Document Type : Research Paper

**Authors**

**Abstract**

This paper presents a mathematical model for a redundancy allocation problem (RAP) for the series-parallel system with k-out-of-n subsystems and failure rate depends on working components of system. It means that failure rate of components increases when a component fails. The subsystems may use either active or cold-standby redundancy strategies, which considered as a decision variable for individual subsystems. Thus, the proposed model and solution methods are to select the best redundancy strategy among active or cold-standby, component type, and levels of redundancy for each subsystem. The objective function is to maximize the system reliability under cost and weight constraints. To solve the model, since RAP belongs to Np-Hard class of the problems, one effective meta-heuristic algorithm named genetic algorithm (GA)is proposed. Then, response surface methodology is applied for algorithm parameter tuning.Finally, we consider the results of solving presented model with a numerical example

**Keywords**

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

Misra,K.B. and Sharma,U., “Reliability optimization ofasystembyzero-oneprogramming”, Microelectronics and Reliability, 1991 31(2/3), 323-32335.

Coit, D.W. and Smith, A., “Optimization Approaches to the Redundancy Allocation to the Redundancy Allocation Problem for Series-Parallel Systems”, Proceedings of the Fourth Industrial Engineering Research Conference, 1995.

Coit D.W. and Liu J.”System reliability optimization with k-out-of-n subsystems”, International Journal of Reliability, Quality and Safety Engineering 2000, 7 (2), pp. 129–43.

Hsieh, Y.C. and You, P.S., “An effective immune based two-phase approach for the optimal reliability–redundancyallocationproblem”,Applied Mathematics and Computation,2012, 218(4), 1297-1307.

Hsieh, T. J. and Yeh, W. C. ”Penalty guided bees search for redundancy allocation problems with a mix of components in series–parallel systems”, Computers & Operations Research 2012, 39(11), pp. 2688-2704.

Coit, D.W. ”Cold-standby redundancy optimization for non-

repairable systems”, IIE Transactions 2001, 33(6), pp.471–478.

Coit D.W. ”Maximization of system reliability with a choice of redundancy strategies”, IIE Transactions 2003, 35(6), pp.535–44.

Tavakkoli-Moghaddam, R. and Safari, J., “A New mathematical model for a redundancy allocation problem with mixing components

redundant and choice of redundancy strategies”. Applied Mathematical Sciences, 2007; 45(1), 2221-2230.

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

Amari, S.V. and Dill, G. “Redundancy optimization problem with warm-standby redundancy”. Reliability and Maintainability Symposium (RAMS), 2010 Proceedings, 1(6), 25-28.

Amari, S.V., “Reliability of k-out-of-n standby systems with gamma distributions”. Reliability and Maintainability Symposium (RAMS), 2012 Proceedings, 1(6), 23-26.

Sharifi, M., Memariani, A. and Noorossana, R. “Real Time Study of a k-out-of-n System n Identical Elements with Constant Fuzzy Failure Rates”. World Applied Science Journal, 2010 8(9),1136-1143.

Wang, Z., Chen, T., Tang, K. and Yao, X. “A multi-objective approach to Redundancy Allocation Problem in parallel-series systems”. In Proceedings of the2009 IEEE Congress onEvolutionary Computation (CEC2009), Trondheim, Norway, 582-589.

Holland, J., 1992, “Adaptation Natural and Artificial ststems”, University of Michigan press, An Arbor, MI, (1975), MIT Press, Cambridge, Ma

Coit DW, Smith A., “Penalty guided genetic search for reliabilitydesign optimization”, Computer and Industrial Engineering 1996;30(4):895–904.

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