RePyability

Reliability engineering tools, open source, for students through to practising professionals.

RePyability builds and analyses systems as reliability block diagrams (RBDs), taking already-fitted lifetime models (from surpyval or anything exposing sf/ff) as its components:

• Fault trees: static fault trees (OR, AND and VOTE gates, repeated events) evaluated exactly, with common-cause groups, cut sets, importance measures, the mean time to the top event, B-lives and hazard, parameter sensitivities, uncertainty from fitted event models, and conversion to and from block diagrams.
• Reliability: exact system reliability, hazard and conditional survival; the exact MTTF (or simulated, with confidence intervals); BX life; uncertainty intervals on the reliability, MTTF, BX life and time to a reliability from uncertain (fitted) component models.
• Networks: undirected networks whose links fail: the exact reliability of the connection between two terminals, by a decision diagram that keeps meshed networks fast.
• Phased missions: missions through phases (take-off, cruise, landing), each with its own diagram over the same components: the exact mission reliability and the chance of failing in each phase.
• Testing: demonstration test plans (the units, or the test time, that demonstrate a reliability or an MTBF), plans that keep both the producer's and the consumer's risk, what a test demonstrated, and the chance a design passes.
• Importance: Birnbaum, improvement potential, RAW, RRW, criticality, Fussell–Vesely, structural importance and parameter sensitivity, on repairable systems in the long run or over time.
• Sensitivity, the Greeks: how far the system moves with each component (delta) and with each lever, a life, a repair, the maintenance or a crew; the shares of a change, which add up (differential importance); whether two improvements are complements or substitutes (gamma); which component is moving the availability now, and which caused the failures (theta, Barlow–Proschan); and whose parameter uncertainty widens the answer (vega).
• Live state: reliability, remaining life and importance given each component's current age, and covariate-dependent components.
• Redundancy and dependence: cold, warm and hot standby; repeated nodes; load sharing; junctions (a vote point that never fails); beta-factor and MGL common-cause groups, splitting a probability or a failure rate, in block diagrams, repairable systems and fault trees.
• Repairable systems: exact long-run availability, failure frequency and MUT/MDT/MTBF; exact availability over time and over a mission, and the unavailability to its own precision (a PFD of 1e-17); simulated histories with criticality measures; shared repair crews, exact for exponential components in the long run and numerical over time, with their importance; repairable standby groups (a duty unit and its spares, repaired one at a time); imperfect repair (Kijima's virtual age), with replacement at the N-th failure; and uncertainty intervals on the availability and the cost rate from uncertain (fitted) models of the lives, repairs and maintenance.
• Capacity: how much a system delivers, from its components' capacities (with several levels, or degrading through stages): the exact distribution of its capacity at a time or in the long run, the probability of meeting a demand, and the production availability.
• 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 for a replenishment lead time, with interchangeable components' spares pooled on one shelf.
• Timelines: up/down histories, from outage logs or simulated, with their measures (time up, failures and who caused them, first failure); merged as a diagram's structure, so a system's history follows from its components', with the component behind each of its outages.
• Simulation: seeded Monte-Carlo run to a tolerance, antithetic pairs, control variates from the system's exact twin, parallel runs, runs split across machines and merged, or sharded through any executor (Ray, Dask, a batch system), comparisons of designs with common random numbers, and small failure probabilities by rare-event simulation (subset simulation, cross-entropy importance sampling); repairable systems simulated compiled, with numba installed.
• Cost, design and maintenance: exact and simulated running costs, including scheduled (age or block) preventive replacement at system level, replacement on condition at periodic inspections and opportunistic maintenance of grouped components at each other's stops, with its intervals chosen for a cost or availability target, hidden failures found by periodic inspection, with the test intervals chosen for a PFDavg target, the total cost of ownership, discounted to a present value from new or in the long run, optimal redundancy allocation (for the lowest total cost of a repairable system, too, with whole trains given copies together), reliability allocation by the classic named methods (equal and ARINC-style apportionment, minimum effort, cost-based), availability allocation to MTTF and MTTR targets, and age-replacement and overhaul policies.
• Saving: diagrams to and from JSON, seeded results that repeat, and every result as plain data (to_dict(), ready for json.dumps).

import surpyval as surv
from repyability import NonRepairableRBD

rbd = NonRepairableRBD(
    [("s", "pump1"), ("s", "pump2"), ("pump1", "valve"), ("pump2", "valve"), ("valve", "t")],
    {
        "pump1": surv.Weibull.from_params([100, 2]),
        "pump2": surv.Weibull.from_params([100, 2]),
        "valve": surv.Weibull.from_params([200, 1.5]),
    },
)
rbd.sf(50)                     # 0.839: system reliability at t = 50
rbd.birnbaum_importance(50)    # which component matters most

New to reliability engineering? The documentation includes Learn, a short course that teaches system reliability from a single part's lifetime to designing and maintaining whole systems, working every idea out by hand and then with RePyability, with exercises and worked answers.

