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Handbook of Performability Engineering pp 477–498Cite as

New Approaches to System Analysis and Design: A Review

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Abstract

Engineering design under uncertainty has gained considerable attention in recent years. A variety of reliability analysis strategies and methodologies are taken into account and applied increasingly to accommodate uncertainties. There exist two different types of uncertainties in practical engineering application: aleatory uncertainty, which is classified as objective and irreducible uncertainty with sufficient information on input uncertainty data and epistemic uncertainty, which is a subjective and reducible uncertainty that stems from a lack of knowledge on input uncertainty data. The nature of uncertainty depends on the mathematical theory within which problem situations are formalized. When sufficient data is available, probability theory is very effective to quantify uncertainty. However, when data is scarce or there is lack of information, the probabilistic methodology may not be appropriate. Among several alternative tools, possibility theory and evidence theory have proved to be computationally efficient and stable tools for reliability analysis under aleatory and/or epistemic uncertainty involved in engineering systems. Thus this chapter first attempts to give a better understanding of uncertainty in engineering design with a holistic view of its classifications, theories and design consideration, and then discusses general topics of foundations and applications of possibility theory and evidence theory. The overview includes theoretical research, computational development and performability improvement about possibilistic and evidential methodologies in the area of reliability during recent years, and it especially reveals the capability and characteristics of quantifying uncertainty from different angles. Finally, perspectives on future research directions are stated.

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References

  1. Klir GJ. Principles of uncertainty: What are they? Why do we need them? Fuzzy Sets and Systems 1995; 74(1): 15–31.

    Article  Google Scholar 

  2. Klir GJ, Folger TA. Fuzzy Sets, uncertainty and information. Prentice Hall, Englewood Cliffs, NJ, 1988.

    MATH  Google Scholar 

  3. Kangas AS, Kangas J. Probability, possibility and evidence: Approaches to consider risk and uncertainty in forestry decision analysis. Forest Policy and Economics 2004; 6(2): 169–188.

    Article  Google Scholar 

  4. Oberkampf WL, DeLand SM, Rutherford B.M, et al., Estimation of total uncertainty in modeling and simulation. Sandia Report 2000-0824, Albuquerque, NM, 2000.

    Google Scholar 

  5. Oberkampf WL, Helton JC, Joslyn CA, et al., Challenge problems: Uncertainty in system response given uncertain parameters. Reliability Engineering and System Safety 2004; 85(1–3): 11–19.

    Article  Google Scholar 

  6. Agarwal H, Renaud JE, Preston EL, et al., Uncertainty quantification using evidence theory in multidisciplinary design optimization. Reliability Engineering and System Safety 2004; 85(1–3): 281–294.

    Article  Google Scholar 

  7. Sugeno M. Fuzzy measures and fuzzy intervals: A survey. In: Gupta MM, Saridis GN, Gaines BR, editors. Fuzzy automata and decision processes. North-Holland, Amsterdam, 1977.

    Google Scholar 

  8. Nikolaidis E, Haftka RT. Theories of uncertainty for risk assessment when data is scarce. http://www.eng.utoledo.edu/-enikolai/

    Google Scholar 

  9. Huang HZ. Fuzzy multi-objective optimization decision-making of reliability of series system. Microelectronics and Reliability 1997; 37(3): 447–449.

    Article  Google Scholar 

  10. Huang HZ. Reliability analysis method in the presence of fuzziness attached to operating time. Microelectronics and Reliability 1995; 35(12): 1483–1487.

    Article  Google Scholar 

  11. Huang HZ. Reliability evaluation of a hydraulic truck crane using field data with fuzziness. Microelectronics and Reliability 1996; 36(10): 1531–1536.

    Article  Google Scholar 

  12. Klir GJ. Fuzzy sets: An overview of fundamentals, applications and personal views. Beijing Normal University Press, 2000.

    Google Scholar 

  13. Zadeh LA. Fuzzy sets as a basis for a theory of possibility. Fuzzy Sets and Systems 1978; 1: 3–28.

    Article  MATH  MathSciNet  Google Scholar 

  14. Fioretti G. Evidence theory: A mathematical framework for unpredictable hypotheses. Metroecnomica 2004; 55(4): 345–366.

