Probability　distributions　of　random　variables　are　necessary　for　reliability　evaluation.　Generally,　probability　distributions　are　determined　using　one　or　two　parameters　evaluated　from　the　mean　and　standard　deviation　of　statistical　data.　However,　these　distributions　are　not　sufficiently　flexible　to　represent　the　skewness　and　kurtosis　of　data.　This　study　therefore　proposes　a　probability　distribution　based　on　the　cubic　normal　transformation,　whose　parameters　are　determined　using　the　skewness　and　kurtosis,　as　well　as　the　mean　and　standard　deviation　of　available　data.　This　distribution　is　categorized　into　six　different　types　based　on　different　combinations　of　skewness　and　kurtosis.　The　boundaries　of　each　type　are　identified,　and　the　completeness　of　each　type　is　proved.　The　cubic　normal　distribution　is　demonstrated　to　provide　significant　flexibility,　and　its　applicable　range　covers　a　large　area　in　the　skewness　kurtosis　plane,　thus　enabling　it　to　approximate　well-known　distributions.　The　distribution　is　then　applied　in　reliability　engineering:　simulating　distributions　of　statistical　data,　calculating　fourth-moment　reliability　index,　finding　optimal　inspection　intervals　for　condition-based　maintenance　system,　and　assessing　the　influence　of　input　uncertainties　on　the　whole　output　of　a　system.　Several　examples　are　presented　to　demonstrate　the　accuracy　and　efficacy　of　the　distribution　in　the　above-mentioned　reliability　engineering　practices.