In order to improve fault detection (FD) performance, integrated design of residual generation and evaluation is investigated in this paper for trade-offs between fault detection rate and false alarm rate (FAR). A set-membership approach is proposed in residual evaluation by adopting a threshold ellipsoid, which enables more design freedom than a conventional threshold value. With the set-based definitions of fault detection rate and FAR, the integrated design problem is formulated by maximizing the FD performance under a predefined FAR. The joint optimal selection of a residual generator and a threshold ellipsoid is equivalently transformed into a simplified optimization problem of determining an optimal threshold ellipsoid for any given residual generator. A suboptimal solution for the set-membership-based integrated FD system design is obtained based on approximated computation of the FD performance. Monte Carlo simulations show the performance improvement of the proposed method compared with an existing integrated design method.