Robust inference in the stress-strength model

We address the problem of robust inference about the reliability parameter R=P(X>Y) in the stress-strength model. Likelihood based procedures for inference on R are available, but it is well-known that they can be badly affected by mild departures from model assumptions, regarding both stress and strength data. The proposed robust method for inference on R relies on M-estimation theo- ry. Large-sample tests with the standard asymptotic behavior and confidence intervals with robustness properties are obtained by resorting to the optimal B-robust estimators. The methodology is illustrated by a numerical study, when both the stress Y and the strength X are exponentially distributed.