The monotone coherent of series-parallel system and parallel-series system

This paper has proved that the series-parallel system and the parallel-series system are the coherent systems. Furthermore, we give the coherent structure function of series-parallel connection system φ (x) = ⁿΠ_j=1^m?_i=1 x_ij and the coherent structure function of parallel-series system φ (x) = ⁿΠ_j=1^m?_i=1 x_ij and we also give the dual coherent structure function.