2.2 Reliability Measures
Several quantitative reliability measures for a nonrepairable unit are presented, including the failure function F(t), reliability function R(t), failure rate function z(t), mean time to failure (MTTF), and mean residual life (MRL). Their definitions are based on a continuous r.v. called time to failure (ttf), which is defined in Section 2.2.1.
2.2.1 Time to Failure
The time to failure T is a continuous r.v. defined as the time elapsing from when the unit is first put into function until its first failure. It models the lifetime of a nonrepairable unit.
2.2.2 Failure Function
The failure function of the unit is given as the cdf of r.v T, that is
where f(x) is the pdf of T. F(t) gives the probability that the unit fails within time interval (0, t].