Consecutive　k-out-of-n:　F　systems　have　applications　in　the　fields　of　telecommunications　and　oil　pumping.　A　consecutive　k-out-of-n:　F　system　fails　if　at　least　consecutive　k　components　fail.　However,　practical　systems　may　fail　due　to　either　the　failure　of　a　number　of　consecutive　components　or　the　failure　of　a　total　number　of　components.　In　this　paper,　we　consider　a　system　with　linearly　arranged　components,　where　the　system　fails　if　at　least　a　pre-specified　number　of　consecutive　components　fail　or　a　pre-specified　total　number　of　components　fail.　The　system　is　termed　as　a　combined　consecutive　k　and　v-out-of-n　system.　The　iterative　relationship　between　the　failure　probability　of　a　consecutive　k-out-of-n:　F　system　has　been　proposed.　This　paper　focuses　on　the　iterative　relationship　between　the　success　probabilities　and　proposes　the　detailed　calculation　process　for　illustrative　purposes.　©　2018　Totem　Publisher,　Inc.　All　rights　reserved.