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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.

License

MIT. See LICENSE.

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.