The Weibull Distribution is used almost exclusively for failure analysis. The most common application is to model the waiting time to failure (life length) or between failures of a component, assuming the failure rate is a polynomial function of time. The Weibull Distribution is also used as a tolerance distribution in the analysis of quantal response data.
The Weibull Distribution is defined for all positive values of x. It has two parameters, k and lamda, both of which must be positive. In addition, k must be an integer. The distribution is:
where x>0, k=1,2,..., and lamda>0.
The equations for the mean and variance are:
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