# Weibull Distribution

The Weibull distribution is a continuous probability distribution. It models a broad range of random variables, largely in the nature of a time to failure.

ChiAha's Weibull distribution uses the two parameter model:

Parameter 1 is the

*scale parameter*Parameter 2 is the

*shape parameter*

Parameter 2 can be interpreted as follows:

A value less than 1 indicates that the failure rate decreases over time. This happens if there are significant pre-mature failures.

A value equal to 1 indicates that the failure rate is constant over time. This might suggest random external events are causing interrupts or failures. The Weibull distribution here reduces to an exponential distribution.

A value greater than 1 indicates that the failure rate increases with time. This happens if there is an "aging" process, or parts that are more likely to fail as time goes on. These are typically described as wear-out failure modes. As the value grows above 1, the Weibull distribution reduces from a lognormal distribution to approaching a normal distribution.

The example below shows the probability density function for 4 Weibull distributions. Each distribution has a parameter 1 value of 1.0 and a range of parameter 2 values from 0.5 to 5.0.

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