An Integrated Framework to Analyze the Performance of Process Industrial Systems Using a Fuzzy and Evolutionary Algorithm



In the design of critical combinations and complex integrations of large engineering systems, their reliability, availability and maintainability (RAM) analysis of the inherent processes in the system and their related equipments are needed to be determined. Although there have been tremendous advances in the art and science of system evaluation, yet it is very difficult to assess these parameters with a very high accuracy or precision. Basically, this inaccuracy in assessment stems mainly from the inaccuracy of data, lack of exactness of the models and even from the limitations of the current methods themselves and hence management decisions are based on experience. Thus the objective of this chapter is to present a methodology for increasing the performance as well as productivity of the system by utilizing these uncertain data. For this an optimization problem is formulated by considering RAM parameters as an objective function. The conflicting nature between the objectives is resolved by defining their nonlinear fuzzy goals and then aggregate by using a product aggregator operator. The failure rates and repair times of all constituent components are obtained by solving the reformulated fuzzy optimization problem with evolutionary algorithms. In order to increase the performance of the system, the obtained data are used for analyzing their behavior pattern in terms of membership and non-membership functions using intuitionistic fuzzy set theory and weakest t-norm based arithmetic operations. A composite measure of RAM parameters named as the RAM-Index has been formulated for measuring the performance of the system and hence finding the critical component of the system based on its performance. Finally the computed results of the proposed approach have been compared with the existing approaches for supremacy the approach. The suggested framework has been illustrated with the help of a case.


  1. Attanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)CrossRefGoogle Scholar
  2. Attanassov, K.T.: More on intuitionistic fuzzy sets. Fuzzy Sets Syst. 33(1), 37–46 (1989)MathSciNetCrossRefGoogle Scholar
  3. Barabady, J., Kumar, U.: Maintenance schedule by using reliability analysis: a case study at jajarm bauxite mine of iran. In: 20th World Mining Congress and EXPO2005, pp. 79–86. Tehran, Iran (2005a)Google Scholar
  4. Barabady, J., Kumar, U.: Reliability and maintainability analysis of crushing plants in jajarm bauxite mine of iran. In: Proceedings of the Annual Reliability and Maintainability Symposium, pp. 109–115 (2005b)Google Scholar
  5. Birolini, A.: Reliability Engineering: Theory and Practice, 5th edn. Springer, New York (2007)MATHGoogle Scholar
  6. Bris, R., Chatelet, E., Yalaoui, F.: New method to minimize the preventive maintenance cost of series-parallel systems. Reliab. Eng. Syst. Saf. 82, 247–255 (2003)CrossRefGoogle Scholar
  7. Bustince, H., Burillo, P.: Vague sets are intuitionistic fuzzy sets. Fuzzy Sets Syst. 79(3), 403–405 (1996)MathSciNetCrossRefMATHGoogle Scholar
  8. Chang, J.R., Chang, K.H., Liao, S.H., Cheng, C.H.: The reliability of general vague fault tree analysis on weapon systems fault diagnosis. Soft. Comput. 10, 531–542 (2006)CrossRefGoogle Scholar
  9. Chen, S.M.: Analyzing fuzzy system reliability using vague set theory. Int. J. Appl. Sci. Eng. 1(1), 82–88 (2003)Google Scholar
  10. Clerc, M., Kennedy, J.F.: The particle swarm: explosion, stability, and convergence in a multi-dimensional complex space. IEEE Trans. Evol. Comput. 6(1), 58–73 (2002)CrossRefGoogle Scholar
