Network reliability analysis: Matrix-exponential approach

Abdullah Alkaff*, Mochamad Nur Qomarudin, Yusuf Bilfaqih

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


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.

Original languageEnglish
Article number107192
JournalReliability Engineering and System Safety
Publication statusPublished - Dec 2020


  • Matrix-exponential distribution
  • Network CVTTF
  • Network MTTF
  • Network hazard function
  • Network reliability function
  • Phase-type distribution
  • Sum of disjoint product


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