Mean Residual Life

Definition

Mean Residual Life $mrl(t)$: $mrl(t)=E\text{[}T-t\mid T>t]=\frac{\int \_t^{\infty }S(u)du}{S(t)}$

The expected remaining time after surviving $t$.

About Mean Residual Life

Interpreting $E\text{[}T-t]$ given $T>t$:

• $T-t$: How much time remains from now ($t$) until the event $(T)$
• $E\text{[}T-t]$: Mean of time left (survival time)

It’s basically the mean of remaining time left before event occurs.

Related

• Mean Residual Life Formula Derivation
• Survival Function