ReliaStats

interpret_weibull_shape

Read-onlyIdempotent

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.

Input Schema

TableJSON Schema

Name	Required	Description	Default
`eta`	No	Optional Weibull characteristic-life parameter η, in the same time units you care about (e.g. hours). When provided, the response includes MTTF + B-life numbers.
`beta`	Yes	Weibull shape parameter β (dimensionless). Typical reliability range 0.3 – 8.0.

TDQS

A4.3/5.0

Behavior4/5

Does the description disclose side effects, auth requirements, rate limits, or destructive behavior?

Annotations already declare readOnlyHint=true, idempotentHint=true, and destructiveHint=false. The description adds valuable context: 'Pure-math + lookup, no engine call, fully deterministic' and includes an anti-fabrication instruction with exact closed-form formulas, going beyond the annotations to clarify deterministic behavior and prevent hallucination.

Agents need to know what a tool does to the world before calling it. Descriptions should go beyond structured annotations to explain consequences.

Conciseness5/5

Is the description appropriately sized, front-loaded, and free of redundancy?

The description is dense but no more than needed: four sentences pack purpose, output elements, usage trigger, and anti-fabrication guidance. It is front-loaded with the core action and avoids redundant phrasing.

Shorter descriptions cost fewer tokens and are easier for agents to parse. Every sentence should earn its place.

Completeness5/5

Given the tool's complexity, does the description cover enough for an agent to succeed on first attempt?

With no output schema, the description fully enumerates what the tool returns (regime, action, MTTF, B-life) and even provides the exact formulas for MTTF and B-life. Combined with rich parameter descriptions and clear annotations, the description gives an agent everything needed to invoke the tool correctly and interpret its result.

Complex tools with many parameters or behaviors need more documentation. Simple tools need less. This dimension scales expectations accordingly.

Parameters3/5

Does the description clarify parameter syntax, constraints, interactions, or defaults beyond what the schema provides?

Schema description coverage is 100%; both beta and eta have detailed descriptions already. The tool description adds interpretive context for beta (bathtub regimes) and ties eta to MTTF/B-life outputs, but these are are return semantics rather than parameter syntax or format details. Baseline 3 is appropriate given the schema covers the mechanics.

Input schemas describe structure but not intent. Descriptions should explain non-obvious parameter relationships and valid value ranges.

Purpose5/5

Does the description clearly state what the tool does and how it differs from similar tools?

The description opens with a specific verb+resource: 'Given a Weibull shape parameter β ... return a plain-language interpretation' and enumerates the exact outputs (bathtub-curve regime, suggested action, MTTF/B-life). It clearly differentiates from siblings by focusing on interpreting β into actionable guidance, and explicitly states it is a pure-math lookup with no engine call.

Agents choose between tools based on descriptions. A clear purpose with a specific verb and resource helps agents select the right tool.

Usage Guidelines4/5

Does the description explain when to use this tool, when not to, or what alternatives exist?

The description provides an explicit usage trigger: 'Use when a user reports a fitted β and wants to know what to DO with it.' It establishes clear context but does not name alternative tools or state when not to use it, so it stops short of a full when/when-not/alternatives treatment.

Agents often have multiple tools that could apply. Explicit usage guidance like "use X instead of Y when Z" prevents misuse.

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TDQS

A4.2/5.0

Disambiguation3/5

Several tools overlap in purpose, particularly the explain_* family: explain_distributions_for_reliability and recommend_distribution both address distribution selection, and explain_distributions also covers Weibull β interpretation, overlapping with interpret_weibull_shape. However, descriptions are detailed enough that careful reading usually disambiguates, so the confusion is moderate rather than severe.

Naming Consistency4/5

Most tools follow a clear verb_noun pattern (compute_, describe_, explain_, interpret_, list_, recommend_), making the naming predictable. Two exceptions, 'system_reliability' and 'weibull_summary', are noun phrases without a verb, which is a minor deviation from the pattern but not disruptive.

Tool Count5/5

With 11 tools, the server is well within the ideal 3–15 range and each tool serves a distinct purpose, from educational explainers to closed-form calculation utilities. The count feels well-scoped for a reliability statistics knowledge and reference server.

Completeness4/5

The tool surface covers fundamentals, distribution guidance, Weibull calculations, availability, system reliability, and paired-model documentation, giving broad coverage of the domain. It intentionally defers fitting to an external sandbox, so the main minor gap is the lack of direct data-fitting or confidence-interval computation tools, but these can be worked around.

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