Best practices for fitting the 1-parameter Weibull distribution

This paper presents an evaluation of different techniques used to fit the 1-parameter Weibull distribution for complete and type-II censored data [1]. Rank regression (RR), maximum likelihood (ML) and reduced bias adjusted maximum likelihood (RBA ML) are compared over a wide range of sample sizes, Weibull slope (β), number of Type-II censored units as well as error in the assumed β value. Similar to the 2-parameter Weibull, rank regression performed most consistently across the range studied, although it was not the lowest biased estimate in all cases [2]. In particular, for complete data of 2 or more samples, RBA MLE provides the lowest bias estimate of the Weibull position parameter (η). For a sample size of 1, RR provides the lowest bias estimate; however, it is biased optimistically. For Type-II censored data, RR provides the lowest bias estimate below ~10 failures, above which ML works best.