Network reliability analysis: matrix-exponential approach

An exact method for analyzing the reliability of networks whose components' lifetimes have matrix-based distributions is proposed. The method produces an add-on algorithm for the available sum of disjoint products (SDP) algorithms so that they can be utilized to calculate the parameters of the network reliability function directly from the parameters of the component reliability functions. Until now, SDP algorithms have only been used to calculate a network reliability value from the reliability values of its components. The advantage is that once the network reliability function is obtained, other reliability measures, such as the network's hazard function, the mean time to failure (MTTF), and the coefficient of variation of the time to failure (CVTTF), can be obtained using only matrix algebra. An extension to general systems containing basic structures that cannot be expressed as an SDP is given. The method is applicable for both phase-type (PH) and matrix-exponential (ME) distributions. The applicability of the method for other distributions is made possible by using PH distributions as their approximation. An application and comparison with a method based on the state-space model are presented to show the superiority of the proposed method, alongside a strategy to reduce its computation time.

Automated summary

An exact method for analyzing network reliability based on matrix-based component lifetimes is proposed, which introduces an add-on algorithm to SDP algorithms for direct calculation of network reliability parameters. Once the network reliability function is obtained using matrix algebra, other reliability measures can be determined. This method is applicable for both phase-type and matrix-exponential distributions, and can be extended to other distributions through the use of PH distributions as approximations.