User guide

The user guide is the how-to reference: every capability, the arguments it takes, what it returns, and its limits. Each page is self-contained and its examples run as written. To learn the ideas step by step, with worked examples and exercises, take the Learn course; for a compact summary of the theory, see Concepts; for every signature and docstring, see the API reference.

Page	What it covers
Building an RBD	Edges and node models, k-out-of-n nodes, junctions (a vote point that never fails), a component that appears in several places, nested RBDs, validation, path and cut sets, and the structural checks.
Fault trees	Static fault trees (OR, AND and VOTE gates, repeated events): the exact top event probability, minimal cut sets ranked by probability, importance measures, common-cause groups, the mean time to the top event, B-lives, hazard, parameter sensitivities and the uncertainty from fitted event models, and conversion to and from block diagrams.
Reliability of a system	sf/ff, density and hazard, conditional survival, per-node values, forcing nodes working or failed, lifetimes and the exact MTTF, inverting reliability to a time (BX life), and the uncertainty that uncertain component models give the system reliability.
Phased missions	Missions through phases (take-off, cruise, landing), each with its own duration and diagram over the same components: the exact mission reliability and the chance of failing in each phase, and their simulation; each component's importance over the mission, and the mission's cut sets.
Networks	Undirected networks whose links (and nodes) fail: the exact reliability of the connection between two terminals, its minimal paths and cuts, the importance measures, B-lives, parameter uncertainty and saving of a diagram, the mean time to disconnection, and their simulation.
Importance measures	Birnbaum, improvement potential, risk achievement and reduction worth, criticality, Fussell–Vesely, structural importance, and parameter sensitivity; on a repairable system in the long run or over time; differential and joint importance, the rate of change split by component, and Barlow–Proschan.
Sensitivities: the Greeks	The sensitivity measures as one family, named after the option Greeks (delta, the levers' deltas, the differential importance, gamma, theta, vega), what they share, and one pumping station run through every one.
Condition-based evaluation	Reliability, remaining life and importance given each component's current age, and covariate-dependent components (fixed operating conditions or a load schedule).
Redundancy models	Cold, warm and hot standby, repeated nodes, repeated standby, and load-sharing groups.
Common-cause failures	Beta-factor and Multiple Greek Letter groups, splitting a probability or a failure rate, in block diagrams, repairable systems (with staggered tests) and fault trees, and where they apply.
Repairable systems	Long-run availability, failure frequency, MUT/MDT/MTBF; the exact availability over time from new and over a mission, and the unavailability to its own precision; junctions; the simulated histories and their criticality measures; shared repair crews, with exact long-run values and importance and numerical values over time for exponential components; standby groups repaired one unit at a time; imperfect repair; nested repairable RBDs, and stepping a simulation by hand.
System capacity	How much a system can deliver: node capacities, components with several levels (derated, or degrading through stages over time), the exact distribution of the system's capacity at a time or in the long run, the probability of meeting a demand, the expected capacity, and the production availability.
Costs	The long-run cost rate in closed form, the simulated cost distribution, costs drawn from distributions, and the total cost of ownership, discounted to a present value, with the redundancy that minimises it, whole trains among it.
Maintaining a system	Scheduled preventive maintenance in a diagram and the intervals that meet a system target, replacement on condition at periodic inspections, opportunistic maintenance, and hidden failures found by periodic inspection (PFDavg for safety functions), with their intervals chosen.
Spares	How many spares each component uses over a horizon, for a system or a fleet, and the stock that meets a fill rate or a stock-out target when each spare used is reordered and arrives a lead time later; interchangeable components' spares pooled on one shelf.
Design and allocation	How many redundant copies to fit (redundancy allocation), apportioning a reliability target among components (reliability allocation), and an availability target, as MTTF and MTTR targets (availability allocation).
Maintenance policies	Age replacement, overhaul under minimal or imperfect repair, failure-count replacement, and the expected time to the n-th failure.
Demonstration testing	How many units, or how long a test, demonstrates a reliability or an MTBF at a confidence level, plans that keep both the producer's and the consumer's risk, what a finished test demonstrated, and the chance a design passes.
Timelines	Up/down histories: a unit's from an outage log or its durations, their measures (time up, failures and planned outages, first failure, outages), merges as a diagram's structure with the component that caused each change, a system's from its components' through its diagram, and a repairable system's simulated histories, kept whole.
Simulation precision and speed	Simulating until an estimate is precise enough, antithetic pairs, parallel runs, and comparing two designs with common random numbers.
Saving, reproducibility and performance	JSON round-trips, results as plain data (to_dict()), seeding, what is exact and what is simulated, and how the engine scales.

Conventions used throughout

Node models. RePyability consumes fitted models; fitting data is surpyval's job. A node model is anything that exposes sf(t) and ff(t): surpyval parametric distributions, FixedEventProbability, and the composite models in this package. Methods that simulate lifetimes also need the model's random(size).

Scalars and arrays. A scalar time returns a float; an array of times returns a numpy array. Per-node methods return a dict keyed by node name whose values follow the same rule.

import surpyval as surv
from repyability import NonRepairableRBD

rbd = NonRepairableRBD(
    [("s", "a"), ("a", "t")], {"a": surv.Weibull.from_params([100, 2])}
)
rbd.sf(50)          # -> 0.7788   a float
rbd.sf([25, 50])    # a numpy array: array([0.9394, 0.7788])

Forcing nodes. Most analysis methods accept working_nodes and broken_nodes: the named nodes are treated as perfectly reliable or as failed. An unknown node, the input or output node, or a node named in both raises ValueError rather than being ignored.

Path sets or cut sets. Exact system quantities accept method="p" (the default) or method="c": whether the engine computes the probability that the system works, or that it fails and returns the complement. Both are exact and give the same answer. (In is_system_working they choose whether the part of the diagram that is not series-parallel is checked through its minimal path sets or cut sets.)

Seeds. Every Monte-Carlo method takes a seed. surpyval samples from numpy's global random number generator, so a seed is applied to it for the duration of the call and the caller's generator state is restored afterwards. A RepairableRBD's simulations draw from random streams of their own (see Saving, reproducibility and performance).

Units. Times are in whatever unit your models use; RePyability never converts them.