A New Approach for Solving Bi-Objective Redundancy Allocation Problem Using DOE, Simulation and ε-Constraint Method

Keshavarz Ghorabaee, Mehdi; Amiri, Maghsoud; Turskis, Zenonas

doi:10.15388/Informatica.2017.121

Informatica

A New Approach for Solving Bi-Objective Redundancy Allocation Problem Using DOE, Simulation and ε-Constraint Method

Volume 28, Issue 1 (2017), pp. 79–104

Mehdi Keshavarz Ghorabaee Maghsoud Amiri Zenonas Turskis

https://doi.org/10.15388/Informatica.2017.121

Pub. online: 1 January 2017 Type: Research Article

Open Access

Received
1 September 2016

Accepted
1 March 2017

Published
1 January 2017

Abstract

The redundancy allocation problem (RAP) has been studied for many different system structures, objective functions, and distribution assumptions. In this paper, we present a problem formulation and a solution methodology to maximize the system steady-state availability and minimize the system cost for the repairable series-parallel system designs. In the proposed approach, the components’ time-to-failure (TTF) and time-to-repair (TTR) can follow any distribution such as the Gamma, Normal, Weibull, etc. We estimate an approximation of the steady-state availability of each subsystem in the series-parallel system with an individual meta-model. Design of experiment (DOE), simulation and the stepwise regression are used to build these meta-models. Face centred design, which is a type of central composite design is used to design experiments. According to a max–min approach, obtained meta-models are utilized for modelling the problem alongside the cost function of the system. We use the augmented ε-constraint method to reformulate the problem and solve the model. An illustrative example which uses the Gamma distribution for TTF and TTR is explained to represent the performance of the proposed approach. The results of the example show that the proposed approach has a good performance to obtain Pareto (near-Pareto) optimal solutions (system configurations).

References

Abouei Ardakan, M., Sima, M., Zeinal Hamadani, A., Coit, D.W. (2016). A novel strategy for redundant components in reliability–redundancy allocation problems. IIE Transactions, 48(11), 1043–1057.

Amari, S.V. (2012). Reliability of k-out-of-n standby systems with gamma distributions. In: Reliability and Maintainability Symposium (RAMS), 2012 Proceedings-Annual. IEEE, pp. 1–6.

Amiri, M., Mohtashami, A. (2012). Buffer allocation in unreliable production lines based on design of experiments, simulation, and genetic algorithm. The International Journal of Advanced Manufacturing Technology, 62(1–4), 371–383.

Amiri, M., Olfat, L., Keshavarz Ghorabaee, M. (2014). Simultaneous minimization of total tardiness and waiting time variance on a single machine by genetic algorithms. The International Journal of Advanced Manufacturing Technology, 72(1–4), 439–446.

Antony, J. (2003). Design of Experiments for Engineers and Scientists. Elsevier.

Ardakan, M.A., Hamadani, A.Z. (2014). Reliability–redundancy allocation problem with cold-standby redundancy strategy. Simulation Modelling Practice and Theory, 42, 107–118.

Ardakan, M.A., Hamadani, A.Z., Alinaghian, M. (2015). Optimizing bi-objective redundancy allocation problem with a mixed redundancy strategy. ISA Transactions, 55, 116–128.

Aytug, H., Dogan, C.A., Bezmez, G. (1996). Determining the number of kanbans: a simulation metamodeling approach. Simulation, 67(1), 23–32.

Azadeh, A., Ghaderi, S.F., Dehghanbaghi, M., Dabbaghi, A. (2010). Integration of simulation, design of experiment and goal programming for minimization of makespan and tardiness. The International Journal of Advanced Manufacturing Technology, 46(5–8), 431–444.

Badkar, D.S., Pandey, K.S., Buvanashekaran, G. (2012). Application of the central composite design in optimization of laser transformation hardening parameters of commercially pure titanium using Nd: YAG laser. The International Journal of Advanced Manufacturing Technology, 59(1–4), 169–192.

Banks, J., Carson, J.S., Nelson, B.L., Nicol, D.M. (2010). Discrete-event System Simulation, 5th ed. Prentice Hall, Upper Saddle River, NJ.

Beji, N., Jarboui, B., Eddaly, M., Chabchoub, H. (2010). A hybrid particle swarm optimization algorithm for the redundancy allocation problem. Journal of Computational Science, 1(3), 159–167.

Caserta, M., Voß, S. (2015). An exact algorithm for the reliability redundancy allocation problem. European Journal of Operational Research, 244(1), 110–116.

Castro, H.F., Cavalca, K.L. (2003). Availability optimization with genetic algorithm. International Journal of Quality and Reliability Management, 20(7), 847–863.

