AbstractIn destructive stress testing, industrial quality control, or other situations, data may consist only of record setting values, such as successive values that are smaller than all previous ones observed. Here, for a two‐parameter Weibull distribution, the performance of the maximum likelihood estimators (MLEs) from record‐breaking data is studied by computer simulations. Comparison of the biases and mean squared errors of these estimators with those of the MLEs for complete samples from the Weibull distribution is discussed and some examples are presen