Thispaperpresentsafactoringalgorithmforcomputingsource-to-Kterminal(SKT)reliability,theprobabilitythatasourceacansendmessagetoaspcifiedsetofterminalsK,inacyclicdirectednetworks(AD-networks)inwhichbothnodesandedgescanfail,BasedonPivotaldecompositiontheorem,anewformulaisdevivedforcomputingtheSKTreliabilityofAD-networks.ByestablishingatopologicalpropertyofAD-networks,itisshownthattheSKTreliabilityofAD-networkscanbecomputedbyrecursivelyapplyingthisformula,TwonewReliabilityPreservingReductionsarealsointroduced.Therecursiontreegeneratedbythepresentedalgorithmhasatmost2^(|V|-|K|-|C|leafnodes,where|V|and|K|arenodessatisfyingsomespecifiedconditions.ThecomputationcomplexityofthenewalgorithmisO(|E|·|V|·2^(|V|-|K|-|C|)intheworstcasewhere|E|isthenumberofedges.Forsource-to-all-terminal(SAT)reliability,itscomputationcomplexityisO(|E|).ComparisonofthenewalgorithmwiththeexistingonesindicatesthatthenewalgorithmismoreefficientforcomputingtheSKTreliabilityofAD-networks.
