This paper presents parallel signature design techniques that guarantee the aliasing probability to be less than 2/L, where L is the test length. Using y signature samples, a parallel signature analysis design is proposed that guarantees the aliasing probability to be less than (y/L)/sup y/2/. Inaccuracies and incompleteness in previously published bounds on the aliasing probability are discussed. Simple bounds on the aliasing probability are derived for parallel signature designs using primitive polynomials.