Statistics

Weibull Distribution Calculator

Find the reliability and mean life of a Weibull distribution.

Calculated Output

P(X ≤ x) 0.5111

Mean 90.275

Formula: P(X ≤ x) = 1 − e^(−(x/λ)^k); mean = λ·Γ(1+1/k)

Step-by-Step Breakdown

1. Values used:

2. Shape (k) = 1.5

3. Scale (λ) = 100

4. Value x = 80

6. P(X ≤ x) = 0.5111

7. Mean = 90.275

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The math behind it

P(X ≤ x) = 1 − e^(−(x/λ)^k). Shape k < 1 means early failures, k > 1 means wear-out.

k 1.5, λ 100, x 80 → P ≈ 0.51, mean ≈ 90.3.

What does the shape tell you?

k = 1 is exponential (random failures); k > 1 indicates aging.