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  "body": "\n## Summary\n\nThe survival function of a lifetime $T$ gives, for each time $t$, the probability that the event has not yet happened at time $t$.\nIt equals one minus the [[cumulative distribution function|0H8H7ZTHW2]] of $T$.\nIt is the main quantity estimated in [[survival analysis|443ZWDX88P]], and it determines the distribution of $T$.\nIn reliability engineering it is called the reliability function.\n\n## Explanations\n\n### L1 human\n\nIf $T$ is the lifetime of a light bulb, $S(1000)$ is the chance that the bulb still works after $1000$ hours.\nThe curve $S$ starts at $1$, because every bulb works at the start, and goes down as time passes.\nIt never goes up again: a broken bulb stays broken.\nFor a lifetime with constant risk of failure, the curve is the decaying exponential $e^{-\\lambda t}$.\n",
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