural reliability analysis.

The FORM estimates the probability of failure by transforming
the basic random variables into standard normal space
and approximating the limit-state function by a first-order
(linear) Taylor expansion at the design point.

The reliability index is defined as the minimum distance
from the origin to the limit-state surface in standard normal space.
The probability of failure is then approximated using
the standard normal cumulative distribution function.
}
\references{
Hasofer, A. M., & Lind, N. C. (1974).
An exact and invariant first-order reliability format.
\emph{Journal of the Engineering Mechanics Division, ASCE},
100(1), 111-121.

Rackwitz, R., & Fieszler, B. (1978).
Structural reliability under combined random load sequences.
\emph{Computers & Structures}, 9(5), 489-494.
}
\author{
(C) 2021-2026 K. Nille-Hauf, J.P. Schulze-Ardey, T. Feiri, M. Ricker, T. Lux -- Hochschule Biberach (until 2022),
TU Dortmund University - Chair of Structural Concrete (since 2023)
}
