A major difficulty with the practical application of the multiple observer based IFDI schemes is the computational burden of the residual generation. In this paper, a new residual generator that employs function observers is proposed to reduce the computational burden, and the design methods of the IFDIS, equipped with the residual generator, are presented. The function observers employed in the residual generator can be considered as a dual of the unknown input (function) observer And it can be designed to estimate the measurement errors that are due to sensor faults. The error estimates are further processed to generate the residuals by which reliable fault detection/isolation result car be obtained. The proposed scheme is more useful, in real-time application, than any other multiple state observer based IFDISs. It can be effectively applied to fault tolerant control because the failure effects can be compensated by the use of the estimates of measurement errors. The proposed IFDI scheme is applied to an inverted pendulum control system for the IFDI of failed sensor and fault compensation.