Recovery tails include incidents that have not finished yet

Detection, mitigation, restoration of user success, removal of backlog, and restoration of redundancy are different events. A service can answer requests again while remaining one fault away from another outage. Choose the endpoint relevant to the decision and record its start rule consistently. Mixing detection-to-mitigation with failure-to-full-repair durations can create a distribution that describes no actual process. Include incident classes, severity, dependencies, staffing context, and observation gaps where they affect interpretation, without slicing the data until every difficult event disappears from the population.

An open incident observed for c minutes gives a right-censored duration: recovery time exceeds c under that endpoint definition. It contributes exposure even though the final time is unknown. Survival methods usually need a noninformative censoring assumption, possibly conditional on recorded covariates. If the hardest incidents are transferred elsewhere and disappear from the dataset, censoring can be informative and the naive estimate biased. Record why observation ended. A resolved ticket is not necessarily a recovered service, and a retired service is not automatically a successful repair at its retirement timestamp.

The Kaplan–Meier estimator multiplies conditional survival fractions at observed recovery times, using the risk set still under observation just before each time. Right-censored cases leave the risk set without causing a recovery step. Under its assumptions, this uses more information than discarding open incidents. It still cannot identify an arbitrary far-tail percentile beyond the observed recovery support. If estimated survival remains above ten percent at the last informative time, the data do not supply a finite nonparametric 90th-percentile recovery estimate merely because a dashboard requires a number.

Heavy-tailed models can describe rare very long durations, but the name is not evidence that a particular Pareto, lognormal, or mixture model fits. Some heavy-tail families have a finite mean and infinite variance; other parameter regimes do not even have a finite mean. Empirical moments can be unstable in sparse incident samples. Plot and compare candidate survival behavior, include uncertainty, and separate fit from extrapolation. Operational changes can also invalidate iid duration assumptions, so a theoretical tail family should not silently replace evidence about how repair work actually proceeds.

Show sample size, completed and censored counts, observation horizon, confidence information, and the region where tail estimates depend on a parametric model. A restricted mean over an observed horizon can be more defensible than an unrestricted mean requiring unsupported tail assumptions. Validate recovery forecasts on later incidents and inspect changing incident mix. For a response plan, ask how much capacity or user exposure remains while recovery is unfinished, not only whether a point estimate of duration improved. The model should support a decision whose risk tolerance is explicit.

The probability lab represents one fixed-threshold recovery question only. Reset, set BOTH p=0.8 and n=10, interpret success as recovered by a hypothetical threshold, predict all-ten probability 0.8¹⁰≈0.1074, then Play or Step. Reset and re-set BOTH p=0.95 and n=10; predict about 0.5987. Edits retain t; playback highlights exact independent counts. There are no durations, censored cases, shared incidents, or fitted tail curves. A threshold success fraction cannot identify the full recovery-time distribution or make a 90th percentile estimable beyond the data.