= Remaining useful life uncertainty
<Remaining useful life uncertainty> describes uncertainty about the future crossing time of a stated <end-of-life criterion>. It can arise from current-condition measurements, degradation parameters, model inadequacy and future operation. The same cycle count need not imply the same condition. NASA's battery-aging dataset explicitly documents variation associated with discharge depth, rest periods and intrinsic differences, and distinguishes discharge-time prediction from long-term aging prediction.<Li-ion Battery Aging Datasets by NASA>[“Intended Use”, variation at equal cycle index and end-of-discharge versus end-of-life prediction]{ref}
For an original two-scenario example, let normalized current damage be0.60 and the threshold1.00. Suppose future damage rate is0.01 per hour with probability0.25 and0.02 per hour with probability0.75. The corresponding <remaining useful life> values are40 and20h. Their expected lifetime is
$$
\operatorname E[R]=0.25(40)+0.75(20)=25\,\mathrm h.
$$
The mean rate is0.0175 per hour, but extrapolating with that rate gives $0.40/0.0175\approx22.86\,\mathrm h$. Averaging the inputs before a nonlinear inverse calculation therefore gives a different answer from averaging the predicted lifetimes.
A forecast can report a <probability distribution> or a <prediction interval> together with the assumed future-use scenarios. A narrow interval for the estimated mean is not automatically a narrow interval for a future component's crossing time. The reported uncertainty must identify the random quantity it covers and the model that supplies its probabilities.
<Remaining-life validation error> compares a forecast made at a specified prediction time with the endpoint subsequently observed. Testing predictions on independent endurance records helps assess whether stated intervals cover observed outcomes at the claimed frequency. Such evaluation must preserve the original endpoint and future-use assumptions; otherwise a numerical disagreement can mix model error with a changed prediction question.
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