    Article  MATH  MathSciNet  Google Scholar 

  15. Beynon M, Curry B, Morgan P. The Dempster–Shafer theory of evidence: an alternative approach to multicriteria decision modeling. Omega 2000; 28(1): 37–50.

    Article  MathSciNet  Google Scholar 

  16. Shafer G. A mathematical theory of evidence. Princeton University Press, 1976.

    Google Scholar 

  17. Dubois D, Prade H. Possibility theory and its applications: A retrospective and prospective view. The IEEE Int. Conf. on Fuzzy Systems; St.Louis, MO; May 25–28, 2003: 3–11.

    Google Scholar 

  18. Bae H-R, Grandhi RV, Canfield RA. Epistemic uncertainty quantification techniques including evidence theory for large-scale structures. Computers and Structures 2004; 82(13–14): 1101–1112.

    Article  Google Scholar 

  19. Möller B, Beer M, Graf W, et al., Possibility theory based safety assessment. Computer-Aided Civil and Infrastructure Engineering 1999; 14(2): 81–91.

    Article  Google Scholar 

  20. Kozine IO, Filimonov YV. Imprecise reliabilities: experiences and advances. Reliability Engineering and System Safety 2000; 67(1): 75–83.

    Article  Google Scholar 

  21. Mourelatos Z, Zhou J. Reliability estimation and design with insufficient data based on possibility theory. 10th AIAA/ISSMO Multidisciplinary Analysis and Optimization International Conference 2004.

    Google Scholar 

  22. Huang HZ, Zuo MJ, Sun ZQ. Bayesian reliability analysis for fuzzy lifetime data. Fuzzy Sets and Systems 2006; 157(12): 1674–1686.

    Article  MATH  MathSciNet  Google Scholar 

  23. Huang HZ, Bo RF, Chen W. An integrated computational intelligence approach to product concept generation and evaluation. Mechanism and Machine Theory 2006; 41(5): 567–583.

    Article  MATH  Google Scholar 

  24. Bae H-R, Grandhia RV, Canfield RA. An approximation approach for uncertainty quantification using evidence theory. Reliability Engineering and System Safety 2004; 86(3): 215–225.

    Article  Google Scholar 

  25. Xu H, Smets Ph. Some strategies for explanations in evidential reasoning. IEEE Transactions on Systems, Man, and Cyberntics. (A) 1996; 26(5): 599–607.

    Google Scholar 

  26. Borotschnig H, Paletta L, Prantl M, et al., A comparison of probabilistic, possibilistic and evidence theoretic fusion schemes for active object recognition. Computing 1999; 62(4): 293–319.

    Article  MATH  MathSciNet  Google Scholar 

  27. Mourelatos ZP, Zhou J. A design optimization method using evidence theory. 31st Design Automation Conference. International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Long Beach, CA, USA; Sept.24–28, 2005.

    Google Scholar 

  28. Limbourg P, Multi-objective optimization of problems with epistemic uncertainty. Coello Coello C.A. et al., Eds. EMO 2005, LNCS 3410, 2005; 413–427.

    Google Scholar 

  29. Delmotte F, Borne P. Modeling of reliability with possibility theory. IEEE Transactions on Systems, Man, and Cybernetics 1998; 20(1): 78–88.

    Google Scholar 

  30. Fan XF, Zuo MJ. Fault diagnosis of machines based on D-S evidence theory. Part 1: D-S evidence theory and its improvement. Pattern Recognition Letters 2006; 27(5): 366–376.

    Article  Google Scholar 

  31. Fan XF, Zuo MJ. Fault diagnosis of machines based on D-S evidence theory. Part 2: Application of the improved D-S evidence theory in gearbox fault diagnosis. Pattern Recognition Letters 2006; 27(5): 377–385.

    Article  Google Scholar 

  32. Cai KY. Wen CY, Zhang ML. Fuzzy variables as a basis for a theory of fuzzy reliability in the possibility context. Fuzzy Sets and Systems 1991; 42(2): 145–172.

