ReliaStats

Given MTBF and MTTR (same time unit), return steady-state availability A = MTBF / (MTBF + MTTR). One-line closed-form, but worth a dedicated tool so LLMs don't fumble the identity (the most common mistake is conflating MTBF with MTTF and silently inflating availability by the MTTR). Use whenever a user supplies an MTBF/MTTR pair and asks for availability. ANTI-FABRICATION: exact closed-form. Quote verbatim.

Given a Weibull shape parameter β (and optionally the characteristic-life parameter η), return a plain-language interpretation: which bathtub-curve regime β implies (infant mortality / random / wearout), what action that suggests (process-of-care / steady-state monitoring / maintenance scheduling), and — if η provided — closed-form MTTF and B-life numbers from the Weibull formulas. Pure-math + lookup, no engine call, fully deterministic. Use when a user reports a fitted β and wants to know what to DO with it. ANTI-FABRICATION: MTTF and B-life are exact closed-form values from the two-parameter Weibull (η · Γ(1+1/β) and η · (-ln(1-p))^(1/β)). Quote them verbatim.

Given a free-text symptom description (e.g. 'manufacturing burn-in', 'bearing wearout under variable load', 'cosmic-ray bit flips'), return an ordered shortlist of distribution candidates with a one-line rationale per recommendation. Keyword-matched against a curated dictionary; ALWAYS treat output as a starting point for fitting work, not a fit. The actual fitting happens in the ReliaStats sandbox (protected/app.html). ANTI-FABRICATION: rationales are written ChiAha content; the algorithm is a deterministic substring match. Quote verbatim.

Given per-component reliabilities and a structure ('series' or 'parallel'), return the system reliability. Series = product (all must work). Parallel = 1 − product(1−Rᵢ) (at least one works). Useful for back-of-envelope RBD calcs before reaching for full RBD tooling. For mixed-structure systems (series with parallel sub-blocks), call this tool repeatedly on the sub-blocks. ANTI-FABRICATION: exact closed-form. Quote verbatim.

Given Weibull two-parameter (β, η), return all the closed-form summary statistics: MTTF (η·Γ(1+1/β)), B10 / B50 / B90 life, characteristic life (just η, surfaced explicitly), and — if evaluateAtT supplied — R(t), F(t), and hazard h(t) at that time. Pure-math, fully deterministic. Use when the user has a fit and wants the numbers downstream tools normally compute (don't recompute these from training-data recall — call this tool). ANTI-FABRICATION: every number is an exact closed-form value. Quote verbatim.

Return the full worked-example doc for the bottling-line paired model — topology (5 machines: Filler/Capper/Labeler/Case Packer/Palletizer, 100 bottles/min, Weibull(30,1) TTF + Weibull(5,1) downtime at the Constraint-Level rollup), the two tracks (CT rollup vs LEDS-Level drill-down to 36 named failure modes), the 4 build sequences (BS1 → BS4), the file-shape mapping between ReliaSim outputs and ReliaStats modes, and a worked cross-MCP tool chain. Optional 'section' parameter narrows to one H2 section. ANTI-FABRICATION: content is sourced from docs/paired-model-bottling-line.md; every claim references the .aidos files or ChapterRegistry.fs in reliasim-site.

Return a textbook-tier explainer of advanced reliability patterns: censored data (right/left/interval — the rule not the exception), Maximum Likelihood Estimation, Goodness-of-Fit tests (Anderson-Darling favored over KS for tail-sensitive reliability work), the Confidence-Interval vs Prediction-Interval distinction that backs the Interrupt Validation scatter, accelerated life testing (Arrhenius / inverse power law / Coffin-Manson), and Bayesian reliability. No inputs. ANTI-FABRICATION: text is sourced from docs/reliability-theory.md.

Return a textbook-tier distribution zoology for reliability work: why Weibull is the default, the shape-parameter β table mapping β-ranges to physical failure modes (β<1 infant mortality, β=1 random, β>1 wearout), when to reach for Exponential / Lognormal / Normal / Gamma, and practitioner heuristics for picking a distribution. No inputs. Use when a user asks 'which distribution should I fit' / 'what does Weibull β mean' / 'when to use Lognormal'. ANTI-FABRICATION: text is sourced from docs/reliability-theory.md. The β-as-failure-mode interpretation is ChiAha's practitioner framing — quote verbatim; do not paraphrase.

Return the specific explainer for the ReliaStats Interrupt Validation scatter chart's red y=x / blue 95% Prediction Interval / teal 99% Confidence Interval reference lines. Use when a user asks 'what do the bands mean' / 'why is my point outside the blue line' / 'how do I read the validation scatter'. The bands are FIXED plotting conventions — they are NOT recomputed from the loaded data; this is anti-fab by design. Text sourced from docs/reliability-theory.md (the 'Confidence intervals vs prediction intervals' sub-section of Advanced Reliability Patterns).

Return a textbook-tier explainer of reliability fundamentals: the four reliability functions R(t)/F(t)/f(t)/h(t), MTBF vs MTTF vs MTTR, the availability identity A = MTBF/(MTBF+MTTR), the bathtub curve, and series/parallel system reliability. No inputs. Use when a user asks 'what is reliability theory' / 'explain MTBF' / 'how does availability work' / 'what's a hazard rate'. ANTI-FABRICATION: text is sourced from docs/reliability-theory.md (the canonical ChiAha reliability primer). Quote sections verbatim; do not paraphrase reliability theory from training-data recall.

Return the catalog of paired models — concrete real-world systems that live in two ChiAha sandboxes simultaneously, one for dynamics (DES via ReliaSim) and one for statistics (distribution fitting + validation via ReliaStats). Today: a single paired model — the bottling line. Returns canonical model IDs + cross-MCP routing metadata (which ReliaSim chapter, which ReliaSim MCP tools, which ReliaStats mode consumes which file shape). Use when a user asks about cross-MCP workflows, paired sandboxes, or the bottling-line example. ANTI-FABRICATION: this is a soft-reference catalog — to actually run a simulation, the LLM client calls ReliaSim's MCP tools directly.