Add is_analytically_solvable() to NonRepairableRBD#28
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Adds a check for whether an RBD's system reliability can be solved
analytically / with the BDD, or whether it requires simulation because
one or more nodes are simulation-based (standby arrangements).
- _node_is_analytic(): classifies a node model, recursing through
RepeatedNode wrappers and nested NonRepairableRBDs.
- get_non_analytic_nodes(): returns {node: model type} for the offending
simulation-based nodes (StandbyModel, RepeatedStandbyNode).
- is_analytically_solvable(): True iff there are no such nodes.
- Records the result in structure_check as "is_analytically_solvable"
and "non_analytic_nodes" at construction time.
Adds tests covering analytic fixtures, standby (non-analytic) fixtures,
repeated nodes/components, and the structure_check wiring.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
Replaces the `dd` Binary Decision Diagram dependency with a pure-Python
exact reliability engine and a direct structure-function evaluation.
- rbd.py: add probability_any_set_satisfied(), an exact Shannon
decomposition over the minimal path/cut sets with memoisation. It
returns the same result as the previous inclusion-exclusion but avoids
the 2^(#sets) blow-up by solving each shared sub-problem once.
- system_probability(): now uses the new engine. method="p" computes
reliability from path sets; method="c" computes unreliability from cut
sets. The approx=True path keeps the first-order rare-event cut-set
approximation, and method="p" + approx=True still raises.
- is_system_working(): re-implemented without a BDD. The system works
iff some minimal path set is fully up ("p") / every minimal cut set has
one component up ("c"). Path/cut sets are cached on first use for the
simulation hot loop.
- Drop compile_bdd() and the BDD bdd_to_string/bdd_to_file helpers from
RBD and RepairableRBD; RepairableRBD now inherits is_system_working.
- Remove dd from requirements.txt and the mypy override list.
Adds test_rbd_exact_probability.py: cross-checks the path-set and cut-set
methods against a brute-force enumeration on a bridge network, and checks
the new is_system_working truth tables. Existing sf()/availability tests
(both methods + approx) continue to pass.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
Ignore __pycache__, compiled files, and pytest/coverage/mypy caches so they are not reported as untracked. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
- minimal_cut_sets_from_path_sets(): computes the minimal cut sets as the
minimal transversals (hitting sets) of the minimal path sets using
Berge's algorithm. It builds the transversals incrementally one path set
at a time and prunes non-minimal candidates at each step, instead of
materialising the full Cartesian product of the path sets and filtering
once at the end. Works directly from the path sets, so it stays correct
for k-out-of-n structures. get_min_cut_sets() now delegates to it; the
now-unused itertools.product import is removed.
- Default the system reliability to the path-set method:
- RBD.system_probability default method "c" -> "p".
- NonRepairableRBD.sf default method is now resolved from None: path
sets by default (avoids deriving the cut sets), falling back to the
cut-set method when approx=True (the approximation only applies to cut
sets). Explicit method="p" with approx=True still raises.
Adds test_rbd_berge_cut_sets.py: cross-checks Berge against the previous
Cartesian-product implementation across every fixture (including the
k-out-of-n ones), checks hand-computed examples, verifies the cut sets are
minimal transversals, and checks the new default sf behaviour.