    Article  MATH  MathSciNet  Google Scholar 

  33. Cai KY, Wen CY, Zhang ML. Posbist reliability behavior of typical systems with two types of failure. Fuzzy Sets and Systems 1991; 43(1): 17–32.

    Article  MATH  MathSciNet  Google Scholar 

  34. Cai KY, Wen CY, Zhang ML. Fuzzy states as a basis for a theory of fuzzy reliability. Microelectronics and Reliability 1993; 33(15): 2253–2263.

    Article  Google Scholar 

  35. Cappelle B, Kerre EE. On a possibilistic approach to reliability theory. Proceedings of the 2nd International Symposium on Uncertainty Analysis, Maryland MD; April 25–28, 1993: 415–418.

    Google Scholar 

  36. Cappelle B, Kerre EE. A general possibilistic framework for reliability theory. IPMU 1994; 311–317.

    Google Scholar 

  37. Cai KY, Wen CY, Zhang ML. Mixture models in profust reliability theory. Microelectronics and Reliability 1995; 35(6): 985–993.

    Article  Google Scholar 

  38. Cai KY, Wen CY, Zhang ML. Posbist reliability behavior of fault-tolerant systems. Microelectronics and Reliability 1995; 35(1): 49–56.

    Article  Google Scholar 

  39. Nikolaidis E, Chen S, Cudney HH, et al., Comparison of probabilistic and possibility theory-based methods for design against catastrophic failure under uncertainty. ASME, Journal of Mechanical Design 2004: 126(3): 386–394.

    Article  Google Scholar 

  40. Utkin LV, Gurov SV. A general formal approach for fuzzy reliability analysis in the possibility context. Fuzzy Sets and Systems 1996; 83(2): 203–213.

    Article  MathSciNet  Google Scholar 

  41. Cappelle B, Kerre EE. An algorithm to compute possibilistic reliability. ISUMA-NAFIPS 1995; 350–354.

    Google Scholar 

  42. Cappelle B, Kerre EE. Computer assisted reliability analysis: An application of possibilistic reliability theory to a subsystem of a nuclear power plant. Fuzzy Sets and Systems 1995; 74(1): 103–113.

    Article  MATH  Google Scholar 

  43. Bai XG. Asgarpoor S. Fuzzy-based approaches to substation reliability evaluation. Electric Power Systems Research 2004; 69(2–3): 197–204.

    Article  Google Scholar 

  44. Utkin LV. Fuzzy reliability of repairable systems in the possibility context. Microelectronics and Reliability 1994; 34(12): 1865–1876.

    Article  Google Scholar 

  45. Huang HZ, Tong X, Zuo MJ. Posbist fault tree analysis of coherent systems. Reliability Engineering and System Safety 2004; 84(2): 141–148.

    Article  Google Scholar 

  46. Dubois D, Prade H. An alternative approach to the handling of subnormal possibility distributions— A critical comment on a proposal by Yager. Fuzzy Sets and Systems 1987; 24(1): 123–126.

    Article  MathSciNet  Google Scholar 

  47. Utkin LV, Coolen FPA. Imprecise reliability: An introductory overview. http://maths.dur.ac.uk/stats.

    Google Scholar 

  48. Walley P. Statistical reasoning with imprecise probabilities. London: Chapman and Hall, 1991.

    MATH  Google Scholar 

  49. Aughenbaugh JM, Paredis CJJ. The value of using imprecise probabilities in engineering design. Design Engineering Technical Conf. and Computers and Information in Engineering Conf., USA, DETC2005-85354, ASME 2005.

    Google Scholar 

  50. Youn BD, Choi KK. Selecting probabilistic approaches for reliability-based design optimization. AIAA Journal 2004; 42(1): 124–131.

    Article  Google Scholar 

  51. Hall J, Lawry J. Imprecise probabilities of engineering system failure from random and fuzzy set reliability analysis. 2nd Int. Symposium on Imprecise Probabilities and Their Applications, Ithaca, NY; June 26–29, 2001: 195–204.

