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Engineering calculator

MSA Hysteresis Calculator

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 Engine tested · Source checked · 8/8 tests · Production surface contract 4/4 · v1.0.0
Input interpretation
Enter values to calculate.
Result
—
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 · 8/8 tests · Production surface contract 4/4 · Source checked · v1.0.0
Named expert review
Optional · Not performed
Sources
  • JCGM 200:2012 — International vocabulary of metrology (VIM) — 4.17 hysteresis
Sources
Evidence
5 boundary · 3 property · Production surface contract 4/4 · Artifact integrity PASS
Production
Embedded snapshot: unpublished · Build schema 1.0.0 ready · Semantic contract ✓ · Attestation report not published on origin · Live production status STALE (1 capability; 156 remain CURRENT) @ 2026-09-14T03:54:53.650Z
Semantic contract
PASS

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

1

Enter y↑

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

2

Enter y↓

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

3

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.

ϟ

Mid-range lag

y↑=0,2,4 · y↓=0,1,4

Δ=[0,1,0]; H=1
H=1 · n=3
ϟ

No lag

y↑=0,2,4 · y↓=0,2,4

Δ=[0,0,0]
H=0

MSA Hysteresis calculator specification

Version 1.0.0 · Engine tested

Calculation status

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 4/4 · 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.
Calculation version
1.0.0

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 1.0.0.

{ "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 .

lin MSA linearity › ε Measurement error › δ Measurement bias (trueness) › Cg Gauge capability (Cg/Cgk) › GRR Gauge R&R › MPE Maximum permissible error MPE › WS Tolerance / Uncertainty Workspace ›
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Frequently asked questions

Key distinctions behind the calculation.

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↓|.

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.

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.

Must y↑ and y↓ be the same length?

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

Where does this run?

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