Advancement　and　application　of　rule-based　expert　systems　have　been　a　key　research　area　in　explainable　artificial　intelligence　(XAI)　because　the　rule-base　is　one　of　the　most　common　and　natural　explainable　frameworks　for　knowledge　representation.　The　present　work　aims　to　design　a　novel　rule-based　system,　called　Cumulative　Belief　Rule-Based　System　(CBRBS),　by　establishing　efficient　rule-base　modeling　and　inference　procedures,　where　the　rule-base　modeling　procedure　includes　the　generation　of　cumulative　belief　rules　via　numeric　data　transformation　and　extended　belief　rule　integration,　and　the　rule-base　inference　procedure　includes　the　inference　of　cumulative　belief　rules　via　consistent　rule　activation　and　activated　rule　integration.　All　these　procedures　enable　CBRBS　to　better　achieve　the　balance　of　explainability,　high-efficiency　(or　computing　complexity),　and　accuracy　to　fit　with　different　application　scenarios,　as　well　as　overcome　the　limitations　of　classical　rule-based　systems.　Extensive　experiments　based　on　the　well-known　pipeline　leak　detection　problem　and　open-source　classification　problems　are　conducted　to　illustrate　the　feature　and　advantage　of　the　CBRBS　over　other　classical　rule-based　systems　and　some　commonly　used　classifiers.　©　2021　Elsevier　B.V.