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
The approx flag was a first-order rare-event approximation that pre-dated the exact engine. It was never actually wired through sf() (only its error-check fired), and the exact path/cut-set computation is now cheap, so the option added API surface without benefit. - RBD.system_probability: drop the approx parameter and the first-order cut-set branch; both methods now always return the exact result. - NonRepairableRBD.sf: drop approx; method now defaults straight to "p" (no None sentinel needed) and the method="p"+approx ValueError is gone. - Remove the corresponding approx tests from test_rbd_sf.py and the approx-routing assertions from test_rbd_berge_cut_sets.py. The separate Fussell-Vesely approx option (_fussel_vesely) is unrelated and left untouched. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
Standby sf/ff were estimated from Monte-Carlo samples via a Kaplan-Meier fit: stochastic, a step function bounded by the sampled support, and the source of intermittent test failures. For cold standby the lifetime is the sum of the components' lifetimes, so its survival function is their convolution, which can be computed directly. - numerical_convolution.py: ConvolvedSurvival computes the survival function of a sum of independent lifetimes by numerically convolving the component densities (FFT) on a fine grid bounded robustly by doubling on sf, integrating to the CDF with trapezoidal quadrature and normalising away discretisation drift. sf()/ff()/mean() then read the precomputed grid -- fast, deterministic and accurate (~1e-3 vs closed forms). - StandbyModel: for k=1 (cold standby = sum) sf/ff now use the exact convolution instead of the KM fit; k>=2 (order-dependent) keeps the Monte-Carlo + KM approximation. - RepeatedStandbyNode: sf/ff use the convolution of `repeats` copies. random()/mean() are deliberately left unchanged (out of scope for this sf work). Note RepeatedStandbyNode.random/mean have a separate pre-existing bug (they sample the KM-of-the-sum and re-sum it, ~repeats x too large), which is why test_rbd_repeated_standby::test_mean expects 9 rather than 3 and remains the only flaky standby test. Adds test_rbd_numerical_convolution.py: checks the convolution against the Erlang (Gamma) and hypoexponential closed forms, array input, the single-model identity, and that StandbyModel(k=1)/RepeatedStandbyNode sf is exact and reproducible. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
Models imperfect switching (failure on demand) for cold standby. Each switch onto the next spare succeeds with a given probability, so the lifetime is a mixture of partial sums: run the primary; if its switch works, run the next component too; and so on. The survival function is the corresponding weighted mixture of the partial-sum convolutions. - ConvolvedSurvival: new switching_probability argument (a scalar applied to every switch, or a per-switch sequence of length n-1). It builds the partial-sum survival functions it already computes incrementally and returns their mixture; default 1.0 reduces exactly to the full convolution. Helpers switch_success_probs()/is_perfect_switching() and the mixture weights are exposed/computed for reuse. - StandbyModel: switching_probability argument for k=1 (passed to the convolution, and random() now also reflects switching via a per-switch Bernoulli). For k>=2 a non-perfect switching probability raises NotImplementedError rather than being silently ignored. - RepeatedStandbyNode: switching_probability argument applied to sf/ff (its random()/mean() still reflect perfect switching, as before). Adds test_rbd_switching_probability.py, verifying against closed forms: single-switch S(t)=e^-t(1+pt), zero-switching = primary only, perfect = full convolution, mean 1+p+p^2 for three components, a per-switch sequence, weight normalisation, the k>=2 NotImplementedError, and input validation. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
random() previously sampled from a Kaplan-Meier fit of the summed lifetime and then re-summed `repeats` of those draws, overcounting by a factor of ~repeats (e.g. a 3-fold standby of Exp(1) reported a mean of ~9 instead of 3). It was also the source of intermittent -inf failures. random() now sums `repeats` independent draws from the base model directly (respecting switching_probability via a per-switch Bernoulli), and mean() returns the exact value from the convolution (E[T] = integral of sf), so both are correct and deterministic. The Kaplan-Meier fit is dropped; the N and lower arguments are kept (unused) for backwards compatibility. Updates test_rbd_repeated_standby::test_mean to assert the correct mean (3, not the previous buggy 9). The standby tests are now deterministic (no more flakiness) and run in a fraction of the time. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
When every standby component is an Exponential with the same rate (and switching is perfect), the k-out-of-n cold standby lifetime is exactly Erlang(N-k+1, k*rate): while k units operate the failure rate is k*rate, and by memorylessness the inter-failure times are i.i.d. Exponential(k*rate). - StandbyModel now detects identical exponential units and uses that closed form (via scipy.stats.gamma) for any k -- deterministic and exact, replacing the Monte-Carlo + Kaplan-Meier fit for k>=2 and the convolution for k=1 in this case. Non-exponential or mixed-rate inputs fall back to the existing convolution (k=1) / Monte-Carlo (k>=2) paths. - mean() now returns the exact value from the analytic model when available (exponential closed form or convolution), only falling back to the Monte-Carlo estimate for the k>=2 general case. Adds test_rbd_exponential_standby.py: checks the closed form against scipy's gamma and surpyval's Gamma for k=1 and k=2, the k=N min-exponential limit, determinism, agreement (in mean) with the priority-queue simulation, and that mixed-rate inputs use the convolution path instead. Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M
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Adds a check for whether an RBD's system reliability can be solved
analytically / with the BDD, or whether it requires simulation because
one or more nodes are simulation-based (standby arrangements).
RepeatedNode wrappers and nested NonRepairableRBDs.
simulation-based nodes (StandbyModel, RepeatedStandbyNode).
and "non_analytic_nodes" at construction time.
Adds tests covering analytic fixtures, standby (non-analytic) fixtures,
repeated nodes/components, and the structure_check wiring.
Co-Authored-By: Claude Opus 4.8 noreply@anthropic.com
Claude-Session: https://claude.ai/code/session_01D3uxEk7qdLTcRhR8Avnk5M