These estimate the survival curve directly from the data, with no assumed shape. That makes them the honest first look — and the right answer when no distribution fits — but they can't extrapolate beyond your last observation, and they give you a curve rather than parameters.
Use one when you want to see what the data says, to check a parametric fit against, or when the shape is genuinely unknown. Use a distribution when you need to predict past the data, or feed a model into an RBD or a replacement calculation.
kaplan_meierThe standard empirical survival estimator. A step function that drops at each failure, with censored units correctly reducing the risk set without causing a step.
R(t) = Π (1 − dᵢ/nᵢ) over failure times tᵢ ≤ t
Use it as the default non-parametric view, and as the backdrop to judge a parametric fit against. Watch out: the curve stops at your last observation — if that's a censoring time, the tail is simply unknown, not flat.
nelson_aalenEstimates the cumulative hazard, then converts to survival — often better behaved than Kaplan-Meier in small samples or heavy censoring.
H(t) = Σ dᵢ/nᵢ , R(t) = exp(−H(t))
Use it when samples are small, or when you want to read the cumulative hazard directly — its slope is the failure rate, which makes trend easy to see. Watch out: it and Kaplan-Meier converge as samples grow; disagreement is a sign of thin data, not of one being wrong.
fleming_harringtonA tie-corrected refinement of Nelson-Aalen, handling simultaneous failures more carefully.
Adjusts each increment for the number of tied failures at that time
Use it when many units fail at exactly the same recorded time — common with inspection-based data where everything lands on the same date. Watch out: if you have no ties it gives you Nelson-Aalen, so it's not a decision worth agonising over.
turnbullThe estimator for interval-censored data — the general case where you know only that failure fell between two inspections.
Iteratively assigns probability mass to the intervals it could have fallen in
Use it when failures were found at inspections rather than observed as they happened, or when you have a mix of exact, interval, left- and right-censored observations. Watch out: the result can have flat regions where the data cannot distinguish when within an interval the failures occurred — that ambiguity is real, not an artifact.