eng Science and Education Publishing American Journal of Applied Mathematics and Statistics 2328-7292 2014-01-07 2 1 29 33 10.12691/ajams-2-1-5 AJAMS2014215 article U.A. Ali 1 Saminu I. Bala 2 3 Ibrahim Yusuf Ibrahimyusuffagge@gmail.com 3 Department of Mathematics, Usmanu Danfodio University, Sokoto, Nigeria Department of Mathematical Sciences, Bayero University, Kano, Nigeria 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. http://pubs.sciepub.com/ajams/2/1/5/ajams-2-1-5.pdf Mean time to system failureonline preventive maintenance