End-of-life criterion

An end-of-life criterion specifies the condition at which a component is treated as having exhausted its useful operation for a stated purpose. It supplies the endpoint needed to define remaining useful life. The criterion may be a performance threshold or an observed failure condition; useful operation can end before complete physical destruction. Its units, measurement procedure and operating conditions belong in the specification.

A primary NASA battery-aging test used30% loss of rated capacity, from2Ah to1.4Ah, as the aging endpoint. The apparatus separately used terminal-potential limits to finish individual discharges. Those two endpoints describe different processes and timescales.^[ref] A prediction stated only as “time until the battery ends” would therefore omit an essential physical definition.

For an illustrative linear capacity model, suppose present capacity is1.8Ah and future fade is0.01Ah per cycle. A1.4Ah end criterion gives40 remaining cycles, whereas a1.2Ah criterion gives60. The assumed degradation path is unchanged; the endpoint definition changes the reported lifetime. The example thresholds and rate are hypothetical, rather than a recommendation or a fit to the NASA data.

Competing end-of-life criteria also need a logical rule. If operation ends when either limit is first reached, the lifetime is $R=\min (R_1,R_2)$. Threshold crossings at12 and20h then give12h. A rule requiring both limits to be exceeded would define another event. Recording the criterion before evaluating a prediction avoids changing the target after observing the result, and supports an interpretable remaining-life validation error.

Competing end-of-life criteria are two or more conditions, any one of which can terminate useful operation under the stated specification. They define a remaining useful life by the earliest relevant crossing. If the prospective crossing times, measured from the present, are $T_1,\dots ,T_n$, thenThis is the event structure studied by competing risks. A condition ending one operating cycle must not inadvertently be treated as the component's aging endpoint: NASA's battery experiment separately defines a terminal-potential discharge cutoff and a30% rated-capacity-loss aging criterion.^[ref]

For an original mechanical example, suppose a component can reach either an unacceptable vibration level in12h or an unacceptable temperature in20h under a specified operating scenario. If either condition stops operation, its predicted useful life is12h. Requiring both conditions would instead define another stopping rule. An observed early crossing also does not establish when the other criterion would have been reached if the test had continued.

For uncertain crossing times, the survival function of useful life isOnly under independence does this equal the product of the individual survival functions. For an explicitly hypothetical independent pair of exponential distributions with rates $0.01{\mathrm{h}}^{-1}$ and $0.02{\mathrm{h}}^{-1}$, the product is $e^{-0.03t}$ when $t$ is measured in hours. The expected first crossing is $1/0.03\approx 33.33\mathrm{h}$, smaller than either individual mean,100h or50h.

The independence assumption is substantive. Shared temperature, load or damage can correlate crossing times, so multiplying marginal survival functions can give the wrong answer. Moreover, an intervention triggered by the first crossing can change the subsequent trajectory. The physical end-of-life criterion, dependence model and assumed future operation therefore belong with any numerical lifetime prediction.