A stochastic order consisting of a shifted version of 

the well-known reversed hazard rate order is proposed. 

Namely, for two continuous random variables $X$ and $Y$ 

we say that $X$ is smaller than $Y$ in the up reversed 

hazard rate order, denoted as $X\LEQ{rh$\uparrow$}Y$, 

if $X-x\LEQ{rh} Y$ for each $x\geq 0$. Some properties 

of such order are presented, including the preservation 

under {\em (i)\/} transformations by strictly monotone 

convex functions, {\em (ii)\/} formation of coherent 

systems, {\em (iii)\/} Poisson shock models.