What is Remaining Useful Life (RUL)?

RUL is the estimated time remaining before an asset reaches a predefined failure threshold. It is a core concept in prognostics and predictive maintenance, defined in ISO 13381.

What regression models are available?

This calculator supports linear (y = a + bx), exponential (y = a·e^(bx)), and second-order polynomial (y = a + bx + cx²) regression models for trend extrapolation.

How is confidence level estimated?

Confidence is derived from the R² (coefficient of determination) of the fitted model. Higher R² indicates a better fit and more reliable RUL prediction.

Free Engineering Tool

Remaining Useful Life (RUL) Prognostics Calculator

Enter trend data points, choose a regression model, set a failure threshold, and estimate the remaining useful life with confidence level per ISO 13381.

ISO 13381-1 Linear / Exponential / Polynomial Up to 8 Points

Regression Model

Failure Threshold (parameter value)

Parameter Name (optional label)

Time Unit

Trend Data Points (minimum 3 required)

#	Time (t)	Parameter Value (y)

Quick presets

Results

Estimated Remaining Useful Life

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Predicted Failure Time

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Model R² (Goodness of Fit)

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Confidence Level

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Current Rate of Change

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Prognostics per ISO 13381-1

ISO 13381-1 defines a framework for condition monitoring and prognostics of machines. The core idea is to track a health indicator over time, fit a degradation model, and extrapolate to a predefined failure threshold.

Regression Models

Three models are supported for fitting trend data:

Linear: y(t) = a + b·t — suitable for steady, constant-rate degradation
Exponential: y(t) = a·e^b·t — suitable for accelerating degradation (e.g. bearing wear)
Polynomial (2nd order): y(t) = a + b·t + c·t² — suitable for non-linear trends with inflection

Goodness of Fit — R²

The coefficient of determination R² measures how well the model fits the data:

R² > 0.95 — Excellent fit, high confidence in RUL estimate
R² = 0.80–0.95 — Good fit, moderate confidence
R² < 0.80 — Poor fit, consider a different model or more data

Practical Example

Example — Bearing Vibration Degradation

Given: Vibration readings at days 0, 30, 60, 90, 120, 150 are: 1.2, 1.8, 2.5, 3.4, 4.1, 5.0 mm/s. Alarm threshold = 7.1 mm/s.

Linear fit: y = 1.14 + 0.0253·t → threshold at t ≈ 236 days → RUL ≈ 86 days from last measurement.

Exponential fit may give a shorter RUL if degradation is accelerating.

⚠️ Note: Prognostic estimates depend heavily on data quality and the assumption that the degradation mechanism remains unchanged. Always combine with engineering judgment and additional condition monitoring data.

RUL Prognostics Calculator | ISO 13381 | Vibromera

Published by Nikolai Shelkovenko on February 15, 2026 March 5, 2026

Results

Prognostics per ISO 13381-1

Regression Models

Goodness of Fit — R²

Practical Example