Engineering calculator

MSA Hysteresis Calculator

Q: Is this the same as MSA linearity?

No. Linearity fits OLS of ε = ylab − xref versus xref. This page compares increasing versus decreasing indications at already-paired stations and reports max |y↑−y↓|.

Q: Is H a fail if it is 0.1?

This page does not issue that verdict. It does not take T and does not compute %Hysteresis against process variation.

Q: Is this Gauge R&R?

No. Gauge R&R composes EV, AV, and PV. Hysteresis is a directional lag on one instrument, not appraiser variation.

Q: Must y↑ and y↓ be the same length?

Yes. Length mismatch is INVALID_INPUT. Pairing is by index.

Q: Where does this run?

Locally in the browser by default. REST and MCP call the same metrology-engine hysteresis op.

Compute VIM / MSA hysteresis as the maximum absolute difference between increasing and decreasing indications at index-paired stations. Runs locally. Not OLS linearity, not a %Hysteresis pass/fail, and not Gauge R&R.

Instant result

Result

—

Enter values to calculate.

Inputs—

Mode—

Formula—

Trust summary CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Hysteresis = max |y_up − y_down| over n≥2 paired stations, + O3 mpmath tabulated hysteresis.

Input interpretation: Enter values to calculate.
Result: —
Verified scope: Hysteresis = max |y_up − y_down| over n≥2 paired stations, + O3 mpmath tabulated hysteresis.
Assurance: Engineering
Declared partition coverage: PASS · 6/6 declared partitions (alias, awkward, two, zero, spread, invalid-domain) · Matrix
Deferred: Not a %Hysteresis verdict and not Gauge R&R.
Numerical scope: O2: max |y_up − y_down| vs a separate-module identity (≤2 ULP). Not a %Hysteresis verdict. ≤2 ULP vs O3 applies only to the published tabulated hysteresis vectors. Not a %Hysteresis verdict.
Known limitations: Core CVP does not include live graph, viewport, or pointer interaction.
Model: Maximum absolute difference between increasing and decreasing indications at paired stations.
Scope: VIM 4.17 hysteresis as max |y_up − y_down| at index-paired stations
Verification: Engine tested · Source checked · v1.0.1 · CVP VERIFIED · CVP protocol 1.0.0-proposed · Engineering assurance · Hysteresis = max |y_up − y_down| over n≥2 paired stations, + O3 mpmath tabulated hysteresis.· View Manifest · CVP overview · Specification
Versions: Calculation 1.0.1 · CVP protocol 1.0.0-proposed · Evidence 2026-09-25.o2-o3
Verification revision: 2026-09-25.o2-o3 · 1/1 property · digest 0c987c084d1c
Legacy regression: 8/8 tests · Production surface contract 6/6
Trust layers: Verification VERIFIED · Production CURRENT · Overall CVP state: VERIFIED under CVP 1.0.0-proposed
Reference: O1 model · O3 expected_values · O3 numerical_behavior · O2 expected_values · O2 numerical_behavior
Interfaces: PASS · UI (SSR) / REST / MCP — ui-ssr is query-result HTML, not a live browser session. Error-path engine·REST·MCP 1/1 (status, code, calculation_version). SSR compared on URL-canonical requested calculations; empty query is idle (not an error) and JSON-typed object/array inputs are REST/MCP-only.
Supplemental domain review: Not performed
Named expert review: Not performed
CVP suite: 4/4 golden · 4/4 CVP boundary · 5/5 invalid · 1/1 property · 1/1 metamorphic · 8/8 O3 · 2/2 cross-interface · 6/6 CVP contract · Manifest
Sources: JCGM 200:2012 — International vocabulary of metrology (VIM) — 4.17 hysteresis
AIAG Measurement Systems Analysis (MSA) — Hysteresis of a measurement system
Sources
Evidence: 1 legacy golden · 4 legacy boundary · legacy regression suite · 4/4 oracle-backed golden · 5/5 invalid · Artifact integrity PASS
Semantic contract: PASS

Full verification

Manifest identity, reference classes, interfaces, suite, and production records.

Formulas

Core equations used by this calculator.

