According to this source, the survival function is defined as

$ S(t) = e^{- \lambda \cdot t} $

while, according to this source, the number at time $ t $ of radioactive atoms is

$ N(t) = N_0 \cdot e^{- \lambda \cdot t } $

which is quite the same, or? In general, survival analysis is described as

Survival analysis is a branch of statistics for analyzing the expected

duration of time until one event occurs, such as death in biological

organisms and failure in mechanical systems.

https://en.wikipedia.org/wiki/Survival_analysis

I just wonder, why I can't see any hint towards the radioactive decay , nor any assignment of radioactive decay to survival analysis, though I browsed for a while.

Is there something different between them?

## Best Answer

$$ N_0 e^{-\lambda t} $$

is just an exponential decay function. It is not specific for survival analysis, nor is the only feature of survival analysis that consists of many more models and tools than this. At the same time, the function describes a physical phenomenon. It doesn't surprise me why physicists using the simple function won't call it "survival analysis", especially since survival analysis is a model popular in medicine, not physics. I also guess that if physicists used other models and tools that emerged from survival analysis, they would call it like this.