  11. Dinesh-Kumar, U., Marquez, J.E.R., Nowicki, D., Verma, D.: A goal programming model for optimizing reliability, maintainability and supportability under performance based logistics. Int. J. Reliab., Qual. Saf. 14(3), 251–261 (2007)CrossRefGoogle Scholar
  12. Eberhart, R., Kennedy, J.: A new optimizer using particle swarm theory. In: Proceedings of the Sixth International Symposium on Micro Machine and Human Science, pp. 39–43 (1995)Google Scholar
  13. Garg, H.: Reliability analysis of repairable systems using Petri nets and Vague Lambda-Tau methodology. ISA Trans. 52(1), 6–18 (2013)CrossRefGoogle Scholar
  14. Garg, H., Rani, M.: An approach for reliability analysis of industrial systems using PSO and IFS technique. ISA Trans. 52(6), 701–710 (2013)CrossRefGoogle Scholar
  15. Garg, H., Rani, M., Sharma, S.P.: Fuzzy RAM analysis of the screening unit in a paper industry by utilizing uncertain data. Int. J. Qual., Stat. Reliab., Article ID: 203,842, 14 p (2012)Google Scholar
  16. Garg, H., Rani, M., Sharma, S.P.: Predicting uncertain behavior of press unit in a paper industry using artificial bee colony and fuzzy Lambda-Tau methodology. Appl. Soft Comput. 13(4), 1869–1881 (2013)CrossRefGoogle Scholar
  17. Garg, H., Rani, M., Sharma, S.P.: An approach for analyzing the reliability of industrial systems using soft computing based technique. Expert Syst. Appl. 41(2), 489–501 (2014a)CrossRefGoogle Scholar
  18. Garg, H., Rani, M., Sharma, S.P., Vishwakarma, Y.: Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment. Expert Syst. Appl. 41, 3157–3167 (2014b)CrossRefGoogle Scholar
  19. Garg, H., Sharma, S.P.: Stochastic behavior analysis of industrial systems utilizing uncertain data. ISA Trans. 51(6), 752–762 (2012)CrossRefGoogle Scholar
  20. Garg, H., Sharma, S.P.: A two-phase approach for reliability and maintainability analysis of an industrial system. Int. J. Reliab., Qual. Saf. Eng. (IJRQSE) 19(3) (2012). doi:10.1142/S0218539312500131
  21. Garg, H., Sharma, S.P.: Multi-objective reliability-redundancy allocation problem using particle swarm optimization. Comput. Ind. Eng. 64(1), 247–255 (2013)CrossRefGoogle Scholar
  22. Garg, H., Sharma, S.P., Rani, M.: Cost minimization of washing unit in a paper mill using artificial bee colony technique. Int. J. Syst. Assur. Eng. Manag. 3(4), 371–381 (2012)CrossRefGoogle Scholar
  23. Gau, W.L., Buehrer, D.J.: Vague sets. IEEE Trans. Syst., Man, Cybern. 23, 610–613 (1993)CrossRefMATHGoogle Scholar
  24. Gen, M., Yun, Y.S.: Soft computing approach for reliability optimization: state-of- the-art survey. Reliab. Eng. Syst. Saf. 91(9), 1008–1026 (2006)CrossRefGoogle Scholar
  25. Goldberg, D.E.: Genetic Algorithm in Search, Optimization and Machine Learning. Addison-Wesley, MA (1989)MATHGoogle Scholar
  26. Holland, J.H.: Adaptation in Natural and Artificial Systems. The University of Michigan Press, Ann Arbor (1975)Google Scholar
  27. Hsieh, T.J., Yeh, W.C.: Penalty guided bees search for redundancy allocation problems with a mix of components in series–parallel systems. Comput. Oper. Res. 39(11), 2688–2704 (2012)MathSciNetCrossRefMATHGoogle Scholar
  28. Juang, Y.S., Lin, S.S., Kao, H.P.: A knowledge management system for series-parallel availability optimization and design. Expert Syst. Appl. 34, 181–193 (2008)CrossRefGoogle Scholar
  29. Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Tech. rep., TR06, Erciyes University, Engineering Faculty, Computer Engineering Department (2005)Google Scholar