Install

RePyability needs Python 3.11 or later. Install it from PyPI:

pip install repyability

Repairable systems simulate about ten times as fast with the optional compiled engine, which needs numba (available for 64-bit Linux, macOS on Apple silicon and Windows):

pip install "repyability[fast]"

What each model can do

The analyses each model type has, and how each family of them is worked out for each kind of node or component: the gaps are where a cell says — or ✗. The tables are made from the code (python -m repyability.tests.capabilities writes them, and a test checks they are current).

Which analyses each model type has (the method; — where it has none):

How each family of analyses is worked out on a diagram with each kind of node or component: E exact, N numerical (to a stated accuracy), S simulated, ✗ refused as not worked out (naming the methods, or counting them, where only some are), – where the diagram has nothing the analysis works on. Made from analysis_routes() on the test catalogue's diagrams.

When is a simulation needed?

RePyability computes exactly by default: by closed forms, or by deterministic numerical methods (quadrature, convolution, renewal equations) that give the same answer every run, to a small stated error. It simulates only when

• the answer is itself random: sampled lifetimes or histories, or the spread of an outcome over a window (a cost's percentiles, how many failures);
• components depend on each other in a way no exact method solves in general; or
• an exact method could exist but has not been written yet.

Exact or numerical, in any architecture (series, parallel, k-out-of-n, bridges and other meshed diagrams, components in several places, nested diagrams):

• components: surpyval lifetime distributions, degradation processes (Wiener and gamma, as the time to their threshold) and fixed probabilities (a diagram refuses a non-parametric fit, such as Kaplan–Meier: fit a parametric distribution in surpyval); repeated nodes; cold standby with one or two units operating (any units) or more (identical units); warm standby with one unit operating, and hot standby (any units); load sharing of identical units; common-cause groups, for the system's reliability, importance, sensitivity and redundancy allocation (and, splitting the failure rate, its MTTF);
• non-repairable questions: reliability, hazard, MTTF, BX life and importance measures at any time, also given each component's current age; the distribution of the system's capacity;
• repairable questions, for independent components repaired when they fail, replaced on age or block schedules or on condition at inspections, or tested for hidden failures (any life, the tests and repairs instant or taking time, the tests finding every failure or missing some): the long-run availability, failure frequency, MUT/MDT/MTBF and cost rate; the availability over time and over a mission, and the expected failures, outages, downtime and cost over a window, from new or from the components' current states (their ages, the repairs going on, where they are in their calendars, or the long run); the capacity distribution in the long run and over time, with the production availability of a window; and the spares used over a horizon, and the stock to hold for a lead time (under block replacement, with repairs and block replacements in no time). Common-cause groups of members with exponential lives, tested or repaired, take nothing away: the long-run values, importance and allocations stay exact, and the values over time from new numerical.

Simulated, or refused with the simulation to run instead:

Where a system's expected values over a window are exact, availability() and cost() give them by default, with no error, and the simulations give their spread. Where a system needs simulating for a few of its nodes (a standby group of other lives, a nested RBD sharing a crew, a unit repaired imperfectly), their mean intervals by default take each simulation's expected values given those nodes' histories, every other node exact given their states: a fraction of the error of the simulations' own. conditional=True simulates only those nodes, for the same means in less time.

For your own diagram, analysis_routes() says how each analysis will be computed (exact, numerical, simulated or refused) and why, without running anything; a refusal's message names the simulation to run instead. The guide lists every method's route.

Documentation

The full documentation — tutorial, user guide, concepts and API reference — is hosted at derrynknife.github.io/RePyability.

It is built with MkDocs from the sources in docs/ and mkdocs.yml, and published to GitHub Pages on every push to master. To build and serve it locally:

pip install -e .[docs]
mkdocs serve            # then open http://127.0.0.1:8000

The source lives in docs/ and mkdocs.yml; start with docs/index.md.

Roadmap

Where RePyability is going, beyond the issue tracker: ROADMAP.md holds the larger ideas and their designs (first among them a net present value simulator for maintenance plans, kept current as the plant changes), and stories/ the questions users and agents should be able to answer, with how we will know they are answered.

Related

Reliafy is a hosted, browser-based app built on RePyability and SurPyval, for building reliability block diagrams and analysing their reliability and availability without writing code.

Contributing

See CONTRIBUTING.md: setting up, the checks a change needs (scripts/check.sh), and the parts of the package that must agree with each other.