Estimation of the stress-threshold for the Weibull inverse power law

Lifetime data on stress rupture of copper joints made with certain lead-free solders suggest that specimens under `stress below a certain threshold´ run indefinitely without failure. A commonly used model for this type of data is the Weibull inverse power law that includes a threshold. If the threshold is unknown, this estimation problem presents several difficulties for statistical treatment. The largest problem is: as the threshold approaches the minimum of the data (stresses) the likelihood approaches infinity, thus there is no global maximum. A modified maximum likelihood approach, in the spirit of Cohen is used to resolve this problem. The method is similar to Cohen´s, but interesting differences occur for censored data. The results show that modifications of the Cohen method produce estimates of the parameters in the Weibull inverse power threshold law