Reliability Modelling of the Redundancy Allocation Problem in the Series-parallel Systems and Determining the System Optimal Parameters


1 Assistant Professor, Faculty of Industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 MSc, Faculty of Industrial & Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran


Considering the increasingly high attention to quality, promoting the reliability of products during designing process has gained significant importance. In this study, we consider one of the current models of the reliability science and propose a non-linear programming model for redundancy allocation in the series-parallel systems according to the redundancy strategy and considering the assumption that the failure rate depends on the number of the active elements. The purpose of this model is to maximize the reliability of the system. Internal connection costs, which are the most common costs in electronic systems, are used in this model in order to reach the real-world conditions. To get the results from this model, we used meta-heuristic algorithms such as genetic algorithm and simulation annealing after optimizing their operators’ rates by using response surface methodology. 


Arulmozhi G, (2002), “Exact equation and an algorithm for reliability for evaluation of K-out-of-N system,” Reliability Engineering and System Safety, vol. 78, pp. 87-91.

Bulfin, R.L. and Liu, C.Y, (1985), “Optimal Allocation of Redundant Components for Large Systems”, IEEE Transactions on Reliability. Vol. 34, pp. 241-7.

Chambari A, Rahmati S.A, Najafi A, Karimi A., (2012), “A bi-objective model to optimize reliability and cost of system with a choice of redundancy strategies”, Computers & Industrial Engineering 63,109–119.

Chen, T. and You, P., (2005), “Immune Algorithms-Based Approach for Redundant Reliability Problems with Multiple Component Choices”, Computers in Industry, Vol. 56, pp.195-205.

Chern, M. S., (1992), “On the Computational Complexity of Reliability Redundancy Allocation in a Series System”, Operation Research Letters. Vol. 11, pp. 309-315.

Coit, D.W. and Konak, A., (2006), “Multiple Weighted Objectives Heuristic for the Redundancy Allocation Problem”, IEEE Transactions on Reliability, Vol. 55, No. 3, pp. 551-558.

Coit, D.W. and Smith, A., (1996), “Penalty Guided Genetic Search for Reliability Design Optimization”, Computers & Industrial Engineering, Vol. 30, pp. 895-904.15

Coit, D.W. and Smith, A., (1996), “Solving the Redundancy Allocation Problem Using a Combined Neural Network/ Genetic Algorithm Approach”, Computers & Operations Research, Vol. 23, pp. 515-526.

Coit, D.W. and Smith, A., (2003), “Stochastic Formulations of the Redundancy Allocation Problem”, Proceedings of the Fifth Industrial Engineering Research Conference, Minneapolis, 1996.

Coit, D.W., (2003), “Maximization of System Reliability with a Choice of Redundancy Strategies”, IIE Transactions, Vol. 35, No. 6, pp. 535-544.

Ebling, C.E., (1997), “An Introduction to Reliability Maintainability Engineering”, New York: McGraw-Hill Co.

Elegbede AOC, Chu C, Adjallah, KH, Yalaoui, F., (2003),  “Reliability allocation through cost minimization,” IEEE Transactions on Reliability, vol. 52, pp. 106-111.

Fyffe, D.E., Hines, W.W. and Lee, N.K., (1968), “System Reliability Allocation and a Computational Algorithm”, IEEE Transactions on Reliability, Vol. 17, pp. 64-69.

Goldberg, D. E. (1989). Genetic algorithms: Search, optimization & machine learning. MA: Addison Wesley, Inc.

Holland, J. H. (1975). Adaptation in natural and artificial system. Ann Arbor, MI: University of Michigan Press. Gen, M., & Cheng, R. (1997). Genetic algorithms and engineering design. MA: Wiley Inder science Publication.

Hsieh, Y-C., (2002), “A Two-Phase Linear Programming Approach for Redundancy Allocation Problems”, Yugoslav Journal of Operations Research, Vol. 12, No. 2, pp. 227- 236. 81

Ida, K., Gen, M. and Yokota, T., (1994), “System Reliability Optimization with Several Failure Modes by Genetic Algorithm”, Proceeding of the 16th International Conference on Computers and Industrial Engineering, Ashikaga of Japan.82

Khalili-Damghani K, Amiri M., (2012), “Solving binary-state multi-objective reliability redundancy allocation series-parallel problem using efficient epsilon-constraint, multi-start partial bound enumeration algorithm, and DEA”, Reliability Engineering and System Safety 103, 35–44.

