Comparison of robust and least-squares regression in computer-generated probability plots

ML-estimators (maximum likelihood) offer a promising alternative to least squares (LS) methods and the best-guess of a researcher when fitting a line to failure-time data plotted on a computer-generated probability plot. In terms or model statistics, these robust regression algorithms performed better than LS in most data sets. The Andrews function and the Ramsay function always performed better than LS. The Huber function and the Hampel function usually performed better than LS except for those data sets where the residuals did not exceed the threshold criteria and all residuals were assigned a weight of 1.0. In those situations, these two ML-estimators provided results which were equivalent to LS. The ML-estimators were particularly effective in situations involving near-neighbors in the low region of the x-space (early contiguous failures). In terms of parameter estimation, there was no noticeable difference between LS and the ML-estimators.