From "faulty" to "how long"
Remaining useful life (RUL) is the time between now and the point where the asset can no longer do its job, or reaches a threshold you have defined as end of life. RUL lets planners batch repairs into scheduled shutdowns, order parts in time and run a degrading machine safely until a convenient stop.
Classical baseline · fixed-interval replacement
Replace bearings every 24 months or every 20,000 hours, based on rated life such as L10 (the life that 90% of a population survives). Fixed intervals ignore the condition of the specific machine: most components are replaced with useful life left, and some still fail early.
Three routes to RUL
| Route | Idea | Data needed | Output |
|---|---|---|---|
| Health indicator + degradation model | fuse features into one health index, fit a trend, extrapolate to a failure threshold | a few run-to-failure histories, or a known threshold | RUL distribution from model uncertainty |
| Direct ML regression | learn a mapping from a window of recent features to RUL | many run-to-failure histories | point estimate, interval via ensembles or quantiles |
| Survival analysis | model the probability of surviving beyond time t given covariates | failure and censored (still running) histories | survival curve per asset |
Health indicators
A health indicator (HI) compresses many features into one number that rises (or falls) steadily as the asset degrades. Good HIs are monotonic (move in one direction), trendable (similar shape across units) and prognosable (end at a similar value at failure). Common constructions:
- An anomaly score from a detector trained on healthy data.
- The first principal component of normalised degradation features.
- A regression output trained to go from 0 (new) to 1 (failed) on historical runs.
Uncertainty is the answer
The explainer fits an exponential degradation model, a common choice for bearings, to the recent health indicator and extrapolates it to the failure threshold. Resampling the fit errors (bootstrapping) gives many plausible futures. Their spread is the uncertainty in RUL.
Planners use the interval differently from the median. For a critical asset, schedule the repair before the lower bound. For a non-critical asset with spares on the shelf, plan around the median and accept some risk.
Machine learning for RUL
Direct regression
Gradient boosting or a neural network maps recent features (for example the last 30 cycles of 14 sensors) to RUL. The NASA C-MAPSS turbofan dataset is the standard benchmark. Two practical tricks: cap the RUL target in early life ("piecewise linear" labels), because a healthy machine shows no degradation signal, and evaluate with a score that penalises late predictions more than early ones.
Sequence models
LSTMs, temporal convolutional networks and transformers read the whole recent history rather than a fixed feature window. They can capture changes in degradation rate but need many complete histories, which most plants do not have for any single asset type.
Survival models
Survival analysis uses the many assets that have not failed yet (censored data), which regression throws away. Cox proportional hazards, Weibull accelerated failure time and random survival forests estimate how condition and operating stress shift each unit's survival curve. This is often the most data-efficient route for fleets.
Physics and Bayesian updating
When histories are scarce, combine a physics-based degradation law (crack growth, wear) with Bayesian updating of its parameters as measurements arrive. Particle filters are the common tool. The prior carries engineering knowledge; the data personalises it to the unit.
Key takeaways
- RUL is a distribution. Communicate an interval and let criticality decide which end to plan for.
- A good health indicator is monotonic, trendable and ends near the same value at failure.
- Survival models use censored data and work with fewer failures than regression.
- Early-life RUL predictions are uncertain by nature; they become useful once degradation is visible.
Try it in the apps
The RUL Predictor learns degradation from a fleet, predicts remaining life with a narrowing interval and compares predictive maintenance with fixed-interval replacement on cost.