Hazard is the probability that an event of interest, in reliability engineering a failure, occurs in the next instant, given that is has survived so far. Therefore, you need the pdf at moment x and you need the reliability at x to calculate the hazard rate at x.
Therefore, the hazard function or hazard rate
Cumulative hazard function H(x) is
An example hazard function is the bathtub curve, which is higher for small values of x, then decreases to some minimum, and thereafter increases again. This curve represents failures at the start of the operation, settling in, followed by an increase in failure due to aging of the equipment.