Point differenceΔᵢ = y↑ᵢ − y↓ᵢ

HysteresisH = max |Δᵢ|

iThis page does not take a tolerance T and does not issue a %Hysteresis verdict against process variation. Pairing is by index — it does not interpolate between unmatched stations.

How to use

Enter y↑

Increasing-direction indications, comma/space/semicolon separated or a JSON array. Need at least two points. Aliases: up, increasing, y_inc, rising.

Enter y↓

Decreasing-direction indications, same length. Aliases: down, decreasing, y_dec, falling.

Read H

H is max |y↑−y↓|. Use Linearity for OLS of error versus xref. This page does not issue pass/fail.

Example calculations

Common configurations with formula and result.

Mid-range lag

y↑=0,2,4 · y↓=0,1,4

Δ=[0,1,0]; H=1

H=1 · n=3

No lag

y↑=0,2,4 · y↓=0,2,4

Δ=[0,0,0]

H=0

MSA Hysteresis calculator specification

Version 1.0.1 · Engine tested

Calculation status

Engine tested 8/8 tests · Production surface contract 6/6
Named expert review Not performed
Calculation version 1.0.1

Review policy · Evidence

Definition: From n≥2 index-paired increasing indications y_up and decreasing indications y_down, H is the maximum of |y_up_i − y_down_i|. The mean of those absolute differences is also reported. Points must already be matched by station.
What it calculates: Maximum absolute difference between increasing and decreasing indications at paired stations.
Inputs: y_up
y_down
Outputs: hysteresis
mean_abs
n
delta
y_up
y_down
Formula: H=max|y↑−y↓|
Assumptions: VIM 4.17 hysteresis as max |y_up − y_down| at index-paired stations
n≥2; pairing is by index, not interpolated vs xref
Not OLS linearity, not a %Hysteresis verdict, and not AIAG GRR
Units: same unit as y↑ and y↓
Boundary conditions: missing y_up or y_down → MISSING_REQUIRED_INPUT
n < 2 → VALUE_OUT_OF_RANGE
length mismatch → INVALID_INPUT
identical curves → H=0 (valid)
Example: y_up=0,2,4 y_down=0,1,4 → H=1
Validation cases: 3 published on this page · 8/8 tests · Production surface contract 6/6 · View evidence
y_up=0,2,4 y_down=0,1,4 → H=1 n=3
y_up=0,2,4 y_down=0,2,4 → H=0
y_up=0 y_down=1 → VALUE_OUT_OF_RANGE
Sources: JCGM 200:2012 — International vocabulary of metrology (VIM) — 4.17 hysteresis
Supports: Difference of indication when the measured quantity is approached from opposite directions.
AIAG Measurement Systems Analysis (MSA) — Hysteresis of a measurement system
Supports: This page takes paired increasing and decreasing indications and reports the largest absolute difference. It does not issue a %Hysteresis verdict.
Calculation version: 1.0.1

Background

Interpretation and common distinctions.

Compute VIM / MSA hysteresis as the maximum absolute difference between increasing and decreasing indications.

Supported and not supported

Supported — H = max |y↑−y↓| · mean |Δ| · API engineering.msa.hysteresis

Not supported — OLS linearity, %Hysteresis vs T or process variation, Gauge R&R, a single-shot measurement error

Agent / API notes

Capability id: engineering.msa.hysteresis · tool id: hysteresis · pin 1.0.1.

{ "y_up": [0, 2, 4], "y_down": [0, 1, 4] }

Aliases: up / increasing / y_inc / rising for y_up; down / decreasing / y_dec / falling for y_down. Errors: MISSING_REQUIRED_INPUT, INVALID_NUMBER, INVALID_INPUT, VALUE_OUT_OF_RANGE.

Calculator URL stays /calc/engineering/hysteresis. There is no /calc/metrology.

Other calculators in this family: MSA linearity, Measurement error, Measurement bias (trueness), Gauge capability (Cg/Cgk), Gauge R&R, Maximum permissible error MPE, Tolerance / Uncertainty Workspace .

Frequently asked questions

Key distinctions behind the calculation.

Is this the same as MSA linearity?