mistral (version 1.1-0)

FORM: FORM method

Description

Calculate failure probability by FORM method and important sampling.

Usage

FORM(f, u.dep, choice.law, N.calls = 1e4, eps = 1e-7,
     Method = "HLRF", IS = FALSE, q = 0.5, copula = "unif")

Arguments

f

the failure fonction

u.dep

a vector, starting point to the research of the design point

choice.law

a list which contains the name of the densityof each input and their parameters

N.calls

Number of calls to f allowed

eps

stop criterion : distance of two points between two iterations

Method

Choice of the method to the research of the design point: "AR" for Abdo-Rackwitz and "HLRF" for Hasofer-Lindt-Rackwitz-Fiessler

IS

"TRUE" for using importance Sampling method (applied after FORM which gives the importance density). Default ="FALSE".

q

ratio of N.calls for the reserach of the design point by FORM. Default = 0.5. 1-q = the remaining ratio to use importance sampling.

copula

choice of the copula. Default = "unif" (uniform copula)

Value

• proba.def
  Failure probability
• indice.reliab
  reliability index
• compt.f
  Number of calls of f
• Design.Point
  Coordinates of the design point
• fact.imp
  Importance factors
• variance
  Standard error of the probability estimator (if IS = TRUE)
• Interval.conf
  Confidence interval of the estimator at 0.95 (if IS = TRUE)
• DOE
  List which contains the design of experiments

References

O. Ditlevsen and H.O. Madsen. Structural reliability methods, Wiley, 1996 M. Lemaire, A. Chateauneuf and J. Mitteau. Structural reliability, Wiley Online Library, 2009.

Examples

distribution = list()
 distribution[[1]] = list("gamma",c(2,1))
 distribution[[2]] = list("gamma",c(3,1))

 func <- function(X){
    X[1]/sum(X) - qbeta((1e-5),2,3)
 }

 res.list <- FORM(func,
                  u.dep = c(0,0.1),
                  choice.law = distribution,
                  N.calls = 1000,
                  eps = 1e-7,
                  Method = "HLRF",
                  IS = "TRUE",
                  q = 0.1,
                  copula = "unif")