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A model-based approach to associate complexity and robustness in engineering systems

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Abstract

Ever increasing functionality and complexity of products and systems challenge development companies in achieving high and consistent quality. A model-based approach is used to investigate the relationship between system complexity and system robustness. The measure for complexity is based on the degree of functional coupling and the level of contradiction in the couplings. Whilst Suh’s independence axiom states that functional independence (uncoupled designs) produces more robust designs, this study proves this not to be the case for max-/min-is-best requirements, and only to be true in the general sense for nominal-is-best requirements. In specific cases, the independence axiom has exceptions as illustrated with a machining example, showing how a coupled solution is more robust than its uncoupled counterpart. This study also shows with statistical significance, that for max- and min-is-best requirements, the robustness is most affected by the level of contradiction between coupled functional requirements (p = 1.4e−36). In practice, the results imply that if the main influencing factors for each function in a system are known in the concept phase, an evaluation of the contradiction level can be used to evaluate concept robustness.

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Adopted from Hillier and Coombes (2004)

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References

  • Albert R, Barabási A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47–97. doi:10.1103/RevModPhys.74.47

    Article  MathSciNet  MATH  Google Scholar 

  • Altshuller G (1996) And suddenly the inventor appeared: TRIZ, the theory of inventive problem solving. Technology

  • Apple (2015) Apple iPhone technical specifications. https://support.apple.com/specs/iphone

  • Box GEP, Meyer RD (1986) An analysis for unreplicated fractional factorials. Technometrics. doi:10.2307/1269599

    MathSciNet  MATH  Google Scholar 

  • Box GEP, Wilson KB (1951) On the experimental attainment of optimum conditions. J R Stat Soc 13(1959):1–45. doi:10.1007/978-1-4612-4380-9_23

    MathSciNet  MATH  Google Scholar 

  • Braha D, Bar-Yam Y (2004) Information flow structure in large-scale product development organizational networks. J Inf Technol 19(4):244–253. doi:10.1057/palgrave.jit.2000030

    Article  Google Scholar 

  • Braha D, Bar-Yam Y (2007) The statistical mechanics of complex product development: empirical and analytical results. Manag Sci 53(7):1127–1145. doi:10.1287/mnsc.1060.0617

    Article  MATH  Google Scholar 

  • Braha D, Maimon O (1998) The measurement of a design structural and functional complexity. IEEE Trans Syst Man Cybern Part A Syst Hum 28(4):527–535. doi:10.1109/3468.686715

    Article  MATH  Google Scholar 

  • Braha D, Brown DC, Chakrabarti A, Dong A, Fadel G, Maier JRA, Wood K (2013) DTM at 25: essays on themes and future directions. In: Proceedings of the 2013 ASME international design engineering technical conferences & computers and information in engineering conference IDETC/CIE. Portland, Oregon, pp 1–17

  • Bras BA, Mistree F (1993) Robust design using compromise decision support problems. Eng Optim. doi:10.1080/03052159308940976

    Google Scholar 

  • Carlson JM, Doyle J (2000) Highly optimized tolerance: robustness and power laws in. Complex Systems. doi:10.1103/PhysRevE.60.1412

    Google Scholar 

  • Chipman H, Hamada M, Wu CFJ (1997) Variable-selection Bayesian approach for analyzing designed experiments with complex aliasing. Technometrics 39:372–381. doi:10.1080/00401706.1997.10485156

    Article  MATH  Google Scholar 

  • Ebro M, Howard TJ (2016) Robust design principles for reducing variation in functional performance. J Eng Des. doi:10.1080/09544828.2015.1103844

    Google Scholar 

  • Ebro M, Howard TJ, Rasmussen JJ (2012) The foundation for robust design: enabling robustness through kinematic design and design clarity. In: Proceedings of international design conference, DESIGN, vol DS 70, pp 817–826

  • Eifler T, Olesen JL, Howard TJ (2014) Robustness and reliability of the GM ignition switch—a forensic engineering case. In: 1st International symposium on robust design, pp. 51–58

  • El-Haik B, Yang K (1999) The components of complexity in engineering design. IIE Trans 31(10):925–934. doi:10.1080/07408179908969893

    Google Scholar 

  • Frey DD, Li X (2008) Using hierarchical probability models to evaluate robust parameter design methods. J Qual Technol 40(1):59–77

    Google Scholar 

  • Frey D, Palladino J, Sullivan J, Atherton M (2007) Part count and design of robust systems. Syst Eng 10(3):203–221. doi:10.1002/sys.20071

    Article  Google Scholar 

  • Göhler SM, Howard TJ (2015) The contradiction index—a new metric combining system complexity and robustness for early design stages. In: Proceedings of the ASME 2015 international design engineering technical conferences & computers and information in engineering conference, pp 1–10

  • Göhler SM, Eifler T, Howard TJ (2016) Robustness metrics: consolidating the multiple approaches to quantify robustness. J Mech Des. doi:10.1115/1.4034112

    Google Scholar 

  • Gribble SD (2001) Robustness in complex systems. In: Proceedings eighth workshop on hot topics in operating systems, pp. 17–22. doi:10.1109/HOTOS.2001.990056

  • Hillier VAW, Coombes P (2004) Hillier’s fundamentals of motor vehicle technology. Nelson Thornes, Cheltenham

    Google Scholar 

  • Jackson A (2013) A road to safety: evolution of car safety features. http://visual.ly/evolution-car-safety-features

  • Kutner MH, Nachtsheim C, Neter J (2004) Applied linear regression models. McGraw-Hill/Irwin, New York

    Google Scholar 

  • Lenth R (1989) Quick and easy analysis of unreplicated factorials. Technometrics. doi:10.2307/1269997

    MathSciNet  Google Scholar 

  • Magee CL, de Weck OL (2004) Complex System Classification. Incose. doi:10.1002/j.2334-5837.2004.tb00510.x

    Google Scholar 

  • Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Tarantola S (2008) Global sensitivity analysis: The primer. Wiley, Chichester

    MATH  Google Scholar 

  • Slagle JC (2007) Architecting complex systems for robustness. In: Master's Thesis, Massachusetts Institute of Technology

  • Sosa M, Mihm J, Browning T (2011) Degree distribution and quality in complex engineered systems. J Mech Des 133(10):101008. doi:10.1115/1.4004973

    Article  Google Scholar 

  • Suh NP (2001) Axiomatic design: advances and applications. Oxford University Press, New York

    Google Scholar 

  • Summers JD, Shah JJ (2010) Mechanical engineering design complexity metrics: size, coupling, and solvability. J Mech Des. doi:10.1115/1.4000759

    Google Scholar 

  • Taguchi G, Chowdhury S, Wu Y (2005) Taguchi’s quality engineering handbook. Wiley, Hoboken

    MATH  Google Scholar 

  • Wu CJ, Hamada MS (2011) Experiments: planning, analysis, and optimization. Wiley, Hoboken

    MATH  Google Scholar 

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Acknowledgments

The authors would like to thank Novo Nordisk for their support for this research project.

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Correspondence to Simon Moritz Göhler.

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Göhler, S.M., Frey, D.D. & Howard, T.J. A model-based approach to associate complexity and robustness in engineering systems. Res Eng Design 28, 223–234 (2017). https://doi.org/10.1007/s00163-016-0236-1

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