Failure Time Distribution

Let be a nonnegative random variable that represents the failure time of an individual from a homogeneous superpopulation. The survival distribution function (also known as the survivor function) of is written as


A mathematically equivalent way of specifying the distribution of is through its hazard function. The hazard function specifies the instantaneous failure rate at . If is a continuous random variable, is expressed as


where is the probability density function of .