This paper discusses the reliability analysis of a three component identical system. The system may affects by two types of failures viz., Lethal Common Cause Shock (LCCS) and Non-Lethal Common Cause Shock (NCCS) failures. By using stochastic process, the set of differential equations of the existing model are derived to attain reliability measures such as system reliability and Mean Time to Failure (MTTF) in both series and parallel cases. In addition, the Maximum Likelihood Estimates (MLE) of the above said measures are derived and shown in numerical illustration by using simulation process. The numerical tables shows the outcomes and recommend that LCCS and NCCS are the most leading causes of failures while studying the performance of the systems in reliability theory.