Chen, Y., Shi, R., Shu, S., Gao, W. (2013). Ensemble and enhanced PM 10 concentration forecast model based on stepwise regression and wavelet analysis. Atmospheric Environment, 74, 346–359.

Chern, M.S. (1992). On the computational complexity of reliability redundancy allocation in a series system. Operations Research Letters, 11(5), 309–315.

Coit, D.W., Liu, J.C. (2000). System reliability optimization with k-out-of-n subsystems. International Journal of Reliability, Quality and Safety Engineering, 7(02), 129–142.

Deb, K. (2001). Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley and Sons, Chichester, UK.

Draper, N.R., Smith, H. (1981). Applied Regression Analysis, 2nd ed. Wiley, New York.

Dzemyda, G., §ˇaltenis, V. (1994). Multiple criteria decision support system: methods, user’s interface and applications. Informatica, 5(1–2), 31–42.

Dzemyda, G., Kurasova, O., Žilinskas, J. (2013). Multidimensional Data Visualization: Methods and Applications. Springer Optimization and Its Applications, Vol. 75. Springer, Berlin.

Ghoreishi, M. (2006). Statistical analysis of repeatability in laser percussion drilling. The International Journal of Advanced Manufacturing Technology, 29(1–2), 70–78.

Gupta, R.K., Bhunia, A.K., Roy, D. (2009). A GA based penalty function technique for solving constrained redundancy allocation problem of series system with interval valued reliability of components. Journal of Computational and Applied Mathematics, 232(2), 275–284.

Høyland, A., Rausand, M. (2004). System Reliability Theory: Models, Statistical Methods, and Applications, 2nd ed. Wiley, NJ.

Karbauskaitė, R., Dzemyda, G. (2015). Optimization of the maximum likelihood estimator for determining the intrinsic dimensionality of high-dimensional data. International Journal of Applied Mathematics and Computer Science, 25(4), 895–913.

Karbauskaitė, R., Dzemyda, G. (2016). Fractal-based methods as a technique for estimating the intrinsic dimensionality of high-dimensional data: a survey. Informatica, 27(2), 257–281.

Keshavarz Ghorabaee, M. (2016). Developing an MCDM method for robot selection with interval type-2 fuzzy sets. Robotics and Computer-Integrated Manufacturing, 37, 221–232.

Keshavarz Ghorabaee, M., Amiri, M., Salehi Sadaghiani, J.S., Hassani Goodarzi, G. (2014). Multiple criteria group decision-making for supplier selection based on COPRAS method with interval type-2 fuzzy sets. The International Journal of Advanced Manufacturing Technology, 75(5–8), 1115–1130.

Keshavarz Ghorabaee, M., Amiri, M., Azimi, P. (2015). Genetic algorithm for solving bi-objective redundancy allocation problem with k-out-of-n subsystems. Applied Mathematical Modelling, 39(20), 6396–6409.

Kleijnen, J.P.C., Sargent, R.G. (2000). A methodology for fitting and validating metamodels in simulation. European Journal of Operational Research, 120(1), 14–29.

Kuo, W., Wan, R. (2007). Recent advances in optimal reliability allocation. IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans, 37(2), 143–156.

Leksakul, K., Limcharoen, A. (2014). Central composite designs coupled with simulation techniques for optimizing RIE process. The International Journal of Advanced Manufacturing Technology, 70(5–8), 1219–1225.

Lin, Y.C., Tsao, C.C., Hsu, C.Y., Hung, S.K., Wen, D.C. (2012). Evaluation of the characteristics of the microelectrical discharge machining process using response surface methodology based on the central composite design. The International Journal of Advanced Manufacturing Technology, 62(9–12), 1013–1023.

Lins, I.D., Droguett, E.L. (2009). Multiobjective optimization of availability and cost in repairable systems design via genetic algorithms and discrete event simulation. Pesquisa Operacional, 29(1), 43–66.

Lins, I.D., Droguett, E.L. (2011). Redundancy allocation problems considering systems with imperfect repairs using multi-objective genetic algorithms and discrete event simulation. Simulation Modelling Practice and Theory, 19(1), 362–381.

Mavrotas, G. (2009). Effective implementation of the ε-constraint method in multi-objective mathematical programming problems. Applied Mathematics and Computation, 213(2), 455–465.

Modarres, M., Kaminskiy, M.P., Krivtsov, V. (2009). Reliability Engineering and Risk Analysis: A Practical Guide, 2nd ed. CRC Press.

Noguera, J.H., Watson, E.F. (2006). Response surface analysis of a multi-product batch processing facility using a simulation metamodel. International Journal of Production Economics, 102(2), 333–343.

