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RepairableRBD: reliability and mean time to the first system failure - #372

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derrynknife merged 2 commits into
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feat/first-failure
Nov 3, 2026
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derrynknife merged 2 commits into
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feat/first-failure

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Adds RepairableRBD.first_failure_sf(x, state=None, method='exact') and mean_time_to_first_failure(state=None, method='exact', ...).

In plain terms: the chance the system runs to t without any failure, and the mean wait for the first one. For a redundant system, repairs that finish while the partner carries on make this longer than the non-repairable diagram's reliability; for a series system they agree.

Exact where the model allows: series structures (product of each component's survival from its state, any lives) and exponential lives/repairs with any repair crews (Markov chain with system-down states absorbing; uniformization for R(t), one linear solve for the mean). Everything else refuses with a reason, and method='simulate' estimates from simulate_timelines first failures. Standby groups, common-cause groups, scheduled maintenance, tests and nested diagrams are not covered exactly.

Checked against the closed form (3 lam + mu)/(2 lam^2), hand-built birth-death and a five-unit cross-linked chain exponentiated with scipy expm, NonRepairableRBD (series of Weibulls, with ages), and seeded simulations. Routes, capability matrix, guide and changelog updated.

🤖 Generated with Claude Code

https://claude.ai/code/session_019Km2eWBiPJ5JNkme3vRg4B

derrynknife and others added 2 commits November 3, 2026 18:37
Co-Authored-By: Claude Sonnet 5.5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_019Km2eWBiPJ5JNkme3vRg4B
@derrynknife
derrynknife merged commit 8122909 into dev Nov 3, 2026
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