Asian Journal of Scientific Research1992-14542077-2076orgz10.3923/ajsr.2017.128.138GenidyMohammed Mohammed ElHebeshyEsraa Ahmed32017103Background and Objective: In engineering, redundancy is the duplication of critical components or functions of a system with the intention of increasing reliability and decreasing the failure rate of the system, usually in the case of fail-safe. This study aimed to create mathematical model to find the optimum values of the distribution parameters of the triple modular redundant system. Therefore, the system will be higher safety, longer lifetime and higher reliability with smaller failure rate. Methodology: The maximum likelihood estimation and order statistics were applied to estimate the optimum values of the failure rate, reliability and lifetime for the Triple Modular Redundancy (TMR) system, which contains three electronic redundancy units with Weibull distribution. Results: The numerical values of the failure rate, reliability and lifetime of the triple modular redundant system were obtained using Weibull distribution. Conclusion: Thus, the designing of TMR system can be longer lifetime and higher safety. Moreover, the risks of sudden failure and economic losses will be decreased.]]>Al Mutairi Alya, O., H.C. Low,2014Alagoz, B.B.,2008Alharpy, A.M. and N.A. Ibrahim,2013El Damsesy, M., M. El Genidy and A. El Gazar,2015El Genidy, M.M.,2012El Genidy, M.M.,2014Pan, K., Y. Guo, G. Ren and H. Lin,2014Reshid, M.N. and M.A. Abd Majid,2011Saat, N.Z.M., A.A. Jemain and S.H.A. Al-Mashoor,2008Zhang, Z., D. Liu, Z. Wei and C. Sun,2006Cai, B., Y. Liu, Z. Liu, X. Tian, X. Dong and S. Yu,2012Dobel, B., H. Hartig and M. Engel,2012Yao, J., S. Okada, M. Masuda, K. Kobayashi and Y. Nakashima,2012Van Gemund, A.J.C. and G.L. Reijns,2012k-out-of-n systems with single cold standby using pearson distributions.]]>Henkel, J., L. Bauer, N. Dutt, P. Gupta and S. Nassif et al.,2013Legat, U., A. Biasizzo and F. Novak,2012Egwutuoha, I.P., D. Levy, B. Selic and S. Chen,2013El-Maleh, A.H. and F.C. Oughali,2014Cai, B., Y. Liu, Z. Liu, X. Tian, Y. Zhang and R. Ji,2013Petrovic, V., M. Ilic, G. Schoof and Z. Stamenkovic,2012