Key takeaway
A record ending without failure says how long the unit was observed, not how long it would have survived.
Choose the clock and the first event
An equipment export often contains an installation date and the last date seen in service. Subtracting them does not automatically produce a failure lifetime. Define the unit, time origin, qualifying first failure and observation end. If repairs reset the unit, or operating hours differ from calendar hours, record those choices before combining histories. This guide concerns a first-event cohort; it does not model recurring repairs.
NIST distinguishes exact failures, right-censored observations and interval-censored failures. A unit still operating when follow-up ends has a lower bound on its lifetime. A unit known to fail between two inspections has a failure interval. Replacing either with an invented exact failure time changes the evidence. Keep the observation status beside the time value in the receiving schema.
Reconstruct a small risk set
In this hypothetical example, five invented units enter observation at hour zero. A fails at hour two, B leaves observation without failure at hour three, C fails at hour four, and D and E remain running when observation stops at hour five. There are no tied times or competing events. The table shows a Kaplan–Meier calculation only under the illustrative assumption that removal does not selectively hide impending failures.
The survival estimate at hour two is 4/5 = 0.80. Before hour four, B has left observation, leaving C, D and E at risk. The next factor is 2/3, giving 0.80 × 2/3 = 0.5333. Counting B as a failure would invent an event; keeping B in the later risk set would invent follow-up. Two failures among five units is a different descriptive count from this time-indexed estimate.
| Event time | Observed status | At risk before failure | Survival estimate |
|---|---|---|---|
| 2 hours | A fails | 5 | 4/5 = 0.80 |
| 3 hours | B removed, still running | No failure step | Remains 0.80 |
| 4 hours | C fails | 3 | 0.80 × 2/3 = 0.5333 |
| 5 hours | D and E follow-up ends | No additional failure | No tail beyond observed follow-up |
Investigate why observation stopped
The risk-set arithmetic cannot validate the removal mechanism. If a technician removes equipment because a warning signal suggests imminent failure, ordinary noninformative-censoring assumptions may be doubtful. Preserve removal reasons such as planned transfer, study end, lost tracking or suspected defect. Ask an analyst to assess the proposed model; an unlabeled last-seen timestamp is not enough.
Distinguish a known event date from the date a report entered the system. For interval failures, retain the last confirmed working inspection and first failed inspection. NIST’s elementary product-limit description requires exact failure times; do not place every interval failure at its midpoint and then cite that description as approval. Interval methods, delayed cohort entry and competing causes need explicit treatment.
Deliver time, status and observation evidence together
A useful field map includes unit key, cohort-entry rule, clock basis, time origin, event or censoring time, event indicator, interval bounds where relevant, observation source and removal reason. Reconcile impossible negative durations and units that appear after observation ended. Report how many histories cannot be classified without assuming facts absent from the archive.
For the example, the bounded conclusion is that the supplied synthetic ledger supports the stated risk-set calculation through hour four. It does not establish a fleet failure distribution, remaining useful life for any real unit or safe maintenance intervals. Keep those limits with any exported summary. Use the inventory tool for unresolved fields and the readiness planner for the domain review; technical interpretability does not supply permission to share an equipment or customer history.