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.

M. Ziaee, "Optimal Redundancy Allocation in Hierarchical Series-Parallel Systems Using Mixed Integer Programming,"

References

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[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

[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