In statistical engineering the "hazard rate" of a distribution is defined as:
where $f(x)$ and $F(x)$ are the PDF and CDF. Basically $r(x)$ is the odds that, having reached a certain point on the abscissa (usually time), you won't get any further. In the study of mechanical failure, the relevant distributions are those with an $r(x)$ that is everywhere increasing for positive x, like the Weibull distribution.
My question is how would you interpret an $r(x)$ whose absolute value is everywhere increasing for positive x, but which is negative? Does the sign matter?