This study will establish a new Markov reliability model using a more generalized approach in the development of an analytical estimation for the reliability of a large repairable computer system. The developed methods will present a precise way to establish reliability for computer systems' use which consist of hardware and software. This generic model, the N-channel and M-voter reliability model, is suitable for analyzing multiprocessor systems, array redundant systems, and larger repairable networked systems. All results are verified through use of currently published reliability models. The first part of the study introduces a general outline for computer hardware and software reliability, goal statement and barriers issues. A review of current literature on Markov system reliability models linked to the research is noted in the second part. The third section deploys new model methodology and solutions. The fourth reveals significant results, analysis and applications. The conclusions and summary are presented in the final chapter. Discussions and recommendations are also presented in the last chapter.