Empirical Bayes decision rule for classification on defective items in Weibull distribution

In this paper, the lifetime of a new item or product, which has a Weibull distribution, is classified into one of good and defective classes or identified as an item produced form one of two production lines. A set of unlabelled samples is used to establish an empirical Bayes (EB) classifier to classify defective items. Our classifier has the following properties: (1) it has the minimum probability of misclassification (no other classifier is better than our classifier), (2) when our classification system is put in use, the new unidentified items will adapt our system to be a better and more accurate classifier, and (3) it can accurately estimate the parameters of two classes (or two production lines). A Monte Carlo simulation using Weibull distribution demonstrates the performance of our classifier.