Redundancy allocation problem with a mixed strategy for a system with k-out-of-n subsystems and time-dependent failure rates based on Weibull distribution: An optimization via simulation approach

Document Type : Article

Authors

1 Department of Industrial Engineering, Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Industrial Management, Management and Accounting Faculty, Allame Tabataba’i University, Tehran, Iran

Abstract

Reliability improvement for electronics and mechanical systems is vital for engineers in order to design of these systems. For this reason, there are many researches in this scope to help engineers in real world applications. One of the useful methods in reliability optimization is redundancy allocation problem (RAP). In the most previous works, the failure rates of system components are considered to be constant based on negative exponential distribution; whereas, nearly all systems in real world have components with time-dependent failure rates; i.e., the failure rates of system components will be changed time by time. In this paper, we have worked on a RAP for a system under k-out-of-n subsystems with time-dependent components failure rates based on Weibull distribution. Also, the redundancy policy of the proposed system is considered as mixed strategy and the optimization method was based on the simulation technique to obtain reliability function as implicit function. Finally, a branch and bound algorithm has been used to solve the model, exactly.

Keywords

Main Subjects


1. Fy_e, D.E., Hines, W.W., and Lee, N.K. System  reliability allocation and a computational algorithm",  IEEE Transactions on Reliability, 17, pp. 64-69  (1968).  2. Nakagawa, Y. and Miyazaki, S. Surrogate constraints  algorithm for reliability optimization problems with  two constraints", IEEE Transactions on Reliability,  30, pp. 175-180 (1981).  3. Misra, K.B. and Sharma, U. Reliability optimization  of a system by zero-one programming", Microelectronics  and Reliability, 31, pp. 323-335 (1991).  4. Pham, H. Optimal design of k-out-of-n redundant  systems", Microelectronics and Reliability, 32, pp. 119-  126 (1992).  5. Pham, H. and Malon, D.M. Optimal design of systems  with competing failure modes", IEEE Transactions on  Reliability, 43, pp. 251-254 (1994).  6. Chern, M.S. On the computational complexity of  reliability redundancy allocation in a series system",  Operation Research Letters, 11, pp. 309-315 (1992).  7. Ida, K., Gen, M., and Yokota, T. System reliability  optimization with several failure modes by genetic  algorithm", Proceeding of the 16th International  Conference on Computers and Industrial Engineering,  Ashikaga of Japan (1994).  8. Painton, L. and Campbell, J. Genetic algorithms in  optimization of system reliability", IEEE Transactions  on Reliability, 44(2), pp. 172-178 (1995).  9. Coit, D.W. and Liu, J. System reliability optimization  with k-out-of-n subsystems", International Journal of  Reliability, Quality & Safety Engineering, 35, pp. 535-  544 (2000).  10. Coit, D.W. Maximization of system reliability with  a choice of redundancy strategies", IEEE Transaction  on Reliability, 35, pp. 535-544 (2003).  11. 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,  93, pp. 550-556 (2008).  12. Ghorabaee, M.K., Amiri, M., and Azimi, P. Genetic  algorithm for solving bi-objective redundancy allocation  problem with k-out-of-n subsystems", Applied  Mathematical Modelling, 39(20) pp. 6396-6409 (2015).  13. Zhang, E. and Chen, Q. Multi-objective reliability  redundancy allocation in an interval environment using  particle swarm optimization", Reliability Engineering  & System Safety, 145, pp. 83-92 (2016).  14. Teimouri, M., Zaretalab, A, Niaki, S.T.A., and Shari_,  M. An e_cient memory-based electromagnetism-like  mechanism for the redundancy allocation problem",  Applied Soft Computing, 38, pp. 423-436 (2016).  