User:Sharon Honecker/BasicStatBackgroundv11

Conditional Reliability Function

Conditional reliability is the probability of successfully completing another mission following the successful completion of a previous mission. The time of the previous mission and the time for the mission to be undertaken must be taken into account for conditional reliability calculations. The conditional reliability function is given by:

[math]\displaystyle{ R(T,t)=\frac{R(T+t)}{R(T)}\ \,\! }[/math]

Mean Life (MTTF)

The mean life function, which provides a measure of the average time of operation to failure of a new component, is given by:

[math]\displaystyle{ \overline{T}=m=\int_{0}^{\infty} t\cdot f(t)dt=\int_{0}^{\infty} R(t)dt\,\! }[/math]

This is the expected or average time-to-failure and is denoted as the MTTF (Mean Time To Failure).

The MTTF, even though an index of reliability performance, does not give any information on the failure distribution of the component in question when dealing with most lifetime distributions. Because vastly different distributions can have identical means, it is unwise to use the MTTF as the sole measure of the reliability of a component.

Mean Remaining Life

The mean remaining life function, which provides a measure of the average time of operation to failure of a component following the successful completion of a previous mission, is given by:

[math]\displaystyle{ L(t)=\int_{0}^{\infty} R(T,t)dt= \frac{\int_{0}^{\infty} R(T+t)dt}{R(T)}\ \,\! }[/math]