In our article "The Evaluation of Median-Rank Regression and Maximum Likelihood Estimation Techniques for a Two-Parameter Weibull Distribution" we sought to provide an objective comparison between median rank regression and maximum likelihood estimation for cases with extremely high censoring rates and very few failures. Through discussion of the article we have had the opportunity to engage with many great minds in the field of reliability analysis and would like to take this chance to highlight some of the key points that we came across in this discussion. We hope our insights prove useful to the Quality Engineering reader. We would like to begin by thanking Dr. Robert Abernethy for his comments. He highlights an important point that we also observed in our simulation studies, that the maximum likelihood estimation (MLE) of beta is usually larger than the median-rank regression (MMR) estimate of beta for few failures and high censoring rates. This has important implications for practitioners, because the shape parameter reflects the failure mechanism.
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