Coherent systems play a key role in the studies of reliability of technical systems in reliability engineering. A system is said to be a coherent system if it does not have any irrelevant component (a component is said to be irrelevant if its performance does not effect on the performance of the system), and the system is not decreasing in each vector argument. In other words a system is "coherent" when each of its working components is beneficial to the system. "Signature" witch introduced by Samaniego, is a very useful concept to study lifetime distributions. One can write the lifetime distribution function of a coherent system as a mixture of the distribution functions of the ordered lifetimes of its component. we introduce some important definitions like Reliability function, Failure rate function, Reversed failure rate function, Mean residual lifetime function, Inactivity lifetime and some ltr"