In this study some mathematical models in reliability systems were investigated, such as series , parallel , series – parallel , parallel – series and complex systems by using some methods such as ; path tracing method, reduction to series element method ,minimal cut method , event space method , composite method and decomposition method . A comparison was done between those methods to get the best reliability. Reliability allocation had been studied .The aim of it is to establish a goal or objective for the reliability of each component. Two methods had been used to find the reliability allocation for series and complex systems. This study also discuss the reliability for non – maintenance depending on the application of Markov and non – Markov models.