Kim, H., Bae, C., and Park, S., (2004), “Simulated Annealing Algorithm for Redundancy Optimization with Multiple Component Choices”, In Advanced Reliability Modeling, Proceedings of the Asian International Workshop, World Scientific, pp. 237–244.

Kuo, W., Prasad, V.R., Tillman, F.A. and Hawang, C., (2001), “Optimal Reliability Design Fundamental and Application”, London: Cambridge University Press.

Liang, Y-C, and Smith, A., (2004), “An Ant Colony Optimization Algorithm for the Redundancy Allocation Problem (RAP)”, IEEE Trans Reliability, Vol. 53, No. 3, pp. 417-423.

Liang, Y-C, and Wu, C-C., (2005), “A Variable Neighborhood Descent Algorithm for the Redundancy Allocation Problem”, Industrial Engineering Management and Systems. Vol. 4, No. 1, pp. 109– 116. 84.

Liang, Y-C. And Chen, Y-C, (2007), “Redundancy Allocation of Series-Parallel Systems Using a Variable Neighborhood Search Algorithm”, Reliability Engineering and System Safety. Vol. 92, pp. 323–331.

Metropolis, N., Rosenbluth, A.W., Rosenbluth, M.N., Teller, A.H., Teller, E. (1953), Equation of State Calculation by Fast Computing Machines. J. of Chem. Phys., 21, 1087-1091.

Misra, K.B. and Sharma, U., (1973), “A New Geometric Programming Formulation for a Reliability Problem”, International Journal of Control, Vol. 18, pp. 497-503.

Mohan, C. and Shanker, K., (1988), “Reliability Optimization of Complex Systems Using Random Search Technique”, Microelectronics and Reliability. Vol. 28, pp. 513- 518.

Nakagawa, Y. and Miyazaki, S., (1981), “Surrogate Constraints Algorithm for Reliability Optimization Problems with Two Constraints”, IEEE Transaction on Reliability. Vol. 30, pp. 175-180.

Prasad VR. Raghavachari M., (1999), “Optimal allocation of s-identical multi-functional spears in a series system,” IEEE Transactions on Reliability, vol. 48, pp.118-126.

Ramirez-Marquez, J.E. and Coit, D.W., (2004), “A Heuristic for Solving the Redundancy Allocation Problem for Multi-State Series-Parallel Systems”, Reliability Engineering and System Safety, Vol. 83, pp. 341-349.

Sharifi, M. and Memariani, A., Noorossana, R., (2010), “Real time study of a k-out-of-n system”, world applied sciences journal,  8(9):1136-1143.

Tavakkoli-Moghaddam, R., Safari, J. and Sassani, F., (2008), “Reliability Optimization of Series-Parallel Systems with a Choice of Redundancy Strategies Using a Genetic Algorithm”, Reliability Engineering and System Safety Vol. 93, pp. 550–556.

Tillman, F.A., Hwang, C.L. and Kuo, W., (1977), “Determining Component Reliability and Redundancy for Optimum System Reliability”, IEEE Transactions on Reliability, Vol. 26, pp. 162-165.

Wang Z, Chen T, Tang K and Yao X., (2009), “A Multi-objective Approach to Redundancy Allocation Problem in Parallel- series Systems”, Authorized licensed use limited to: UNIVERSITY OF BIRMINGHAM.

Yokota, T., Gen, M. and Ida, K., (1995), “System Reliability of Optimization Problems with Several Failure Modes by Genetic Algorithm”, Japanese Journal of Fuzzy Theory and systems, Vol. 7, pp. 117-135.

Yun, W-Y, and Kim, J-W., (2004), “Multi-Level Redundancy Optimization in Series Systems”, Computers & Industrial Engineering, Vol. 46, pp. 337-346. 85.