Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2 1 2014 01 07 Evaluation of Mean Time to System Failure of a Repairable 3-out-of-4 System with Online Preventive Maintenance 29 33 EN U.A. Ali Saminu I. Bala Ibrahim Yusuf Department of Mathematical Sciences, Bayero University, Kano, Nigeria AJAMS2014215 10.12691/ajams-2-1-5 2013 08 14 2013 11 24 2014 01 07 Most of the literature assumed that systems undergo preventive maintenance. Little literature is found on whether the preventive maintenance is online or offline. It is known that most of the engineering systems undergo both online and offline preventive maintenance. In this paper, we studied the mean time to system failure of a repairable redundant 3-out-of-4 system with online preventive maintenance involving four types of failures. We develop the explicit expressions for mean time to system failure for the system using Chapman-Kolmogorov equations. Various cases are analyzed graphically to investigate the impact of system parameters on mean time to system failure. Results have shown that system with online preventive maintenance is better in terms of mean time to system failure of system than system without preventive maintenance.