A Quick Inclusion-Exclusion technique.

Highlights • A Quick Inclusion-Exclusion (QIE) technique is proposed. • The proposed QIE is for multi-state flow network reliability problems. • The proposed QIE is easy to code and only needs one comparision in each (intersection) term. • The proposed QIE is simpler than the traditional IE. • The proposed QIE is faster than the RSDP which is the most popular sum-of-disjoint product method. Abstract The reliability of modern information systems modeled as multi-state flow networks (MFNs) is a crucial concern the planning, design and control of these systems. The inclusion-exclusion technique (IET) is a popular tool for assessing MFN reliability because it is simple and easily understood. However, it is less efficient than other methods, like the sum-of-disjoint product method (SDP), for example. This paper proposes a new IET, called the Quick Inclusion-Exclusion technique (QIE) to increase the efficiency of the IET and reduce the amount of memory required in MFNs. The correctness and the time complexity of QIE is analyzed and proven. An MFN reliability example is implemented to illustrate the proposed QIE. In order to demonstrate its performance, the proposed QIE is compared with the most popular SDP, the recursive SDP (RSDP) in 20 benchmark networks taken from the literature. Numerical examples demonstrate that the proposed QIE outperforms RSDP in terms of both efficiency and memory use. This result differs significantly from those obtained by traditional methods. [ABSTRACT FROM AUTHOR]