Ever since Gaver (1963) made an attempt to analyse a two unit parallel redundant system, several attempts have been made by many applied probabilists, engineers to analyse two-unit parallel redundant systems. While various authors have analysed systems with different assumptions on the failure and repair time distribution of the units, the solution to the case where both the failure and repair time distributions are arbitrary does not seem to be easy. In this article a systematic review of the methods that are available to solve the above mentioned system is made. Also, it explains why this particular case is not solvable by the methods like Semi Markov Process and regenerative process etc. Finally, it provides expressions for the measures like reliability, mean time to system failure, and availability for the most general soluable case.