15. Pourkarim Guilani, P., Niaki, S.T.A., Zaretalab, A.,  and Pourkarim Guilani, P. A bi-objective model to  optimize reliability and cost of three-state systems with  k-out-of-n subsystems", Sciantia Iranica, 24(3), pp.  1585-1602 (2017).  16. Garg, H., Rani, M., Sharma, S.P., and Vishwakarma,  Y. Bi-objective optimization of the reliabilityredundancy  allocation problem for series-parallel system",  Journal of Manufacturing Systems, 33(3), pp.  335-347 (2014).  17. Garg, H., Rani, M., Sharma, S.P., and Vishwakarma,  Y. Intuitionistic fuzzy optimization technique for  solving multi-objective reliability optimization problems  in interval environment", Expert Systems with  Applications, 41(7), pp. 3157-3167 (2014).  18. Garg, H. An e_cient biogeography based optimization  algorithm for solving reliability optimization problems",  Swarm and Evolutionary Computation, 24, pp.  1-10 (2015).  19. Garg, H. An approach for solving constrained  reliability-redundancy allocation problems using  cuckoo search algorithm", Beni-Suef University  Journal of Basic and Applied Sciences, 4(1), pp. 14-25  (2015).  20. Ardakan, M.A. and Hamadani, A.Z. Reliability optimization  of series-parallel systems with mixed redundancy  strategy in subsystems", Reliability Engineering  and System Safety, 130, pp. 132-139 (2014).  21. Ardakan, M.A., Hamadani, A.Z., and Alinaghian,  M. Optimizing bi-objective redundancy allocation  problem with a mixed redundancy strategy", ISA  Transactions, 55, pp. 116-128 (2015).  22. Gholinezhad, H. and Hamadani, A.Z. A new model  for the redundancy allocation problem with component  mixing and mixed redundancy strategy", Reliability  Engineering & System Safety, 164, pp. 66-73 (2017).  23. Nourelfath, M., Ch^atelet, E., and Nahas, N. Joint  redundancy and imperfect preventive maintenance  optimization for series-parallel multi-state degraded  systems", Reliability Engineering and System Safety,  103, pp. 51-60 (2012).  24. Pourkarim Guilani, P., Shari_, M., Niaki, S.T.A., and  Zaretalab, A. Reliability evaluation of non-reparable  three-state systems using Markov model and its comparison  with the UGF and the recursive methods",  Reliability Engineering and System Safety, 129, pp.  29-35 (2014).  25. Kim, H. and Kim, P. Reliability-redundancy allocation  problem considering optimal redundancy strategy  using parallel genetic algorithm", Reliability Engineering  and System Safety, 159, pp. 153-160 (2017).  26. Chang, K.H. and Kuo, P.Y. An e_cient simulation  optimization method for the generalized redundancy  allocation problem", European Journal of Operational  Research, 265(3), pp. 1094-1101 (2018).  27. Azimi, P., Hemmati, M., and Chambari, A. Solving  the redundancy allocation problem of k-out-of-n  with non-exponential repairable components using optimization  via simulation approach", Scientia Iranica,  24(3), pp. 1547-1560 (2017).  28. Ardakan, M.A., Mirzaei, Z., Hamadani, A.Z., and  Elsayed, E.A. Reliability optimization by considering  time-dependent reliability for components", Quality  and Reliability Engineering International, 33(8), pp.  1641-1654 (2017).  29. Pourkarim Guilani, P., Azimi, P., Niaki, S.T.A., and  Niaki, S.A.A. Redundancy allocation problem of a  system with increasing failure rates of components  based on Weibull distribution: A simulation-based  optimization approach", Reliability Engineering and  System Safety, 152, pp. 187-196 (2016).  30. Garg, H., Sharma, S.P., and Rani, M. Behavior  analysis of pulping unit in a paper mill with Weibull  fuzzy distribution function using ABCBLT technique",  International Journal of Applied Mathematics and  Mechanics, 8(4), pp. 86-96 (2012).  31. Garg, H., Sharma, S.P., and Rani, M. Weibull fuzzy  probability distribution for analysing the behaviour  of pulping unit in a paper industry", International  Journal of Industrial and Systems Engineering, 14(4),  pp. 395-413 (2013).