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.