Estimation of Weibull Distribution Shape Parameter When No More Than Two Failures Occur per Lot

An estimate, with limits of uncertainty, is given for the shape parameter of the Weibull distribution when failure experience results from lots having different quality levels. The data result from the following situation. Lots are removed from service at some target value, normally after experiencing no failures. Some lots experience one failure, and the remaining non-failed items remain in service until the target value is reached. Finally, there are a few lots in which two failures occur. In this instance, all remaining non-failed items are removed immediately after the second failure occurs. It is assumed that all lots have the same shape parameter, with lot differences, when they exist, appearing as differences in the scale parameter value.