How Do Your Components Fail? Weibull, With Censoring Done Right

How it works

The analysis fits a two-parameter Weibull life distribution by maximum likelihood with right-censoring, using survival::survreg. survreg estimates the accelerated-failure-time form log(T) = mu + sigma times a standard extreme-value term; the module converts that to the reliability convention R(t) = exp(-(t/eta)^beta), where the shape is beta = 1/sigma and the scale is eta = exp(mu), and carries the conversion through to every confidence interval. Shape and scale intervals come from the fit's own covariance; B10, B50 and mean life get delta-method intervals on the log scale. The failure mode is decided by where the shape's 95% interval sits relative to 1, never by the point estimate. Fit quality is scored two ways: the R-squared of the Kaplan-Meier plotting positions in Weibull coordinates, and the largest gap between the fitted reliability curve and the distribution-free Kaplan-Meier curve.

Use it when the question is how a population of units fails over its life — a B10 or MTBF number, a reliability curve you can project forward, or a read on whether failures are early-life, random, or wear-out — and some units are still running.

Not for comparing survival between groups (the survival analysis tool does Kaplan-Meier and Cox for that), not for repairable systems with repeated failures per unit, and not when the probability plot shows two distinct straight segments — that is more than one failure mode and needs them separated before fitting.

What data do you need?

One row per unit: its life, and whether it failed. For example, a bearing life test:

Minimum 20 rows · Best with 50-50,000 units with at least 20 observed failures

What's in the report?

Standard-library analysis: how do components fail over time? Fits a two-parameter Weibull life distribution to your time-to-failure data with right-censoring handled properly — units still running when observation stopped are counted for exactly as long as they lasted instead of being dropped or treated as failures. You get the shape parameter beta with a confidence interval and the failure-mode reading that comes with it (below 1 = infant mortality, around 1 = random failure, above 1 = wear-out), the characteristic life eta, B10 and B50 life, MTBF, the reliability curve R(t) with a clearly-labelled forward projection, the hazard curve, and a Weibull probability plot with the fitted line so you can see whether the distribution actually fits. Works on any life data: map a duration column and a failure flag.