Industrial engineers use another type of statistical technique called reliability, a system that always produces the same results and that hopefully meets or exceeds its specifications. A product is analyzed using the reliability function (or survivor function): the probability of a unit in a system that does not fail in a certain specified time interval. If the unit does fail in a system, it means the end of the unit’s ability to perform the required function. This is determined by the failure distribution function, or the probability of an item failing in a specific time interval.

Calculations involving the common failure rates of various mechanical devices often results in a graph with a bathtub-shaped curve.