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Independent research · 2026 – present · Saurabh Sagar Shinde

Decision-Theoretic Predictive Maintenance with Calibrated Predictive Uncertainty for Remaining Useful Life Prediction

Can remaining-useful-life predictions be made calibrated enough to act on — and does acting on the full predictive distribution lead to better maintenance decisions than acting on a point estimate?

Status
Manuscript in preparation
Data
NASA C-MAPSS turbofan engine degradation simulation
Empirical results on this page
None yet — see Results
Paper, code, preprint
Not public yet — see Reproducibility

Overview

A remaining-useful-life (RUL) model that is accurate on average can still be wrong in exactly the cases that matter: an engine that fails sooner than predicted. Maintenance decisions are asymmetric — servicing too early wastes useful life, servicing too late risks failure — so a single predicted number is not enough to decide well.

This project treats prediction, uncertainty and the maintenance decision as one pipeline, and evaluates it on what the decision costs, not only on prediction error.

Problem formulation

For an engine observed up to cycle t through a window of multivariate sensor readings x, predict its remaining useful life R together with an interval [L, U] that contains R with a chosen probability 1 − α. Then choose a maintenance time m that minimises the expected cost of the decision:

P( L(x) ≤ R ≤ U(x) ) ≥ 1 − α

m* = argminm E[ cF·1{R ≤ m} + cE·(R − m)+ ]

cF is the cost of an unplanned failure and cE the cost of each cycle of useful life discarded by maintaining early. The asymmetry between them is what makes the interval, not just the point prediction, decision-relevant.

Intended contribution

  • A unified framework connecting RUL prediction, calibrated prediction intervals, an expected-loss maintenance decision layer and business-value evaluation.
  • A comparison of uncertainty methods and predictive baselines under one protocol that reports statistical, calibration and decision metrics together.

Intended contribution of the manuscript in preparation — not yet a reported finding.

Method

Being implementedPlanned

Sensor and time-series inputs

In progress

Run-to-failure sensor trajectories from NASA C-MAPSS, cut into multivariate time windows.

  • Each training example is a window of recent sensor readings from one engine.
  • The target is that engine’s remaining useful life at the end of the window.
In
Simulated turbofan sensor histories
Out
Multivariate sensor windows
Fig. 1 — The research pipeline, from sensor data to a maintenance decision and its evaluation. Select a stage to read what it does. Stage status follows the CV; nothing here reports a result.
Components of the framework, as described on the CV.
DataNASA C-MAPSS turbofan degradation benchmark (simulated run-to-failure sensor trajectories).
BackboneHybrid TCN + Transformer encoder with temporal attention pooling.
Prediction headMulti-quantile regression of remaining useful life.
UncertaintyConformalized quantile regression for calibrated intervals.
Decision layerExpected maintenance loss with asymmetric early-maintenance and failure costs.

Two demonstrations of the idea

These figures are built from documented formulas, not from the trained model. They explain what the calibration and decision stages are for.

Predicted remaining useful life with a prediction interval

Illustrative · synthetic values
  • True RUL
  • Predicted RUL
  • Prediction interval
  • Safety margin (20 cycles)
Illustrative predicted remaining useful life with a prediction intervalSynthetic data. True remaining useful life is capped at 125 cycles, then falls to zero at cycle 200. The prediction interval narrows as failure approaches, from about 36 cycles wide at cycle 30 to about 8 cycles wide at cycle 190. At the selected cycle 110, the predicted RUL is 99 with interval 86 to 113; the true RUL is 90, which is inside the interval. A simple rule raises a maintenance alert when the interval’s lower bound first reaches the 20-cycle safety margin, at cycle 175; at the selected cycle it has not yet been raised.050100150050100150200Operating cycleRUL (cycles)Safety marginFailure (RUL = 0)
Predicted RUL
99
Interval
[86, 113]
Width
28
True RUL inside?
Yes (90)
Alert raised?
Not yet

Fig. 2 — What a calibrated interval is meant to do: contain the true remaining life at a stated rate, and tighten as evidence of degradation accumulates. Drag the cycle to see where this synthetic interval does and does not contain the truth, and when a simple interval-based rule would call for maintenance.

How it was generated: true RUL = min(125, 200 − cycle); predicted = true RUL plus a smooth deterministic error; interval half-width = 3 + 0.12 × true RUL. No model was trained. Real coverage is measured across many held-out engines, not along one trajectory. The alert rule (lower bound ≤ 20 cycles) is a teaching device, not the expected-loss policy studied in the research.

Expected maintenance loss by maintenance timing

Illustrative · synthetic values
  • Expected loss
  • Failure-risk term
  • Wasted-life term
Illustrative expected maintenance loss as a function of maintenance timingToy model with predicted RUL 60 cycles and predictive standard deviation 12 cycles, failure cost 20, and 0.25 per cycle of unused life. Expected loss is lowest when maintaining 42.5 cycles from now, with expected loss 5.9 and a 7.2 percent chance of failing first. Maintaining at the point prediction, cycle 60, has expected loss 11.2.010.821.60306090120Maintain in m cyclesExpected loss (cost units)Point predictionPast m*: waiting adds more risk than it savesMinimum at m = 42.5
Best timing m*
42.5
P(fail before m*)
7.2%
E[loss] at m*
5.9
Trigger level cE/cF
0.0125
E[loss] at point prediction
11.289% higher than at m*

Change a cost or the uncertainty to see why the best time moves.

