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A multi-objective reliability-redundancy allocation problem with active redundancy and interval type-2 fuzzy parameters

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Abstract

This paper considers a multi-objective reliability-redundancy allocation problem (MORRAP) of a series-parallel system, where system reliability and system cost are to be optimized simultaneously subject to limits on weight, volume, and redundancy level. Precise computation of component reliability is very difficult as the estimation of a single number for the probabilities and performance levels are not always possible, because it is affected by many factors such as inaccuracy and insufficiency of data, manufacturing process, environment in which the system is running, evaluation done by multiple experts, etc. To cope with impreciseness, we model component reliabilities as interval type-2 fuzzy numbers (IT2 FNs), which is more suitable to represent uncertainties than usual or type-1 fuzzy numbers. To solve the problem with interval type-2 fuzzy parameters, we first apply various type-reduction and defuzzification techniques, and obtain corresponding defuzzified values. As maximization of system reliability and minimization of system cost are conflicting to each other, so to obtain compromise solution of the MORRAP with defuzzified parameters, we apply five different multi-objective optimization methods, and then corresponding solutions are analyzed. The problem is illustrated numerically for a real-world MORRAP on pharmaceutical plant, and solutions are obtained by standard optimization solver LINGO, which is based on gradient-based optimization—Generalized Reduced Gradient technique.

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References

  • Akalin O, Akay KU, Sennaroglu B, Tez M (2010) Optimization of chemical admixture for concrete on mortar performance tests using mixture experiments. Chemometr Intell Lab Syst 104:233–242

    Article  Google Scholar 

  • Aliev IM, Kara Z (2004) Fuzzy system reliability analysis using time dependent fuzzy set. Control Cybern 33(4):653–662

    Google Scholar 

  • Ardakan MA, Rezvan MT (2018) Multi-objective optimization of reliability-redundancy allocation problem with cold-standby strategy using NSGA-II. Reliab Eng Syst Saf 172:225–238

    Article  Google Scholar 

  • Bit AK, Biswal MP, Alam SS (1993) Fuzzy programming approach to multi-objective solid transportation problem. Fuzzy Sets Syst 57:183–194

    Article  Google Scholar 

  • Cao D, Murat A, Chinnam RB (2013) Efficient exact optimization of multi-objective redundancy allocation problems in series-parallel systems. Reliab Eng Syst Saf 111:154–163

    Article  Google Scholar 

  • Caserta M, Voß S (2015) An exact algorithm for the reliability redundancy allocation problem. Eur J Oper Res 244(1):110–116

    Article  Google Scholar 

  • Chen SM (1994) Fuzzy system reliability analysis using fuzzy number arithmetic operations. Fuzzy Sets Syst 64:31–38

    Article  Google Scholar 

  • Cheng CH, Mon DL (1993) Fuzzy system reliability analysis by interval of confidence. Fuzzy Sets Syst 56:29–35

    Article  Google Scholar 

  • Coupland S, John R (2007) Geometric type-1 and type-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 15(1):3–15

    Article  Google Scholar 

  • Garg H, Sharma SP (2013) Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Comput Ind Eng 64:247–255

    Article  Google Scholar 

  • Garg H, Rani M, Sharma SP (2013) Reliability analysis of the engineering systems using intuitionistic fuzzy set theory. J Qual Reliab Eng 943972:1–10

    Google Scholar 

  • Garg H, Rani M, Sharma SP, Vishwakarma Y (2014) Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment. Expert Syst Appl 41(7):3157–3167

    Article  Google Scholar 

  • Hesamian G (2017) Measuring similarity and ordering based on interval type 2 fuzzy numbers. IEEE Trans Fuzzy Syst 25(4):788–798

    Article  Google Scholar 

  • Huang H-Z, Qu J, Zuo MJ (2009) Genetic-algorithm-based optimal apportionment of reliability and redundancy under multiple objectives. IIE Trans 41(4):287–298