    Google Scholar 

  52. Papalambros PY, Michelena NF. Trends and challenges in system design optimization. Proceedings of the International Workshop on Multidisciplinary Design Optimization, Pretoria, S. Africa; August 7–10, 2000: 1–15.

    Google Scholar 

  53. Youn BD, Choi KK, Park YH. Hybrid analysis method for reliability-based design optimization. Journal of Mechanical Design 2003; 125(2): 221–232.

    Article  Google Scholar 

  54. Choi KK, Du L, Youn BD. A new fuzzy analysis method for possibility-based design optimization. 10th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, AIAA-2004-4585, Albany, New York, 2004.

    Google Scholar 

  55. Youn BD, Choi KK. Enriched performance measure approach for reliability-based design optimization. AIAA Journal 2005; 43(4): 874–884.

    Article  Google Scholar 

  56. Youn BD, Choi KK, Du L. Integration of reliability-and possibility-based design optimizations using performance measure approach. SAE World Congress, Detroit, MI; April 11–14, 2005, Keynote Paper.

    Google Scholar 

  57. Tu J, Choi KK. A new study on reliability-based design optimization. Journal of Mechanical Design, Transactions of the ASME 1999; 121(4): 557–564.

    Article  Google Scholar 

  58. Bae H-R, Grandhi RV, Canfield RA. Uncertainty quantification of structural response using evidence theory. 43rd Structures, Structural Dynamics, and Materials Conference, AIAA 2002.

    Google Scholar 

  59. Langley RS. Unified approach to probabilistic and possibilistic analysis of uncertain systems. Journal of Engineering Mechanics 2000; 126(11): 1163–1172.

    Article  Google Scholar 

  60. Youn BD. Integrated framework for design optimization under aleatory and/or epistemic uncertainties using adaptive-loop method. ASME 2005-85253. Design Engineering Technical and Computers and Information in Engineering Conference. Long Beach, CA 2005.

    Google Scholar 

  61. Youn BD, Choi KK, Du L, et al., Integration of possibility-based optimization to robust design for epistemic uncertainty. 6th World Congress of Structural and Multidisciplinary Optimization. Rio de Janeiro, Brazil, May 30–June 3, 2005.

    Google Scholar 

  62. Du X, Sudjianto A, Chen W. An integrated framework for probabilistic optimization using inverse reliability strategy. Design Engineering Technical and Computers and Information in Engineering Conference, Chicago, Illinios, Sept. 2–6, 2003;1–10.

    Google Scholar 

  63. Hall DL, Llinas J. An introduction to multisensor data fusion. Proceeding of the IEEE 1997; 85(1): 6–23.

    Article  Google Scholar 

  64. Zhuang ZW, Yu WX, Wang H, et al., Information fusion and application in reliability assessment (in Chinese). Systems Engineering and Electronics 2000; 22(3): 75–80.

    Google Scholar 

  65. Sentz K, Ferson S. Combination of Evidence in Dempster-Shafer Theory. SAND2002-0835 Report, Sandia National Laboratories 2002.

    Google Scholar 

  66. Cai KY. System failure engineering and fuzzy methodology: An introductory overview. Fuzzy Sets and Systems 1996; 83(2): 113–133.

    Article  Google Scholar 

  67. Misra KB, editor. New trends in system reliability evaluation. Elsevier, New York, 1993.

    MATH  Google Scholar 

  68. Kaufmann A. Advances in fuzzy sets: An overview. In: Wang Paul P, editor. Advances in fuzzy sets, possibility theory, and applications. Plenum Press, New York, 1983.

    Google Scholar 

  69. Ghosh Chaudhury S, Misra KB. Evaluation of fuzzy reliability of a non-series parallel network, Microelectronics and Reliability 1992; 32(1/2):1–4.

    Google Scholar 

  70. Tanaka H, Fan LT, Lai FS, et al., Fault-tree analysis by fuzzy probability. IEEE Transactions on Reliability 1983; 32(5):453–457.

