mistral (version 2.1.0)

MRM: MRM method

Description

Estimate a failure probability by MRM method.

Usage

MRM(f, inputDimension, inputDistribution, dir.monot, N.calls, Method, silent = FALSE)

Arguments

f

a failure fonction

inputDimension

dimension of the inputs

inputDistribution

a list of length ‘inputDimension’ which contains the name of the input distribution and their parameters. For the input "i", inputDistribution[[i]] = list("name_law",c(parameters1,..., parametersN))

dir.monot

vector of size inputDimension which represents the monotonicity of the failure function. dir.monot[i] = -1 (resp. 1) if the failure function f is decreasing (resp. increasing) according with direction i.

N.calls

Number of calls to f allowed

Method

there is two methods available. "MC" is an adapation of the Monte Carlo method under constraints of monotony. "MRM" is based on a sequential sampling.

silent

if silent = TRUE, print curent number of call to f. Default: FALSE.

Value

Um

Exact lower bounds of the failure probability

UM

Exact upper bounds of the failure probability

MLE

Maximum likelihood estimator of the failure probability

IC.inf

Lower bound of the confidence interval of the failure probability based on MLE

IC.sup

Upper bound of the confidence interval of the failure probability based on MLE

CV.MLE

Coefficient of variation of the MLE

X

design of experiments

Y

value of f on X

N.tot

Total number of simulation (only for "MC_monotone")

Details

These methods compute the probability that the output of the failure function is negative

References

Bousquet, N. (2012) Accelerated monte carlo estimation of exceedance probabilities under monotonicity constraints. Annales de la Faculte des Sciences de Toulouse. XXI(3), 557-592.

Examples

# NOT RUN {
  inputDistribution <- list()
  inputDistribution[[1]] <- list("norm",c(4,1))
  inputDistribution[[2]] <- list("norm",c(0,1))
  inputDistribution[[3]] <- list("norm",c(-1,3))

  inputDimension <- length(inputDistribution)

  p <- 1e-5

  threshold <- qnorm(p, 3, sqrt(11))

  f <- function(Input){
    sum(Input) - threshold
  }

  dir.monot <- c(1, 1, 1)

  N.calls <- 300
 
  res.MRM <- MRM(f, inputDimension, inputDistribution,
                  dir.monot, N.calls, Method = "MRM", silent = FALSE)

  N <- 1:dim(res.MRM[[1]])[1]
  
  plot(N, res.MRM[[1]][, 1],
        col = "black", lwd=2, type='l', ylim=c(0, 50*p),
        xlab="Number of runs to the failure function",
        ylab="")
  lines(N, res.MRM[[1]][, 2], col = "black", lwd = 2)
  lines(N, res.MRM[[1]][, 3], col = "red", lwd = 2)
  lines(N, res.MRM[[1]][, 7], col = "blue", lwd = 2, lty = 2)
  lines(N, rep(p, length(N)), lwd= 2, col= "orange", lty=3 )
  legend("topright",
          c("Exact Bounds", "MLE","p.hat", "p"), 
          col = c("black", "red", "blue", "orange"),
          text.col = c("black", "red", "blue", "orange"),
          lty = c(1, 1, 2, 3),
          merge = TRUE)

# }
# NOT RUN {
# }