AM  Vol.4 No.1 , January 2013
Optimal Redundancy Allocation in Hierarchical Series-Parallel Systems Using Mixed Integer Programming
Abstract: Reliability optimization plays an important role in design, operation and management of the industrial systems. System reliability can be easily enhanced by improving the reliability of unreliable components and/or by using redundant configuration with subsystems/components in parallel. Redundancy Allocation Problem (RAP) was studied in this research. A mixed integer programming model was proposed to solve the problem, which considers simultaneously two objectives under several resource constraints. The model is only for the hierarchical series-parallel systems in which the elements of any subset of subsystems or components are connected in series or parallel and constitute a larger subsystem or total system. At the end of the study, the performance of the proposed approach was evaluated by a numerical example.
Cite this paper: M. Ziaee, "Optimal Redundancy Allocation in Hierarchical Series-Parallel Systems Using Mixed Integer Programming," Applied Mathematics, Vol. 4 No. 1, 2013, pp. 79-83. doi: 10.4236/am.2013.41014.

[1]   C. Ha and W. Kuo, “Reliability Redundancy Allocation: An Improved Realization for Nonconvex Nonlinear Programming Problems,” European Journal of Operational Research, Vol. 171, No. 1, 2006, pp. 24-38. doi:10.1016/j.ejor.2004.06.006

[2]   J.-H. Zhao, Z. Liu and M.-T. Dao, “Reliability Optimization Using Multi-Objective Ant Colony System Approaches,” Reliability Engineering and System Safety, Vol. 92, No. 1, 2007, pp. 109-120. doi:10.1016/j.ress.2005.12.001

[3]   M. Nourelfath and Y. Dutuit, “A Combined Approach to Solve the Redundancy Optimization Problem for Multi-State Systems under Repair Policies,” Reliability Engineering and System Safety, Vol. 86, No. 3, 2004, pp. 205-213. doi:10.1016/j.ress.2004.01.008

[4]   A. Azaron, H. Katagiri, M. Sakawa and M. Modarres, “Reliability Function of a Class of Time-Dependent Systems with Standby Redundancy,” European Journal of Operational Research, Vol. 164, No. 2, 2005, pp. 378-386. doi:10.1016/j.ejor.2003.10.044

[5]   P.-S. You and T.-C. Chen, “An Efficient Heuristic for Series-Parallel Redundant Reliability Problems,” Computers & Operations Research, Vol. 32, No. 8, 2005, pp. 2117-2127. doi:10.1016/j.cor.2004.02.003

[6]   Y.-C. Liang and A. E. Smith, “An Ant Colony Optimization Algorithm for the Redundancy Allocation Problem (RAP),” IEEE Transactions on Reliability, Vol. 53, No. 3, 2004, pp. 417-423. doi:10.1109/TR.2004.832816

[7]   P. S. Shelokar, V. K. Jayaraman and B. D. Kulkarni, “Ant Algorithm for Single and Multi-Objective Reliability Optimization Problems,” Quality and Reliability Engineering International, Vol. 18, No. 6, 2002, pp. 497-514. doi:10.1002/qre.499

[8]   N. Nahas and M. Nourelfath, “Ant System for Reliability Optimization of a Series System with Multiple-Choice and Budget Constraints,” Reliability Engineering and System Safety, Vol. 87, No. 1, 2005, pp. 1-12. doi:10.1016/j.ress.2004.02.007

[9]   G. S. Mahapatra and T. K. Roy, “Fuzzy Multi-Objective Mathematical Programming on Reliability Optimization Model,” Applied Mathematics and Computation, Vol. 174, No. 1, 2006, pp. 643-659. doi:10.1016/j.amc.2005.04.105

[10]   M. Ouzineb, M. Nourelfath and M. Gendreau, “An Efficient Heuristic for Reliability Design Optimization Problems,” Computers & Operations Research, Vol. 37, No. 2, 2010, pp. 223-235. doi:10.1016/j.cor.2009.04.011

[11]   C.-Y. Li , X. Chen, X.-S. Yi and J.-Y. Tao, “Heterogeneous Redundancy Optimization for Multi-State Series-Parallel Systems Subject to Common Cause Failures,” Reliability Engineering & System Safety, Vol. 95, No. 3, 2010, pp. 202-207. doi:10.1016/j.ress.2009.09.011

[12]   V. K. Sharma, M. Agarwal and K. Sen, “Reliability Evaluation and Optimal Design in Heterogeneous Multi-State Series-Parallel Systems,” Information Sciences, Vol. 181, No. 2, 2011, pp. 362-378. doi:10.1016/j.ins.2010.09.015

[13]   M. S. Chern, “On the Computational Complexity of Reliability Redundancy Allocation in a Series System,” Operations Research Letters, Vol. 11, No. 5, 1992, pp. 309-315. doi:10.1016/0167-6377(92)90008-Q

[14]   S. B. Graves, D. C. Murphy and J. L. Ringuest, “Acceptance Sampling and Reliability: The Tradeoff between Component Quality and Redundancy,” Computers & Industrial Engineering, Vol. 38, No. 1, 2000, pp. 79-91. doi:10.1016/S0360-8352(00)00030-9

[15]   T. Nakagawa and K. Yasui, “Note on Optimal Redundant Policies for Reliability Models,” Journal of Quality in Maintenance Engineering, Vol. 11, No. 1, 2005, pp. 82-96. doi:10.1108/13552510510589398

[16]   K. Y. K. Ng and N. G. F. Sancho, “A Hybrid Dynamic Programming/Depth-First Search Algorithm with an Application to Redundancy Allocation,” IIE Transactions, Vol. 33, No. 12, 2001, pp. 1047-1058. doi:10.1080/07408170108936895