hazard rate

[Karen]

When studying, I came across the following:
For a continuous random variable, the hazard rate or failure rate is h(x)=f(x) divided by (1-F(x))

Could someone explain what this is and when it is used?
Thanks!

[FSA]

It's the density of a left-truncated distribution function.

It can be viewed as the probability of failure at a time x given that failure has not already occured prior to x.

[krzysio]

This conditional probability definition of the harard rate needs to be slightly more precise. The hazard rate becomes that probability only approximately and only in the short interval just beyond x, i.e., x + dx, after it is multiplied by dx. But the best strategy about the hazard rate is to accept instantly the idea that it is very important, because for X being the length of life, the hazard rate is the force of mortality, and, well, half of exam M is about the force of mortality.

Yours,
Krzys'