Majority systems, whose correct operation usually requires a specific number of components, are ubiquitous and have been used in various critical infrastructures. To capture a deeper understanding, we consider several types of majority systems, i.e., consecutive (i.e., linear and circular ones) and symmetrical systems. Moreover, to enhance the accuracy and efficiency of reliability evaluation, stochastic analysis architectures are proposed: input signal probabilities of any distributions can be addressed efficiently with the adoption of non-Bernoulli sequences, consisting of random permutations of fixed numbers of ones and zeros. Via propagating the sequences within constructed stochastic architectures, we can derive the system reliability. Moreover, various benchmarks are analyzed through stochastic analysis, and we also compare the corresponding results with those obtained using other approaches. Though the accuracy of stochastic analysis is largely affected by the employed sequence length, an acceptable accuracy can be attained with the adoption of a reasonable sequence length. In this line, the optimal design is also investigated for different implementations.