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The Weibull distribution is the workhorse of reliability engineering. Its shape parameter controls the failure pattern: k < 1 gives decreasing hazard (infant mortality), k = 1 constant hazard, and k > 1 wear-out.
Weibull CDF
F(x) = 1 − exp(−(x/λ)ᵏ)
Mean life
E = λ·Γ(1 + 1/k)
F = 1 − e^(−0.64) ≈ 0.4727, so reliability is about 52.7% and the mean life is 100·Γ(1.5) ≈ 88.62.
The Weibull reduces to the exponential distribution with a constant hazard rate — failures are memoryless.