This paper proposes an optimal guaranteed robust fault detection and isolation (FDI) method combing the set-theoretic unknown input observer (SUIO) and the robust positively invariant (RPI) sets for linear time-invariant (LTI) systems. The optimality of the proposed FDI method is achieved under a two-layer framework. The first layer allows to design a single optimal FDI-oriented SUIO with RPI set separation based guaranteed FDI conditions to reduce the FDI conservatism of single observer. The second layer consists in designing an optimal observer configuration for a bank of optimal SUIOs to reduce the FDI conservatism of all the SUIOs together. Finally, the effectiveness of the proposed guaranteed robust FDI method is illustrated by using a four-tank system. (C) 2019 Elsevier Ltd. All rights reserved.