Statistics for Maintenance Modelling: Continuous Lifetime Distributions 1

# The Weibull Distribution¤

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Weibull distributions are widely used for modelling lifetime distributions. One of the main reasons for this is the flexibility of the distribution shapes that can be approximated by varying the Weibull's two parameters. The pdf is given by:

Here is the scale parameter and is the shape parameter (sometimes is referred to as the characteristic life as it is the time at which 63.2% of the population will have failed). Click here to see an alternative parameterisation for the Weibull distribution which is also used frequently throughout this module.

If is 1, then we have the exponential distribution, and .

The mean of the distribution is: and the standard deviation is: .

Here is the gamma function defined by for t > 0 (click here for more on the gamma function).

Hence for the exponential distribution, the mean is (since (2) = 1).