The estimation of optimal support boundaries under the monotonicity constraint is relatively unexplored and still in full development. This article examines a new extreme-value based model which provides a valid alternative for completely envelopment frontier models that often suffer from lack of precision, and for purely stochastic ones that are known to be sensitive to model misspecification. We provide different motivating applications including the estimation of the minimal cost in production activity and the assessment of the reliability of nuclear reactors.