    Article  Google Scholar 

  • Jamkhaneh EB, Nozari A (2012) Fuzzy system reliability analysis based on confidence interval. Adv Mater Res 433–440:4908–4914

    Article  Google Scholar 

  • Karnik NN, Mendel JM (2001) Centroid of a type-2 fuzzy set. Inf Sci 132(1–4):195–220

    Article  Google Scholar 

  • Khalili-Damghani K, Abtahi A-R, Tavana M (2013) A new multi-objective particle swarm optimization method for solving reliability redundancy allocation problems. Reliab Eng Syst Saf 111:58–75

    Article  Google Scholar 

  • Kumar M, Yadav SP (2012) A novel approach for analyzing fuzzy system reliability using different types of intuitionistic fuzzy failure rates of components. ISA Trans 51(2):288–297

    Article  Google Scholar 

  • Kundu P, Kar S, Maiti M (2014) Multi-objective solid transportation problems with budget constraint in uncertain environment. Int J Syst Sci 45(8):1668–1682

    Article  Google Scholar 

  • Kuo W, Prasad VR (2000) An annotated overview of system-reliability optimization. IEEE Trans Reliab 49(2):176–187

    Article  Google Scholar 

  • Liu F (2008) An efficient centroid type-reduction strategy for general type-2 fuzzy logic system. Inf Sci 178:2224–2236

    Article  Google Scholar 

  • Liu F, Mendel JM (2008) Encoding words into interval type-2 fuzzy sets using an interval approach. IEEE Trans Fuzzy Syst 16(6):1503–1521

    Article  Google Scholar 

  • Mahapatra GS, Roy TK (2006) Fuzzy multi-objective mathematical programming on reliability optimization model. Appl Math Comput 174:643–659

    Google Scholar 

  • Malenović A, Dotsikas Y, Mašković M, Jančić-Stojanović B, Ivanović D, Medenica M (2011) Desirability-based optimization and its sensitivity analysis for the perindopril and its impurities analysis in a microemulsion LC system. Microchem J 99:454–460

    Article  Google Scholar 

  • Mendel J M (2003). Fuzzy sets for words: a new beginning. In: Proceedings of IEEE international conference on fuzzy systems, pp 37-42, St. Louis, MO

  • Mendel JM (2007a) Computing with words: zadeh, turing, popper and occam. IEEE Comput Intell Mag 2(4):10–17

    Article  Google Scholar 

  • Mendel JM (2007b) Computing with words and its relationships with fuzzistics. Inf Sci 177:988–1006

    Article  Google Scholar 

  • Mendel JM, John RI (2002) Type-2 fuzzy sets made simple. IEEE Trans Fuzzy Syst 10(2):307–315

    Article  Google Scholar 

  • Mendel JM, Liu F (2007) Super-exponential convergence of the Karnik–Mendel algorithms for computing the centroid of an interval type-2 fuzzy set. IEEE Trans Fuzzy Syst 15(2):309–320

    Article  Google Scholar 

  • Mendel JM, John RI, Liu FL (2006) Interval type-2 fuzzy logical systems made simple. IEEE Trans Fuzzy Syst 14(6):808–821

    Article  Google Scholar 

  • Miettinen K (2012) Nonlinear multiobjective optimization. Springer, New York

    Google Scholar 

  • Miettinen K, Mäkelä MM (2006) Synchronous approach in interactive multiobjective optimization. Eur J Oper Res 170(3):909–922

    Article  Google Scholar 

  • Miller S, Gongora M, Garibaldi J, John R (2012) Interval type-2 fuzzy modelling and stochastic search for real-world inventory management. Soft Comput 16:1447–1459

    Article  Google Scholar 

  • Muhuri PK, Ashraf Z, Lohani QMD (2018) Multi-objective reliability-redundancy allocation problem with interval type-2 fuzzy uncertainty. IEEE Trans Fuzzy Syst 26(3):1339–1355

