Technical Report on the Evaluation of Median Rank Regression and Maximum Likelihood Estimation Techniques for a Two-Parameter Weibull Distribution

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Virginia Tech


Practitioners frequently model failure times in reliability analysis via the Weibull distribution. Often risk managers must make decisions after only a few failures. Thus, an important question is how to estimate the parameters of this distribution for small sample sizes. This study evaluates two methods: maximum likelihood estimation and median rank regression. Asymptotically, we know that maximum likelihood estimation has superior properties; however, this study seeks to evaluate these two methods for small numbers of failures and high degrees of censoring. Specifically, this paper compares the two estimation methods based on their ability to estimate the individual parameters, and the methods’ ability to predict future failures. The last section of the paper provides recommendations on which method to use based on sample size, the parameter values, and the degree of censoring present in the data.