    Article  MATH  Google Scholar 

  71. Furuta H, Shiraishi N. Fuzzy importance in fault tree analysis. Fuzzy Sets and Systems 1984; 12(3): 205–214.

    Article  MATH  Google Scholar 

  72. Singer D. A fuzzy set approach to fault tree and reliability analysis. Fuzzy Sets and Systems 1990; 34(2): 145–155.

    Article  Google Scholar 

  73. Soman KP, Misra KB. Fuzzy fault tree analysis using resolution identity and extension principle, International Journal of Fuzzy Mathematics 1993; 1: 193–212.

    MATH  MathSciNet  Google Scholar 

  74. Misra KB, Soman KP. Multistate fault tree analysis using fuzzy probability vectors and resolution identity. In: Onisawa T, Kacprzyk J, editors. Reliability and safety analysis under fuzziness. Heidelberg: Physica-Verlag, 1995; 113–125.

    Google Scholar 

  75. Pan HS, Yun WY. Fault tree analysis with fuzzy gates. Computers and Industrial Engineering 1997; 33(3–4): 569–572.

    Article  Google Scholar 

  76. Keller AZ, Kara-Zaitri C. Further applications of fuzzy logic to reliability assessment and safety analysis, Microelectronics and Reliability 1989; 29(3): 399–404.

    Article  Google Scholar 

  77. Cayrac D, Dubois D, Prade H. Handling uncertainty with possibility theory and fuzzy sets in a satellite fault diagnosis application. IEEE Transactions on Fuzzy Systems 1996; 4(3): 251–269.

    Article  Google Scholar 

  78. Misra KB, Weber GG. A new method for fuzzy fault tree analysis, Microelectronics and Reliability 1989; 29(2): 195–216.

    Article  Google Scholar 

  79. Huang HZ, Wang P, Zuo MJ, et al., A fuzzy set based solution method for multi-objective optimal design problem of mechanical and structural systems using functional-link net. Neural Computing Applications 2006; 15(3–4): 239–244.

    Article  Google Scholar 

  80. Huang HZ, Gu YK, Du XP. An interactive fuzzy multi-objective optimization method for engineering design. Engineering Applications of Artificial Intelligence 2006; 19(5): 451–460.

    Article  Google Scholar 

  81. Cremona C, Gao Y. The possibilistic reliability theory: Theoretical aspects and applications. Structural Safety 1997; 19(2): 173–201.

    Article  Google Scholar 

  82. Liu J, Yang J.B, Wang J, et al., Engineering system safety analysis and synthesis using the fuzzy rule-based evidential reasoning approach. Quality and Reliability Engineering International 2005; 21:387–411.

    Article  MATH  MathSciNet  Google Scholar 

  83. Misra KB, Weber GG. Use of fuzzy set theory for level-I studies in probabilistic risk assessment, Fuzzy Sets and Systems 1990; 37(2): 139–160.

    Article  MathSciNet  Google Scholar 

  84. Darby JL. Evaluation of risk from acts of terrorism: the adversary/defender model using belief and fuzzy sets. SAND2006-5777, Sandia National Laboratories 2006.

    Google Scholar 

  85. C Bos-Plachez. A possibilistic ATMS contribution to diagnose analog electronic circuits. International Journal of Intelligent Systems 1998; 12(11–12): 849–864.

    Google Scholar 

  86. Murthy DNP, Djamaludin I. New product warranty: A literature review. International Journal of Production Economics 2002; 79(3): 231–260.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu, Sichuan, 610054, China

    Hong-Zhong Huang

  2. School of Mechanical Engineering, Dalian University of Technology, Dalian, Liaoning, 116023, China

    Liping He

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  1. Hong-Zhong Huang
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  1. RAMS Consultants, 71 Vrindaban Vihar, Ajmer Road, Jaipur (Rajasthan), 302019, India

    Krishna B. Misra (Principal Consultant) (Principal Consultant)

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Huang, HZ., He, L. (2008). New Approaches to System Analysis and Design: A Review. In: Misra, K.B. (eds) Handbook of Performability Engineering. Springer, London. https://doi.org/10.1007/978-1-84800-131-2_31

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