Data　envelopment　analysis　(DEA)　has　been　extended　to　handle　random　inputs　and　outputs　by　using　chance　constrained　programming.　In　this　paper,　for　DMUs　with　random　inputs　and　outputs,　we　aim　to　measure　a　kind　of　relative　efficiency,　and　achieve　it　from　the　optimistic　viewpoint　and　the　pessimistic　viewpoint　respectively.　Considering　the　quantile　of　the　distribution　of　the　weighted　output-input　ratio　of　each　DMU,　we　develop　two　stochastic　DEA　models　to　obtain　the　upper　and　lower　bounds　of　the　quantile　efficiency　under　a　constraint,　and　then　achieve　an　interval　efficiency　evaluation.　The　best　quantile　efficiency　and　the　worst　quantile　efficiency　achieved　by　our　models　are　closely　similar　to　the　CCR　efficiency　and　belong　to　relative　efficiencies.　Further,　the　deterministic　equivalents　of　our　models　are　developed　when　the　input　and　output　vector　of　each　DMU　follows　a　multivariate　joint　normal　distribution.　Finally,　three　examples　are　presented　to　illustrate　the　performance　of　our　approach.　©　2017　Elsevier　Ltd