Uniqueness of maximum likelihood estimators of the 2-parameter Weibull distribution

We present a simple statistic, calculated from either complete failure data or from right-censored data of type-I or -II. It is useful for understanding the behavior of the parameter maximum likelihood estimates (MLE) of a 2-parameter Weibull distribution. The statistic is based on the logarithms of the failure data and can be interpreted as a measure of variation in the data. This statistic provides: (a) simple lower bounds on the parameter MLE, and (b) a quick approximation for parameter estimates that can serve as starting points for iterative MLE routines; it can be used to show that the MLE for the 2-parameter Weibull distribution are unique.