Reliability Analysis of Regular Distributed Chain Structures

This paper considers the reliability analysis of chain structures of identical sections. The sections are distributed in the sense that there is more than one input and output node to each section. System failure occurs if no path exists between system input and output. (System branch failures are by open circuit only.) This model is particularly applicable to redundant communication systems. It is shown that the distributed chain structure is asymptotically equivalent to a series structure of identical equivalent sections, assuming that the number of sections is large and that the branch reliabilities are equal. The reliability of the equivalent section is obtained as the subdominant eigenvalue of a transition matrix. The error in this representation is negligible for system branch reliabilities large.