It is identical in concept to failure rate, also called hazard function, in reliability theory.
In a life table, we consider the probability of a person dying from age x to x + 1, called qx.
The force of mortality μ(x) uniquely defines a probability density function fX(x).
This is expressed in symbols as or equivalently In many instances, it is also desirable to determine the survival probability function when the force of mortality is known.
To do this, integrate the force of mortality over the interval x to x + t By the fundamental theorem of calculus, this is simply Let us denote then taking the exponent to the base e, the survival probability of an individual of age x in terms of the force of mortality is