Survival Curve Explanation

What is the Weibull Survival Function?

The Weibull survival function is a mathematical model used in reliability engineering, survival analysis, and medicine to describe how the chance of survival changes over time. It has two key parameters:

• λ (lambda): Controls the overall timescale — larger λ means longer typical lifespans.
• β (beta): Controls the shape of the curve — how the risk of death increases or decreases with age.

When β = 1, the model reduces to the exponential distribution (constant risk over time). When β > 1, the risk of death increases with age, which often reflects real-world human aging.

A survival curve represents the probability S(t) that an individual will survive beyond age t. We use the Weibull survival function to model this:

S(t) = e^-(t/λ)β

Use the sliders below to adjust the parameters and age, then observe survival probability.

The median survival age is the age at which 50% of the population is expected to have survived. On the graph, this is shown as the point where the survival curve crosses the 0.5 level.

Question: At what age does the survival probability reach approximately 50%?
→ Use the sliders to test different values of β and see how the median survival age changes.