dist.structure-package: dist.structure: Structured Random Variables for Reliability...

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

dist.structure: Structured Random Variables for Reliability System Distributions

Description

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, arbitrary topologies). Every dist_structure object is also a dist, so the full distribution algebra works automatically via default methods that compose component-level distributions through the topology.

Two algebras, one hierarchy

algebraic.dist provides the base algebra of random variables: density, surv, hazard, sampler, mean, vcov, expectation, and arithmetic on RVs (transformations).

dist.structure extends it with structure-preserving operations for reliability systems: component-wise decomposition, structure function evaluation, path and cut sets, system signature, critical states, dual structures, and Birnbaum importance measures. Because every dist_structure is a dist, the base algebra inherits automatically.

Primitives implementors provide

• ncomponents(): number of components m

• component(): return the j-th component as a dist

• One of phi() or min_paths(): the other defaults automatically

Topology queries (default methods on dist_structure)

phi(), min_paths(), min_cuts(), critical_states(), system_signature(), system_lifetime(), system_censoring(), dual(), is_coherent(), structural_importance(), reliability()

Distribution queries (default methods via component composition)

algebraic.dist::surv(), algebraic.dist::cdf(), algebraic.dist::sampler(). Further base dist methods (mean, vcov, expectation) inherit from univariate_dist via numerical integration of surv. Implementors override any default for speed.

Reference implementations

• coherent_dist(): general coherent system given minimal path sets + components

• Topology shortcuts: series_dist(), parallel_dist(), kofn_dist(), bridge_dist(), consecutive_k_dist()

• IID convenience: min_iid(), max_iid(), order_statistic()

• Coercions: as_dist_structure()

Closed-form specializations

Fast analytical paths for common (component family, topology) pairs. Override the generic defaults for speed without changing semantics:

• Series: exp_series(), wei_series(), wei_homogeneous_series(), gamma_series(), lognormal_series()

• Parallel: exp_parallel()

• k-out-of-n: exp_kofn(), wei_kofn()

Importance measures

Both topology-only and reliability-aware:

• structural_importance(): Birnbaum's structural measure (topology only)

• birnbaum_importance(): Birnbaum's reliability measure

• criticality_importance(): criticality importance

• vesely_fussell_importance(): Vesely-Fussell importance

Compositional operations

Build new systems from existing ones while preserving the protocol:

• substitute_component(): replace component j with a sub-system

• compose_systems(): compose two systems (cartesian product of paths)

Non-coherent systems

cold_standby_dist() models a cold-standby spare arrangement (system lifetime is the sum of component lifetimes). It is deliberately not a dist_structure (no static structure function), but it shares the ncomponents()/component() generics so user code can iterate uniformly.

Author(s)

Maintainer: Alexander Towell [e-mail] (ORCID)

See Also

Useful links:

• https://github.com/queelius/dist.structure

• Report bugs at https://github.com/queelius/dist.structure/issues

dist.structure documentation built on May 13, 2026, 1:07 a.m.