This paper presents the reliability modelling and analysis of a complex industrial system with two units operating in parallel. To facilitate the study, real failure-maintenance data of the system arecollected. Data depicts that a unit is repaired upon failure by a single repairman. Reliability indices of the system such as mean time between failures, availability, expected number of repairs, and expected busy period of the repairman are estimated using semi-Markov processes and regenerative processes. Finally, a comparative analysis between the reliability indices of three reliability models for the system is presented.