Fig. 3 — Why the decision needs the whole distribution. With remaining life R ~ Normal(60, σ) and maintenance scheduled m cycles from now, the expected loss is

E[L(m)] = cF·P(R ≤ m) + cE·E[(R − m)+]

The first term is the chance of failing before maintenance times the failure cost; the second is the useful life thrown away by maintaining early. The minimum satisfies h(m*) = cE/cF, where h is the hazard rate of the predictive distribution. Expensive failures pull m* earlier; when failure is cheap relative to wasted life, more uncertainty can push it later.

Toy model for explanation only: Normal predictive distribution (negative-RUL mass not truncated), static linear costs, one unit, no scheduling constraints, and cost units with no real-world calibration. It is not an evaluated maintenance policy and the numbers are not results.

Experimental design

Status reflects the CV. Nothing marked planned or in progress is reported here as a finding.

  • Hybrid temporal backbone

    TCN + Transformer encoder + temporal attention pooling + multi-quantile head.

    In progress

  • Conformalized quantile regression

    Calibrated intervals evaluated by coverage, interval width and calibration metrics.

    In progress

  • Risk-aware decision layer

    Expected maintenance loss under asymmetric early-maintenance and failure costs.

    In progress

  • Uncertainty-method comparison

    CQR against the six uncertainty baselines listed below.

    In progress

  • Predictive baselines

    Statistical, classical ML, deep-learning and Transformer-based models.

    In progress

  • Ablation studies

    Contribution of each backbone component and of calibration.

    Planned

  • Sensitivity analysis

    How decisions and losses change with the assumed cost parameters.

    Planned

  • Statistical significance testing

    Whether differences between methods exceed run-to-run variation.

    Planned

  • Decision and economic evaluation

    Expected maintenance loss and economic metrics alongside predictive metrics.

    Planned

Uncertainty baselines

  • Split conformal prediction
  • Uncalibrated quantile regression
  • MC dropout
  • Deep ensembles
  • Bayesian neural networks
  • Evidential deep learning

Predictive baselines

Linear
Linear, Ridge, Lasso, Elastic Net
Classical ML
Random Forest, SVR, Gradient Boosting, XGBoost, LightGBM
Recurrent and convolutional
CNN, LSTM, GRU, BiLSTM-Attention, CNN-LSTM, CNN-BiLSTM-Attention
Temporal / attention
TCN, Transformer

What the evaluation measures

Empirical coverage
Share of test cases whose true RUL falls inside the prediction interval, compared with the nominal target.
Interval width
How wide the intervals are. At equal coverage, narrower intervals carry more information.
Calibration
Whether predicted quantiles behave like quantiles — e.g. the 90th percentile is exceeded about 10% of the time.
Expected maintenance loss
Average cost of the maintenance decisions the model leads to, under stated early-maintenance and failure costs.

Dataset version, C-MAPSS subsets, and the exact training / validation / calibration / test split will be stated with the manuscript. A calibration split disjoint from training is required by conformalized quantile regression.

Results

No empirical results are reported yet

The experiments are in progress and the manuscript is in preparation. When they are complete, this section will show coverage against the nominal target, interval width, calibration diagnostics and decision loss across cost ratios — each with its configuration, data split and run count.

What has been verified so far

Software, not performance. Cumulative unit and integration tests of the research codebase, as reported on the CV (Aug 2026).

Passed
448
Failed
0
Skipped
32

Skipped: dependency-specific tests skipped when required ML libraries are unavailable.

  • End-to-end CQR calibration behaviour
  • Prediction-interval ordering (lower ≤ upper)
  • Deterministic reload of calibration artifacts
  • Deep-ensemble epistemic-uncertainty behaviour

Reproducibility

ArtifactAvailability
Source codePrivate while the manuscript is in preparation; available on request.
Experiment configurationsTo be released with the manuscript.
DataNASA C-MAPSS is a public benchmark; preprocessing will be documented with the code.
Evaluation scriptsTo be released with the manuscript.
Paper draft or preprintNot yet public.

To discuss the code or methodology before release, email saurabhsshinde16@gmail.com.

Discussion and limitations

What this approach could contribute is a pipeline that is judged by its decisions rather than its error alone. What it depends on, and where it could fail:

Coverage is a marginal guarantee
Conformal methods guarantee coverage on average across test cases, under exchangeability. They do not guarantee coverage for every engine, every operating regime or every stage of life — which is where maintenance risk concentrates.
Exchangeability can fail
Overlapping windows from the same engine are correlated, and fleets drift as operating conditions and fault modes change. Both can weaken the calibration guarantee in practice.
Simulated benchmark
C-MAPSS is a simulation. Good behaviour on it does not establish behaviour on real fleets with sensor faults, missing data and censored histories.
Costs are assumptions
The decision layer is only as good as its cost model. Results should be reported across a range of cost ratios, not at one convenient setting.
Single-unit decisions
Minimising expected loss one engine at a time ignores fleet constraints such as maintenance capacity, spare parts and scheduling windows.

Further validation would need conditional coverage by operating regime and life stage, results across a range of cost ratios, and — eventually — data from a real fleet.