Cold standby redundancy optimization for nonrepairable series-parallel systems: Erlang time to failure distribution

Document Type : Research Paper


Department of Industrial Engineering, K. N. Toosi University of Technology


In modeling a cold standby redundancy allocation problem (RAP) with imperfect switching mechanism, deriving a closed form version of a system reliability is too difficult. A convenient lower bound on system reliability is proposed and this approximation is widely used as a part of objective function for a system reliability maximization problem in the literature. Considering this lower bound does not necessarily lead to an optimal solution. In this study by assuming that working time of switching mechanism is exponentially distributed, exact value of system reliability is derived analytically through applying Markov process and solving a relevant set of differential-difference equations. The Runge-Kutta numerical scheme is also employed to verify the accuracy of the results. It is assumed that components time to failure follow an Erlang distribution which is appropriate for most engineering design problems by giving the possibility of modeling different increasing hazard functions. A new mathematical model is presented and its performance is evaluated through solving a well-known example in the literature. Results demonstrate that a higher level of system reliability is achievable through implementing the proposed model.  


Main Subjects

Ardakan, M. A., & Hamadani, A. Z. (2014). Reliability optimization of series–parallel systems with mixed redundancy strategy in subsystems. Reliability Engineering & System Safety, 130, 132-139.
Bellman, R., & Dreyfus, S. (1958). Dynamic programming and the reliability of multicomponent devices. Operations Research, 6(2), 200-206.
Bulfin, R. L., & Liu, C. Y. (1985). Optimal allocation of redundant components for large systems. IEEE Transactions on Reliability, 34(3), 241-247.
Chambari, A., Najafi, A. A., Rahmati, S. H. A., & Karimi, A. (2013). An efficient simulated annealing algorithm for the redundancy allocation problem with a choice of redundancy strategies. Reliability Engineering & System Safety, 119, 158-164.
Chambari, A., Rahmati, S. H. A., & Najafi, A. A. (2012). A bi-objective model to optimize reliability and cost of system with a choice of redundancy strategies. Computers & Industrial Engineering, 63(1), 109-119.
Coit, D. W. (2001). Cold-standby redundancy optimization for nonrepairable systems. Iie Transactions, 33(6), 471-478.
Coit, D. W. (2003). Maximization of system reliability with a choice of redundancy strategies. IIE transactions, 35(6), 535-543.
Coit, D. W., & Smith, A. E. (1996). Reliability optimization of series-parallel systems using a genetic algorithm. IEEE Transactions on reliability, 45(2), 254-260.
Djerdjour, M., & Rekab, K. (2001). A branch and bound algorithm for designing reliable systems at a minimum cost. Applied Mathematics and Computation, 118(2), 247-259.
Federowicz, A. J., & Mazumdar, M. (1968). Use of geometric programming to maximize reliability achieved by redundancy. Operations Research, 16(5), 948-954.
Fyffe, D. E., Hines, W. W., & Lee, N. K. (1968). System reliability allocation and a computational algorithm. IEEE Transactions on Reliability, 2, 64-69.
Govil, K. K., & Agarwala, R. A. (1983). Lagrange multiplier method for optimal reliability allocation in a series system. Reliability Engineering, 6(3), 181-190.
Kuo, W., & Prasad, V. R. (2000). An annotated overview of system-reliability optimization. IEEE Transactions on reliability, 49(2), 176-187.
Misra, K. B., & Sharma, U. (1991). An efficient algorithm to solve integer-programming problems arising in system-reliability design. IEEE Transactions on Reliability, 40(1), 81-91.
Nakagawa, Y., & Miyazaki, S. (1981). Surrogate constraints algorithm for reliability optimization problems with two constraints. IEEE Transactions on Reliability, 30(2), 175-180.
Sadjadi, S. J., & Soltani, R. (2015). Minimum–maximum regret redundancy allocation with the choice of redundancy strategy and multiple choice of component type under uncertainty. Computers & Industrial Engineering, 79, 204-213.
Safari, J. (2012). Multi-objective reliability optimization of series-parallel systems with a choice of redundancy strategies. Reliability Engineering & System Safety, 108, 10-20.
Soltani, R. (2014). Reliability optimization of binary state non-repairable systems: A state of the art survey. International Journal of Industrial Engineering Computations, 5(3), 339.
Soltani, R., Sadjadi, S. J., & Tavakkoli-Moghaddam, R. (2014). Interval programming for the redundancy allocation with choices of redundancy strategy and component type under uncertainty: Erlang time to failure distribution. Applied Mathematics and Computation, 244, 413-421.
Tavakkoli-Moghaddam, R., Safari, J., & Sassani, F. (2008). Reliability optimization of series-parallel systems with a choice of redundancy strategies using a genetic algorithm. Reliability Engineering & System Safety, 93(4), 550-556.
Yalaoui, A., Chu, C., & Châtelet, E. (2005). Reliability allocation problem in a series–parallel system. Reliability engineering & system safety, 90(1), 55-61.