Weighted likelihood based inference for P(X < Y)

This contribution deals with the statistical problem of evaluating the stress–strength reliability parameter R = P(X < Y), when both stress and strength data are prone to contamination. Standard likelihood inference can be badly affected by mild data inadequacies, that often occur in the form of several outliers. Then, robust tools are recommended. Here, inference relies on the weighted likelihood methodology. This approach has the advantage to lead to robust estimators, tests, and confidence intervals that share the main asymptotic properties of their classical counterparts. The accuracy of the proposed methodology is illustrated both by numerical studies and real-data applications.