Weibull Distribution
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Tap a term to see what it means, or .
Calculate
Example: the life of a light bulb, in thousands of hours, follows a Weibull with shape 1.5 and scale 10. What is the chance it burns out before 5,000 hours? Change the values to work out your own case.
Step by step
What each term means
- Density (f(x))
- The height of the curve at time x. The area under it up to x is the chance that the failure has already happened.
- Shape over Scale (k/λ)
- Sets the scale of the failure rate. The shape k decides whether the risk falls (k < 1), stays constant (k = 1) or grows with age (k > 1).
- Relative Age ((x/λ)ᵏ⁻¹)
- Time measured in units of λ. Together with k/λ, it forms the failure rate: the risk of breaking now, for something that has lasted until now.
- Survival (e^(−(x/λ)ᵏ))
- The chance of lasting beyond x. At x = λ it equals e⁻¹ ≈ 37%, whatever the shape: λ is the characteristic life.