mistral (version 2.1.0)

mistral-package: Methods In Structural Reliability Analysis

Description

Provide tools for structural reliability analysis (failure probability, quantile).

Details

Package:	mistral	Type:
Package	Version:	2.1.0 Date:
2016-04-03	Package:	mistral

This package provides tools for structural reliability analysis:

• Calculate failure probability with FORM method and importance sampling,

• Calculate failure probability with crude Monte Carlo method,

• Calculate failure probability with Subset Simulation algorithm,

• Calculate failure probability with Monotonic Reliability Methods (MRM),

• Calculate failure probability with metamodel based algorithms : AKMCS, SMART and MetaIS,

• Calculate failure probability with a metamodel based Subset Simulation : S2MART,

• Wilks formula: Compute a quantile (or tolerance interval) with a given confidence level from a i.i.d. sample,

• Wilks formula: Compute the minimal sample size to estimate a quantile with a given confidence level,

• Calculate a quantile under monotonicity constraints.

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.

J. Morio and M. Balesdent. Estimation of rare event probabilities in complex aerospace and other systems, WP, 2016.

S.S. Wilks. Determination of Sample Sizes for Setting Tolerance Limits. Annals Mathematical Statistics, 12:91-96, 1941.

Examples

# NOT RUN {
########## FORM ###########

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

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

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

########### Wilks ##########

N <- WilksFormula(0.95,0.95,order=1)
print(N)

# }