= Remaining useful life
<Remaining useful life> is the future time, cycle count or other usage until a component reaches a specified <end-of-life criterion>, conditional on its current condition and assumed future operation. The endpoint must be stated: crossing a performance limit, exhausting a discharge and reaching a long-term degradation threshold are different events. For an increasing damage variable $D$, threshold $D_c$ and present time $t$, a mathematical definition is the <first-passage time>
$$
R_t=\inf\{\tau\ge0:D(t+\tau)\ge D_c\}.
$$
A prediction of this quantity supports <condition-based maintenance>, while requiring more than detection of existing damage.
For an illustrative deterministic model, let current normalized damage be0.60, the end threshold1.00 and future damage rate0.02 per hour. Linear extrapolation gives $R=(1-0.60)/0.02=20\,\mathrm h$. If the plausible future rate instead ranges from0.015 to0.025 per hour, the corresponding times range from about26.67 down to16h. <Remaining useful life uncertainty> therefore includes future operating conditions and degradation-model uncertainty, as well as measurement error.
A primary NASA battery-aging dataset makes the endpoint concrete. A custom testbed cycled <electric batteries> under controlled load and temperature, recording quantities including <electric potential difference>, <electric current> and <temperature>. The reported aging endpoint was30% loss of rated capacity, from2Ah to1.4Ah. That long-term endpoint is distinct from the terminal-potential threshold used to end an individual discharge.<Li-ion Battery Aging Datasets by NASA>[Dataset description, end-of-life criterion and Data Acquisition apparatus list]{ref}
A useful validation compares predictions made before the endpoint with subsequently observed crossing times under documented operation. Reporting one predicted number without its endpoint, usage assumptions or uncertainty can conceal the main sources of disagreement between a model and a real endurance test.
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