Sensitivity analysis using the pinching approach.

Function for conducting a sensitivity analysis using the pinching approach of Ferson and Tucker (2006).

Usage

sensi_pinching(Z0, Z0p, mode = "global", 
         threshold = NULL, level = NULL, disc=0.01)

Arguments

Z0

Output of the uncertainty propagation function PROPAG().

Z0p

Output of the pinching function pinching_fun().

mode

String to specify the mode to represent the epistemic uncertainty:

• If "proba": interval of exceedance probability given the threshold.

• If "quantile": interval of quantile given the level.

• If "global": global indicator of uncertainty corresponding to the area between the upper and lower CDFs.

threshold

Threshold value to compute the interval of exceedance probabilities.

level

Level value to compute the interval of quantiles.

disc

discretisation value to compute the global indicator

Value

A number between 0 and 100

References

Ferson, S., & Tucker, W. T. (2006). Sensitivity analysis using probability bounding. Reliability Engineering & System Safety, 91(10), 1435-1442.

See also

pinching_fun

Examples

if (FALSE) {
#################################################
#### EXAMPLE 1 of Dubois & Guyonnet (2011)
#### Probability and Possibility distributions
#################################################

#### Model function
FUN = function(X){
  UER = X[1]
  EF = X[2]
  I = X[3]
  C = X[4]
  ED = X[5]
  return(UER*I*C*EF*ED/(70*70*365))
}

ninput = 5 #Number of input parameters
input = vector(mode="list", length=ninput) # Initialisation

input[[1]] = create_input(
    name = "UER",
    type = "possi",
    distr = "triangle",
    param = c(2.e-2, 5.7e-2, 1.e-1),
    monoton = "incr"
    )
input[[2]] = create_input(
    name = "EF",
    type = "possi",
    distr = "triangle",
    param = c(200,250,350),
    monoton = "incr"
    )
input[[3]] = create_input(
    name = "I",
    type = "possi",
    distr = "triangle",
    param = c(1,1.5,2.5),
    monoton = "incr"
    )
input[[4]] = create_input(
    name = "C",
    type = "proba",
    distr = "triangle",
    param = c(5e-3,20e-3,10e-3)
    )
input[[5]] = create_input(
    name = "ED",
    type = "proba",
    distr = "triangle",
    param = c(10,50,30)
    )

####CREATION OF THE DISTRIBUTIONS ASSOCIATED TO THE PARAMETERS
input = create_distr(input)

####VISU INPUT
plot_input(input)

#################################################
#### PROPAGATION

#OPTIMZATION CHOICES
choice_opt=NULL #no optimization needed
param_opt=NULL

#PROPAGATION RUN
Z0_IRS = propag(N = 250, input, FUN, choice_opt, param_opt, mode = "IRS")

#################################################
#### PINCHING
Z0p = pinching_fun(
  which=1,##first input variable
  value = 5.7e-2, ##pinched at the scalar value of 5.7e-2
  N = 250,
  input,
  FUN,
  choice_opt,
  param_opt,
  mode="IRS"
  )

# VISU - PROPAGATION
plot_cdf(Z0_IRS, xlab = "Z", ylab = "CDF", main = "EX PINCHING", lwd=1.5)
plot_cdf(Z0p, color1 = 3, color2 = 4, new = FALSE, lwd = 1.5)

# sensitivity measure
sensi.global = sensi_pinching(Z0_IRS, Z0p)
print(paste("global sensitivity measure: ",sensi.global,sep=""))

}