Two-Point Vibration Threshold Extrapolation Worksheet

Compare two deliberately assumed mathematical continuations of two comparable vibration observations. The worksheet reports arithmetic crossings of your own controlled reference levels; it does not estimate remaining useful life or failure time.

Not RULNo embedded ISO valuesTwo scenarios shown togetherNo operating action

Boundary: two observations cannot establish model adequacy, residual scatter, outliers, confidence or prediction intervals. A mathematical crossing is not an alarm, danger state, maintenance interval, failure prediction, ISO compliance or permission to continue operating.

Controlled observation and reference record

工况 / 计算 IDUnique traceable identifier; no default case is assumed.

Asset / machine set

Measurement point, axis and sensor chainInclude mounting, positive direction and any channel processing relevant to comparability.

Quantity, unit, band and amplitude conventionExample format only: velocity, mm/s RMS, stated band. Do not copy an example as evidence.

Baseline observation ID / timestamp

Current observation ID / timestamp

Baseline operating and measurement condition

Current operating and measurement condition

Baseline value V0Positive value in the exact declared quantity/unit/convention.

Current value V1

Elapsed time Δt

Time unit for Δt and horizon

Reference level APositive user-supplied level from the exact controlled source below.

Reference A basisDocument/procedure, edition/revision, clause/table/page, applicability and accountable owner.

Reference level B (optional)If supplied, its basis is mandatory. No alarm/danger meaning is inferred.

Reference B basis (required only when B is supplied)

Future comparison horizon hUses the same selected time unit as Δt.

Reviewer and review date

Eight applicability and decision gates

Same point, axis, sensor, mounting and acquisition/processing chain are confirmed.
Same physical quantity, unit, frequency band and RMS/peak convention are confirmed.
Speed, load, temperature and process conditions are comparable or normalized by a controlled method.
Both observations and the measurement system have traceable IDs and quality review.
Interventions, step changes and known external events between observations were reviewed.
The user accepts that both curves are unvalidated scenarios, not fitted/selected prognosis models.
Each entered reference level is applicable and traceable to a controlled source.
An accountable owner will make any action separately; this worksheet never recommends operation or shutdown.

Cannot calculate:

No result

0 of 8

Enter a traceable record and submit explicitly.

Relative change from V0 to V1—

Current state versus reference A—

Linear rate m—

Log-linear rate k—

Linear remaining time to A—

Log-linear remaining time to A—

Linear remaining time to B—

Log-linear remaining time to B—

Linear value after horizon h—

Log-linear value after horizon h—

Scenario difference at horizon |VE − VL|—

No preferred model is selected. The difference between scenarios is not a confidence interval and does not cover measurement or model uncertainty.

Equations, dimensions and decision boundary

Place the baseline at t=0 and the current observation at t=Δt. Both scenarios pass exactly through the same two points, so neither has a residual-based goodness-of-fit advantage.

Linear: m = (V1 − V0) / Δt; VL(t) = V0 + m t

Log-linear: k = ln(V1 / V0) / Δt; VE(t) = V0 exp(k t)

Future horizon: VL(Δt+h) = V1 + m h; VE(Δt+h) = V1 exp(k h)

If R > V1 and the rate is positive: τL = (R − V1)/m; τE = ln(R/V1)/k

V0, V1 and each reference R must have the same declared vibration dimension and amplitude convention. m has vibration-unit/time and k has 1/time. Crossing time has the selected time unit. If the current value is at or above a reference, the worksheet reports that state instead of a fictitious positive remaining time. A non-increasing scenario has no future upward crossing.

Normative boundary: these equations are elementary scenario arithmetic, not formulas issued by ISO 13381, ISO 17359 or ISO 20816. No ISO numerical boundary is embedded. Exact prognosis-process, condition-monitoring and machine-vibration requirements require the applicable licensed controlled documents.

Source register and use boundary

ID	Source and lifecycle	Used for	Not used for
S1	ISO 13381-1:2025, Edition 3 — Published	Current prognosis-process public scope and lifecycle.	No two-point RUL formula, limit, confidence or action inferred. Protected requirements: NEEDS_LICENSED_SOURCE.
S2	ISO 13381-1:2015, Edition 2 — Withdrawn; replaced by 2025 edition	Historical lifecycle only.	Not current authority.
S3	ISO 17359:2018, Edition 3 — Published; confirmed 2023	Public scope for a controlled condition-monitoring programme.	No universal threshold, interval or action inferred. Protected procedures: NEEDS_LICENSED_SOURCE.
S4	NIST/SEMATECH 4.1.4.1 — Linear least squares	Model fitting, residual concept and warnings about extrapolation/outliers.	Does not validate two-point RUL or vibration limits.
S5	NIST/SEMATECH 4.1.4.2 — Nonlinear least squares	Parameter-estimation and model-validation context.	Does not support a hidden fixed p=2 power model.
S6	ISO 20816-1:2016, Edition 1 — Published; to be revised	Public measurement/evaluation and operational-limit scope.	No RUL equation or generic 4.5/7.1/8.5/11.2 values inferred. NEEDS_LICENSED_SOURCE.
S7	ISO/FDIS 20816-1, Edition 2 — Under development, stage 50.00	Pending lifecycle only.	Not a published replacement.
S8	ISO 20816-3:2022, Edition 1 — Published; to be revised	Public industrial-machine scope and machine-specific caution.	No preset or automatic action inferred. NEEDS_LICENSED_SOURCE.
S9	ISO 10816-1:1995 + Amd 1:2009 — Withdrawn	Obsolete lifecycle.	Not used for current limits or actions.
S10	ISO 7919-1:1996, Edition 2 — Withdrawn	Obsolete shaft-vibration lifecycle.	Not mixed with casing-velocity reference levels or RUL.

Source access and technical review: 17 July 2026. Recheck lifecycle before later normative use.

Corrections made to the former page

“Remaining useful life” was removed

A crossing of a user-entered reference under an assumed curve is not component life, failure time or RUL. The replacement reports threshold-extrapolation arithmetic only.

The hidden p=2 power law was removed

Two observations cannot estimate both a free power exponent and scale while also validate the model. The old code fixed p=2 while claiming adaptation.

Universal presets and ISO values were removed

No pump, motor or turbine level is assumed. Every reference must have an exact controlled source and applicability record.

Alarm, danger and shutdown outputs were removed

The worksheet compares numbers but never names a condition zone or recommends continued operation, maintenance or shutdown.

Both assumptions are shown together

The page no longer lets a selector hide model-form uncertainty. Linear and log-linear results are displayed side by side.

Two-point limitations are explicit

There is no residual scatter, fit statistic, outlier assessment or confidence/prediction interval from two exact points.

Unsafe parsing and persistence were removed

No parseFloat, preset, auto-calculate, URL state, browser storage, clipboard or dynamic result HTML remains.

Current standard lifecycle was added

ISO 13381-1:2025 is current. ISO 10816-1 and ISO 7919-1 are withdrawn; ISO 20816 limits remain machine- and measurement-specific licensed-source topics.