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.
Results
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·eb·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
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 is the estimated time remaining before an asset reaches a predefined failure or alarm threshold. It is a core concept in prognostics and predictive maintenance defined by ISO 13381-1.
RUL estimation allows maintenance to be planned proactively, avoiding unexpected downtime while maximizing asset utilization.
The choice depends on the degradation pattern:
- Linear — constant-rate degradation (e.g. gradual wear, steady contamination buildup)
- Exponential — accelerating degradation (e.g. bearing spalling, fatigue crack growth)
- Polynomial — non-linear trends where rate changes (e.g. initial break-in followed by stable degradation then rapid failure)
Compare R² values to find the best fit for your data.
A minimum of 3 data points is required for any regression. For better confidence:
- Linear model: 4–5 points recommended
- Exponential: 5–6 points recommended
- Polynomial: 6+ points recommended
More data points, especially near the current operating time, improve the prediction.
Confidence is derived from the R² (coefficient of determination) of the fitted model:
- High (R² ≥ 0.95) — Model fits data very well, RUL estimate is reliable
- Moderate (R² 0.80–0.95) — Reasonable fit, use with caution
- Low (R² < 0.80) — Poor fit, consider a different model or more data points
This calculator supports multiple parameter types (vibration, temperature, wear particles, etc.), multiple regression models, quantitative goodness-of-fit assessment, and extrapolation to a user-defined threshold — providing a full prognostic analysis rather than just a visual trend.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional condition monitoring and vibration analysis instruments. Predict failures before they happen. Used in 50+ countries.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