    Google Scholar 

  • Nie M, Tan WW (2008) Towards an efficient type-reduction method for interval type-2 fuzzy logic systems. In: IEEE international conference on fuzzy systems, pp 1425–1432

  • Pagola M, Lopez-Molina C, Fernandez J, Barrenechea E, Bustince H (2013) Interval type-2 fuzzy sets constructed from several membership functions: application to the fuzzy thresholding algorithm. IEEE Trans Fuzzy Syst 21(2):230–244

    Article  Google Scholar 

  • Prasad VR, Kuo W (2000) Reliability optimization of coherent systems. IEEE Trans Reliab 49(3):323–330

    Article  Google Scholar 

  • Rao SS, Dhingra AK (1992) Reliability and redundancy apportionment using crisp and fuzzy multi-objective optimization approaches. Reliab Eng Syst Saf 37:253–261

    Article  Google Scholar 

  • Roy P, Mahapatra BS, Mahapatra GS, Roy PK (2014) Entropy based region reducing genetic algorithm for reliability redundancy allocation in interval environment. Expert Syst Appl 41(14):6147–6160

    Article  Google Scholar 

  • Safari J (2012) Multi-objective reliability optimization of series-parallel systems with a choice of redundancy strategies. Reliab Eng Syst Saf 108:10–20

    Article  Google Scholar 

  • Sahoo L, Bhunia AK, Kapur PK (2012) Genetic algorithm based multi-objective reliability optimization in interval environment. Comput Ind Eng 62:152–160

    Article  Google Scholar 

  • Sriramdas V, Chaturvedi S, Gargama H (2014) Fuzzy arithmetic based reliability allocation approach during early design and development. Expert Syst Appl 41(7):3444–3449

    Article  Google Scholar 

  • Wang Z, Chen T, Tang K, Yao X (2009) A multi-objective approach to redundancy allocation problem in parallel-series systems. In: Proceedings of IEEE congress on evolutionary computation, pp 582–589

  • Wu D, Mendel JM (2002) Uncertainty bounds and their use in the design of intervaltype-2 fuzzy logic systems. IEEE Trans Fuzzy Syst 10(5):622–639

    Article  Google Scholar 

  • Xu Y, Liao H (2016) Reliability analysis and redundancy allocation for a one-shot system containing multifunctional components. IEEE Trans Reliab 65(2):1045–1057

    Article  Google Scholar 

  • Yao JS, Su JS, Shih TS (2008) Fuzzy system reliability analysis using triangular fuzzy numbers based on statistical data. J Inf Sci Eng 24:1521–1535

    Google Scholar 

  • Yetilmezsoy Y (2012) Integration of kinetic modeling and desirability function approach for multi-objective optimization of UASB reactor treating poultry manure wastewater. Bioresour Technol 118:89–101

    Article  Google Scholar 

  • Zeleny M (1973) compromising programming, multiple criteriadecision making. University of South Carolina Press, Columbia

    Google Scholar 

  • Zhang E, Chen Q (2016) Multi-objective reliability redundancy allocation in an interval environment using particle swarm optimization. Reliab Eng Syst Saf 145:83–92

    Article  Google Scholar 

  • Zimmermann H-J (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Sets Syst 1:45–55

    Article  Google Scholar 

Download references

Acknowledgements

The authors are thankful to the Editor and the anonymous Reviewers for valuable suggestions which lead to an improved version of the manuscript.

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  1. Decision Science and Operations Management, School of Management, Birla Global University, Bhubaneswar, Odisha, 751003, India

    Pradip Kundu

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  1. Pradip Kundu
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Kundu, P. A multi-objective reliability-redundancy allocation problem with active redundancy and interval type-2 fuzzy parameters. Oper Res Int J 21, 2433–2458 (2021). https://doi.org/10.1007/s12351-019-00531-y

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  • DOI: https://doi.org/10.1007/s12351-019-00531-y

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