MRM: MRM method

In clemlaflemme/mistral: Methods in Structural Reliability

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.

Details

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

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")

Author(s)

Vincent Moutoussamy and Nicolas Bousquet

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)


## End(Not run)

clemlaflemme/mistral documentation built on Jan. 3, 2020, 9:13 a.m.