Structured Random Variables for Reliability System Distributions

Extends the 'algebraic.dist' distribution algebra to random variables with internal structure: coherent reliability systems decomposed into components arranged by a structure function (series, parallel, k-out-of-n, bridge, and arbitrary topologies via minimal path sets). Every 'dist_structure' object is a 'dist', so the full distribution algebra (mean, vcov, sampler, surv, cdf) works automatically via default methods that compose component-level distributions through the topology. Adds structural queries: structure function evaluation, minimal path and cut sets, system signature, critical states, dual, Birnbaum structural importance, and system reliability. Topology shortcut constructors (series_dist, parallel_dist, kofn_dist, bridge_dist) produce ready-to-use dists from component dists and a chosen structure.

dist.structure

Structured random variables for reliability system distributions. dist.structure extends the algebraic.dist distribution algebra to random variables with internal structure: coherent reliability systems decomposed into components arranged by a structure function (series, parallel, k-out-of-n, bridge, consecutive-k, and arbitrary topologies via minimal path sets).

Every dist_structure object is a dist, so the full distribution algebra (mean, vcov, sampler, surv, cdf) works automatically via default methods that compose component-level distributions through the topology. dist.structure adds structural queries (phi, min_paths, min_cuts, system_signature, critical_states, dual, is_coherent), importance measures (Birnbaum structural, Birnbaum reliability, criticality, Vesely-Fussell), and compositional operations (substitute_component, compose_systems).

Installation

From r-universe:

install.packages("dist.structure",
  repos = c("https://queelius.r-universe.dev", "https://cran.r-project.org"))

From GitHub:

# install.packages("remotes")
remotes::install_github("queelius/dist.structure")

Quick tour

library(dist.structure)

# A 2-out-of-3 system of independent exponentials.
sys <- exp_kofn(k = 2, rates = c(1, 2, 3))

# Distribution queries (inherited from algebraic.dist).
algebraic.dist::surv(sys)(1)           # system survival at t = 1
algebraic.dist::sampler(sys)(10)       # 10 system-lifetime samples

# Topology queries.
phi(sys, state = c(1, 1, 0))           # system functions? -> 1
min_paths(sys)                         # minimal path sets
system_signature(sys)                  # Samaniego signature

# Importance.
structural_importance(sys, j = 1)      # fraction of pivotal states
birnbaum_importance(sys, j = 1, p = 0.8)  # dR/dp_j at p = 0.8
reliability(sys, p = 0.9)              # system reliability

# Composition.
sys2 <- substitute_component(sys, j = 2,
  new_component = algebraic.dist::weibull_dist(shape = 2, scale = 1))

See vignette("getting-started", package = "dist.structure") for a longer tour, and the other vignettes (coherent-systems, distribution-interface, importance-measures, composition, non-coherent) for deeper topics.

Ecosystem

dist.structure sits at the bottom of the reliability ecosystem. It depends only on algebraic.dist. Downstream packages implement the protocol on their own subclasses:

serieshaz registers dist.structure methods on dfr_dist_series so series systems built from arbitrary dynamic failure rate components get the protocol for free.
kofn provides maximum likelihood estimation for k-out-of-n systems, using dist.structure as its DGP and topology layer.
maskedcauses wraps its exponential-series API over dist.structure::exp_series.