Weibull Distribution

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The 'Swiss Army Knife' of failure analysis, capable of modeling infant mortality, random failures, and wear-out.

Parameters

Shape Parameter (k)

Scale Parameter (λ)

Evaluation Point (x)

Distribution Results

Prob P(X ≤ x)94.09%

Infant Mortality

Random Failure

Wear-out

Reliability R(x)5.91%

Mean Life0.9027

Median Life0.7832

Mode0.4807

Std Deviation0.6129

Density0.1254

About this calculator

Overview

The Weibull distribution is a versatile probability distribution used extensively in reliability engineering and failure analysis. By adjusting the shape parameter (k), it can model many different types of failure rates, from "infant mortality" (decreasing failure rate) to "wear-out" (increasing failure rate).

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Pro Tips

Use k < 1 to model products that fail early due to manufacturing defects.
Use k > 1 to model mechanical components that wear out over time.
The scale parameter (λ) is the characteristic life; it represents the time at which 63.2% of the population will have failed.

Fun Facts

"When k = 3.4, the Weibull curve looks almost exactly like a Normal distribution."
"If k = 1, it is identical to the Exponential distribution, representing random failures with a constant rate."
"The Weibull distribution is named after Swedish mathematician Waloddi Weibull, who described it in 1951."

Formula: CDF: 1 - e^{-(x/λ)^k}