inst/doc/importance-measures.R

In dist.structure: Structured Random Variables for Reliability System Distributions

## ----include = FALSE----------------------------------------------------------
knitr::opts_chunk$set(collapse = TRUE, comment = "#>")

## ----setup--------------------------------------------------------------------
library(dist.structure)
library(algebraic.dist)

## -----------------------------------------------------------------------------
sys <- bridge_dist(replicate(5, exponential(1), simplify = FALSE))
min_paths(sys)
min_cuts(sys)

## -----------------------------------------------------------------------------
sapply(1:5, function(j) structural_importance(sys, j))

## -----------------------------------------------------------------------------
p <- 0.9
sapply(1:5, function(j) birnbaum_importance(sys, j, p))

## -----------------------------------------------------------------------------
t_vals <- c(0.1, 0.5, 1, 2)
sapply(t_vals, function(t) {
  sapply(1:5, function(j) criticality_importance(sys, j, t))
})

## -----------------------------------------------------------------------------
t0 <- 1
sapply(1:5, function(j) vesely_fussell_importance(sys, j, t0))

## -----------------------------------------------------------------------------
# Build a comparison table at p = 0.9 and t s.t. S(t) = 0.9 for all components.
# For iid Exp(1), S(t) = 0.9 -> t = -log(0.9)
t_star <- -log(0.9)

tab <- data.frame(
  j = 1:5,
  structural = sapply(1:5, function(j) structural_importance(sys, j)),
  birnbaum = sapply(1:5, function(j) birnbaum_importance(sys, j, 0.9)),
  criticality = sapply(1:5, function(j) criticality_importance(sys, j, t_star)),
  vesely_fussell = sapply(1:5, function(j) vesely_fussell_importance(sys, j, t_star))
)
tab

## -----------------------------------------------------------------------------
# Series: Birnbaum importance of j equals product of the OTHER p's.
series3 <- series_dist(replicate(3, exponential(1), simplify = FALSE))
p_vec <- c(0.9, 0.8, 0.7)
birnbaum_importance(series3, j = 1, p = p_vec)
prod(p_vec[-1])

## -----------------------------------------------------------------------------
# Parallel: Birnbaum importance of j equals product of the OTHER (1 - p_i).
parallel3 <- parallel_dist(replicate(3, exponential(1), simplify = FALSE))
birnbaum_importance(parallel3, j = 1, p = p_vec)
prod(1 - p_vec[-1])

## -----------------------------------------------------------------------------
# Series: Vesely-Fussell equals F_j / F_sys at time t, since each
# component forms its own min cut.
t0 <- 1
F_j_1 <- 1 - exp(-t0)
F_sys <- 1 - exp(-3 * t0)   # Exp(sum(rates) = 3)
vesely_fussell_importance(series3, j = 1, t = t0)
F_j_1 / F_sys