Network reliability analysis: matrix-exponential approach

Highlights: • An exact algebraic method for generating networks' reliability and hazard functions • It can be used also for calculating networks' mean and variance of time to failure • Process components' reliability functions using sums of disjoint products algorithm • Components' lifetimes have matrix-exponential, phase-type, and other distributions • Applicable for general structure systems 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.