# MRM: MRM method In mistral: Methods in Structural Reliability Analysis

## Description

Estimate a failure probability by MRM method.

## Usage

 `1` ```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 â€˜inputDimensionâ€™ 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

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43``` ```## 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) ```

mistral documentation built on May 1, 2019, 10:17 p.m.