reliability: reliability

In ShinsukeSakai0321/LimitState: Package supporting FORM approach

Description

This function executes reliability analysis by limit state function method. Returned object is GeneralTreat class which is inheritted from LSFM class.

Usage

reliability(g = "R-S", var = c("R", "S"), dist = c("normal", "normal"), muX = c(200, 100), sigmmaX = c(10, 20))

Arguments

g	character expression of limit state fuction
var	array of variables written in character type
dist	array of distribution type written in character type: one of "normal","lognormal","gumbel","weibull"
muX	array of mean value for variables
sigmmaX	array of sd. value for variables

Value

GetPOF()	returns POF value
GetAlpha()	returns Alpha vector
GetBeta()	returns reliability index
GetDP()	returns Design Points
GetPSF()	returns PSF vector

Author(s)

Shinsuke Sakai

See Also

Returned object is GeneralTreat class which is inheritted from LSFM class. As for public function of LSFM class, see LSFM class by help command.

Examples

#Example1
aa <- reliability()
aa$GetPOF()
aa$GetAlpha()
aa$GetBeta()
aa$GetDP()
aa$GetPSF()
# correct answer  3.872108e-06
#
# Example2
#"Probability, Reliability and Statistical Methods in
#  Engineering Design"
# Achintya Haldar  & Sankaran Mahadevan
#  P.218 Table 7.5, 7.6
g<-"As*fy*d*(1.0-eta*As*fy/b/d/fcd)-M"
var <- c("As","fy","fcd","b","d","eta","M")
muX <- c(1.56, 47.7, 3.5, 8.0, 13.2, 0.59, 326.25)
covX <- c(0.036, 0.15, 0.21, 0.045, 0.086, 0.05, 0.17)
sigmmaX <- muX*covX
dist <- c("normal", "normal", "normal", "normal" ,"normal" ,"normal" ,"normal" )
aa <-reliability(g=g,var=var,dist=dist,muX=muX,sigmmaX=sigmmaX)
a1 <- aa$GetBeta()
dist[7] <- "lognormal"
aa <-reliability(g=g,var=var,dist=dist,muX=muX,sigmmaX=sigmmaX)
a2 <- aa$GetBeta()
dist <- c("lognormal", "lognormal", "lognormal", "lognormal" ,"lognormal" ,"lognormal" ,"normal" )
aa <-reliability(g=g,var=var,dist=dist,muX=muX,sigmmaX=sigmmaX)
a3 <- aa$GetBeta()
dist <- c("lognormal", "lognormal", "lognormal", "lognormal" ,"lognormal" ,"lognormal" ,"lognormal" )
aa <-reliability(g=g,var=var,dist=dist,muX=muX,sigmmaX=sigmmaX)
a4 <- aa$GetBeta()
c(a1,a2,a3,a4)
#expected output
# 3.833028 3.761254 4.387684 4.090647
#Example3
# Checking lack of invariance
aa<-reliability()
bb<-reliability(g="1-R/S")
cc<-reliability(g="log(R)-log(S)")
aa$GetBeta()
bb$GetBeta()
cc$GetBeta()
##########################
#Example in text p.Basic2.30
aa<-reliability( muX = c(400, 300), sigmmaX = c(20, 30))
aa$GetBeta()
#correct answer:  2.773501
#Example in text p.Basic2.37
g<-"Sb*A-P"
var <- c("Sb","A","P")
muX <- c(400, 100*10*10, 3000e3)
sigmmaX <- c(20, 5*10*10, 300e3)
dist <- c("normal", "normal", "normal" )
aa <-reliability(g=g,var=var,dist=dist,muX=muX,sigmmaX=sigmmaX)
aa$GetBeta()
aa$GetAlpha()
aa$GetDP()
#Correct answer
#> aa$GetBeta()
#[1] 2.458772
#> aa$GetAlpha()
#[1]  0.4696243  0.4696243 -0.7476002
#> aa$GetDP()
#[1]     376.906    9422.650 3551453.579
############################
#Example in text p.Basic2.44
aa<-reliability( muX = c(400, 300), sigmmaX = c(20, 30))
aa$GetPSF()
#[1] 0.9230769 1.2307692
############################
#Example in text Basic3.12
dist <- c("lognormal", "normal" )
aa<-reliability(dist=dist, muX = c(40, 25), sigmmaX = c(4, 5))
aa$GetBeta()
aa$GetPOF()
#> aa$GetBeta()
#[1] 2.377765
#> aa$GetPOF()
#[1] 0.008708954

ShinsukeSakai0321/LimitState documentation built on Dec. 26, 2019, 11:31 a.m.