This paper discusses the parity space-based fault detection (FD) method for a class of linear discrete-time systems with integral measurements.The integral measurements are functions of the system states over a given time window.We establish a novel parity relation to tackle integral measurements.The parameters of the FD unit are redesigned such that the generated residual signal is simultaneously decoupled from initial states,robust against disturbances,and sensitive to the faults.We employ the singular value decomposition algorithm to calculate parity space matrices.Finally,an experiment is presented to show the effectiveness of the proposed method.