Radziukynienė, I., Žilinskas, A. (2014). Comparison of several methods for Pareto set generation in multi-criteria portfolio optimization. International Journal of Computing, 7(3), 22–29.

Ralston, A., Wilf, H.S. (Eds.) (1960). Mathematical Methods for Digital Computers. Wiley, New York.

Ramirez-Marquez, J.E., Coit, D.W., Konak, A. (2004). Redundancy allocation for series-parallel systems using a max–min approach. IIE Transactions, 36(9), 891–898.

Roy, R.K. (2001). Design of Experiments Using the Taguchi Approach: 16 Steps to Product and Process Improvement. Wiley-Interscience, New York.

Sokolowski, J.A., Banks, C.M. (Eds.) (2011). Principles of Modeling and Simulation: A Multidisciplinary Approach. John Wiley & Sons, Hoboken.

Soylu, B., Kapan Ulusoy, S. (2011). A preference ordered classification for a multi-objective max–min redundancy allocation problem. Computers & Operations Research, 38(12), 1855–1866.

Wang, Y., Li, L. (2014). A PSO algorithm for constrained redundancy allocation in multi-state systems with bridge topology. Computers & Industrial Engineering, 68, 13–22.

Wang, G.G., Shan, S. (2007). Review of metamodeling techniques in support of engineering design optimization. Journal of Mechanical Design, 129(4), 370–380.

Yang, T., Tseng, L. (2002). Solving a multi-objective simulation model using a hybrid response surface method and lexicographical goal programming approach—a case study on integrated circuit ink-marking machines. Journal of the Operational Research Society, 53(2), 211–221.

Yeh, W.C., Hsieh, T.J. (2011). Solving reliability redundancy allocation problems using an artificial bee colony algorithm. Computers & Operations Research, 38(11), 1465–1473.

Zakerifar, M., Biles, W.E., Evans, G.W. (2011). Kriging metamodeling in multiple-objective simulation optimization. Simulation: Transactions of the Society for Modeling and Simulation International, 87(10), 843–856.

Zhang, E., Wu, Y., Chen, Q. (2014). A practical approach for solving multi-objective reliability redundancy allocation problems using extended bare-bones particle swarm optimization. Reliability Engineering & System Safety, 127, 65–76.

Žilinskas, A., Zhigljavsky, A. (2016). Stochastic global optimization: a review on the occasion of 25 years of Informatica. Informatica, 27(2), 229–256.

Zoulfaghari, H., Zeinal Hamadani, Z., Abouei Ardakan, M. (2014). Bi-objective redundancy allocation problem for a system with mixed repairable and non-repairable components. ISA Transactions, 53(1), 17–24.

Biographies

Keshavarz Ghorabaee Mehdi

m.keshavarz_gh@yahoo.com

M. Keshavarz Ghorabaee received the BS degree in electrical engineering from University of Guilan, Rasht, Iran in 2010 and the MS degree in production management from Allameh Tabataba’i University, Tehran, Iran in 2013. He is currently working toward the PhD degree in Operations Research at Allameh Tabataba’i University. He has published some papers in leading international journals such as Robotics and Computer-Integrated Manufacturing, The International Journal of Advanced Manufacturing Technology, Journal of Cleaner Production and Applied Mathematical Modelling. His research interests include multi-criteria decision making (MCDM), multi-objective evolutionary algorithms, genetic algorithm, fuzzy MCDM, inventory control, supply chain management, scheduling and reliability engineering.

Amiri Maghsoud

amiri@atu.ac.ir

M. Amiri is a professor at the Department of Industrial Management, Allameh Tabataba’i University, Tehran, Iran. He received PhD degree in industrial engineering from Sharif University of Technology, Tehran, Iran. He has published many papers in leading international journals. His research interests include multi-criteria decision-making (MCDM), data envelopment analysis (DEA), design of experiments (DOE), response surface methodology (RSM), fuzzy MCDM, inventory control, supply chain management, simulation and reliability engineering.

Turskis Zenonas

zenonas.turskis@vgtu.lt

Z. Turskis is Prof. Dr. of Technical Sciences, Chief Research Fellow at the Laboratory of Construction Technology and Management, Vilnius Gediminas Technical University. Research interests: building technology and management, decision-making theory, computer-aided automation in design, expert systems. He is the author of more than 110 research papers, which are referred in the WoS database.

Full article Related articles Cited by

Open access article under the CC BY license.

Keywords

redundancy allocation problem bi-objective RAP design of experiment simulation ε-constraint method

Metrics

since January 2020

1120 Article info views	898 Full article views
529 PDF downloads	240 XML downloads

RSS

Authors

Abstract

References

Biographies

Export citation

Copy and paste formatted citation

Download citation in file