Let and be two nonnegative absolutely continuous random
variables with respective distribution functions and such that ,
right-continuous inverse functions and , and survival functions
and , respectively. We write , and say is
smaller than in the DMRL (decreasing mean residual life) order, if the function
is increasing in .
Some characterization properties of the DMRL order are investigated. The closure
and reversed closure properties of the DMRL order are obtained. Meanwhile, some illustrative
examples that meet the DMRL order are shown as well.