This paper proposes an improved interleaved voltage measurement method for battery packs in electric vehicles, which can distinguish between the sensor fault and cell fault without hardware or software redundancy. The coprime constraint in the basic interleaved measurement method is revisited with a new proof, and a graphical interpretation is introduced to visualize the constraint. Based on that, an improved measurement topology is developed to remove the coprime constraint which enables broader application. Moreover, the hardware implementation of the improved method is discussed based on cost and circuit design. The associated improvement in noise performance is mathematically formulated, and the noise limit and trend of the interleaved measurement method are derived. Simulation results match the noise analysis and experiments validate the broader application of the improved method.