  30. Karaboga, D., Akay, B.: A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214(1), 108–132 (2009)MathSciNetMATHGoogle Scholar
  31. Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Global Optim. 39, 459–471 (2007)MathSciNetCrossRefMATHGoogle Scholar
  32. Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: IEEE International Conference on Neural Networks, vol. 4, pp. 1942–1948. Piscataway, Seoul (1995)Google Scholar
  33. Khan, F.I., Haddara, M., Krishnasamy, L.: A new methodology for risk-based availability analysis. IEEE Trans. Reliab. 57(1), 103–112 (2008)CrossRefGoogle Scholar
  34. Knezevic, J., Odoom, E.R.: Reliability modeling of repairable systems using Petri nets and Fuzzy Lambda-Tau Methodology. Reliab. Eng. Syst. Saf. 73(1), 1–17 (2001)CrossRefGoogle Scholar
  35. Kumar, A., Yadav, S.P., Kumar, S.: Fuzzy reliability of a marine power plant using interval valued vague sets. Int. J. Appl. Sci. Eng. 4(1), 71–82 (2006)Google Scholar
  36. Kumar, M., Yadav, S.P.: A novel approach for analyzing fuzzy system reliability using different types of intuitionistic fuzzy failure rates of components. ISA Trans. 51(2), 288–297 (2012)CrossRefGoogle Scholar
  37. Kuo, W., Prasad, V.R., Tillman, F.A., Hwang, C.: Optimal Reliability Design—Fundamentals and Applications. Cambridge University Press, Cambridge (2001)Google Scholar
  38. Liberopoulos, G., Tsarouhas, P.: Systems analysis speeds up chipita’s food processing line. Interfaces 32(3), 62–76 (2002)CrossRefGoogle Scholar
  39. Rajpal, P.S., Shishodia, K.S., Sekhon, G.S.: An artificial neural network for modeling reliability, availability and maintainability of a repairable system. Reliab. Eng. Syst. Saf. 91(7), 809–819 (2006)CrossRefGoogle Scholar
  40. Ross, T.J.: Fuzzy Logic with Engineering Applications, 2nd edn. Wiley, New York (2004)MATHGoogle Scholar
  41. Sharma, R.K., Kumar, S.: Performance modeling in critical engineering systems using RAM analysis. Reliab. Eng. Syst. Saf. 93(6), 913–919 (2008)MathSciNetCrossRefGoogle Scholar
  42. Shi, Y., Eberhart, R.C.: Parameter selection in particle swarm optimization. evolutionary programming VII. In: EP 98, pp. 591–600. Springer, New York (1998)Google Scholar
  43. Taheri, S., Zarei, R.: Bayesian system reliability assessment under the vague environment. Appl. Soft Comput. 11(2), 1614–1622 (2011)CrossRefGoogle Scholar
  44. Yang, X.S., Deb, S.: Cuckoo search via lévy flights. In: Proceedings of World Congress on Nature & Biologically Inspired Computing (NaBIC 2009), pp. 210–214. IEEE Publications, USA (2009)Google Scholar
  45. Yeh, W.C., Hsieh, T.J.: Solving reliability redundancy allocation problems using an artificial bee colony algorithm. Comput. Oper. Res. 38(11), 1465–1473 (2011)MathSciNetCrossRefGoogle Scholar
  46. Yeh, W.C., Su, J.C.P., Hsieh, T.J., Chih, M., Liu, S.L.: Approximate reliability function based on wavelet latin hypercube sampling and bee recurrent neural network. IEEE Trans. Reliab. 60(2), 404–414 (2011)CrossRefGoogle Scholar
  47. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)CrossRefMATHGoogle Scholar
  48. Zavala, A., Diharce, E., Aguirre, A.: Particle evolutionary swarm for design reliability optimization. In: Lecture Notes in Computer Science 3410, Presented at the Third International Conference on Evolutionary Multi-Criterion Optimization, pp. 856–869, Guanajuato (2005)Google Scholar

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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.School of MathematicsThapar University PatialaPatialaIndia

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