---
title: "ISA 530 Audit Sampling + MUS Calculator"
method: POST
path: "/v1/tools/compute_isa530_audit_sampling_mus"
tags: ["audit_sampling", "monetary_unit_sampling", "mus", "benford_screen", "misstatement_projection", "isa530", "mcp:compute_isa530_audit_sampling_mus"]
---

# ISA 530 Audit Sampling + MUS Calculator

`POST /v1/tools/compute_isa530_audit_sampling_mus`

## Request

- Base URL: `https://ainumbers.co`
- URL: `https://ainumbers.co/v1/tools/compute_isa530_audit_sampling_mus`
- Auth: none declared

Deterministic audit-sampling arithmetic in three caller-declared functions dispatched on method. monetary_unit_sampling sizes a MUS engagement: n = ceil(book_value * confidence_factor / (performance_materiality - expected_misstatement)) and sampling interval = round(book_value / n), failing closed whenever expected_misstatement >= performance_materiality. misstatement_projection applies the tainting method to caller-supplied sampled items (taint = (book - audited) / book, projected misstatement = sum of taint * interval) and adds the basic-precision figure confidence_factor * interval. benford_screen compares the observed first-significant-digit distribution of caller-supplied positive amounts against the Benford expected proportions with a chi-square deviation flag at the 5% level (8 degrees of freedom, critical value 15.507). The method's source standard is ISA 530 (iaasb.org): this node computes the arithmetic of the method and never certifies compliance with any standard, never opines on audit sufficiency, and never selects sample items. No randomness of any kind: any selection start point a caller uses is a caller-declared input, never generated here.

**Tool URL:** https://ainumbers.co/chaingraph/art-693-isa530-audit-sampling-mus.html
**AP2/Policy Mandate export:** yes

## Request body

- object
  - `method` 'monetary_unit_sampling' | 'misstatement_projection' | 'benford_screen', required
  - `book_value` number
  - `performance_materiality` number
  - `expected_misstatement` number
  - `confidence_factor` number
  - `sampling_interval` integer
  - `sampled_items` unknown[]
    - unknown
  - `amounts` unknown[]
    - unknown

## Response `200`

Successful tool execution result

- object
  - `sample_size` integer, nullable
  - `sampling_interval` integer, nullable
  - `tolerable_misstatement` number, nullable
  - `confidence_factor` number, nullable
  - `item_count` integer
  - `usable_item_count` integer
  - `usable_count` integer
  - `per_item` object[]
    - `seq` integer
    - `book_amount` number
    - `audited_amount` number
    - `taint_percent` number
    - `projected_amount` number
  - `projected_misstatement` number, nullable
  - `basic_precision` number, nullable
  - `basic_precision_note` string
  - `first_digit_counts` object, nullable
  - `chi_square_statistic` number, nullable
  - `critical_value` number
  - `deviation_flag` boolean, nullable
  - `trace` string, required
  - `overall` 'SAMPLE_COMPUTED' | 'PROJECTED' | 'SCREENED_CONSISTENT' | 'SCREENED_DEVIATES' | 'INPUT_REJECTED', required
  - `warnings` string[]

---

[API](https://skmtc.dev/ainumbers/apis/ainumbers-co-fintech-intelligence-suite.md) · [All operations](https://skmtc.dev/ainumbers/apis/ainumbers-co-fintech-intelligence-suite/llms.txt) · [OpenAPI document](https://skmtc.dev/ainumbers/apis/ainumbers-co-fintech-intelligence-suite/revisions/b462e4f5bb28?raw)