Research in Engineering Design

, Volume 28, Issue 2, pp 223–234 | Cite as

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

  • Simon Moritz Göhler
  • Daniel D. Frey
  • Thomas J. Howard
Original Paper


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.


Robust design Complexity Axiomatic design Coupling Contradiction 



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


  1. Albert R, Barabási A-L (2002) Statistical mechanics of complex networks. Rev Mod Phys 74(1):47–97. doi: 10.1103/RevModPhys.74.47 MathSciNetCrossRefMATHGoogle Scholar
  2. Altshuller G (1996) And suddenly the inventor appeared: TRIZ, the theory of inventive problem solving. TechnologyGoogle Scholar
  3. Apple (2015) Apple iPhone technical specifications.
  4. Box GEP, Meyer RD (1986) An analysis for unreplicated fractional factorials. Technometrics. doi: 10.2307/1269599 MathSciNetMATHGoogle Scholar
  5. 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 MathSciNetMATHGoogle Scholar
  6. 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 CrossRefGoogle Scholar
  7. 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 CrossRefMATHGoogle Scholar
  8. 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 CrossRefMATHGoogle Scholar
  9. 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 1–17Google Scholar
  10. Bras BA, Mistree F (1993) Robust design using compromise decision support problems. Eng Optim. doi: 10.1080/03052159308940976 Google Scholar
  11. Carlson JM, Doyle J (2000) Highly optimized tolerance: robustness and power laws in. Complex Systems. doi: 10.1103/PhysRevE.60.1412 Google Scholar
  12. 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 CrossRefMATHGoogle Scholar
  13. 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
  14. 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 817–826Google Scholar
  15. 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. 51–58Google Scholar
  16. 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
  17. Frey DD, Li X (2008) Using hierarchical probability models to evaluate robust parameter design methods. J Qual Technol 40(1):59–77Google Scholar
  18. 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 CrossRefGoogle Scholar
  19. 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 1–10Google Scholar
  20. 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
  21. 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
  22. Hillier VAW, Coombes P (2004) Hillier’s fundamentals of motor vehicle technology. Nelson Thornes, CheltenhamGoogle Scholar
  23. Jackson A (2013) A road to safety: evolution of car safety features.
  24. Kutner MH, Nachtsheim C, Neter J (2004) Applied linear regression models. McGraw-Hill/Irwin, New YorkGoogle Scholar
  25. Lenth R (1989) Quick and easy analysis of unreplicated factorials. Technometrics. doi: 10.2307/1269997 MathSciNetGoogle Scholar
  26. Magee CL, de Weck OL (2004) Complex System Classification. Incose. doi: 10.1002/j.2334-5837.2004.tb00510.x Google Scholar
  27. Saltelli A, Ratto M, Andres T, Campolongo F, Cariboni J, Gatelli D, Tarantola S (2008) Global sensitivity analysis: The primer. Wiley, ChichesterMATHGoogle Scholar
  28. Slagle JC (2007) Architecting complex systems for robustness. In: Master's Thesis, Massachusetts Institute of TechnologyGoogle Scholar
  29. 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 CrossRefGoogle Scholar
  30. Suh NP (2001) Axiomatic design: advances and applications. Oxford University Press, New YorkGoogle Scholar
  31. Summers JD, Shah JJ (2010) Mechanical engineering design complexity metrics: size, coupling, and solvability. J Mech Des. doi: 10.1115/1.4000759 Google Scholar
  32. Taguchi G, Chowdhury S, Wu Y (2005) Taguchi’s quality engineering handbook. Wiley, HobokenMATHGoogle Scholar
  33. Wu CJ, Hamada MS (2011) Experiments: planning, analysis, and optimization. Wiley, HobokenMATHGoogle Scholar

Copyright information

© Springer-Verlag London 2016

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringTechnical University of DenmarkKgs. LyngbyDenmark
  2. 2.Department of Mechanical EngineeringMassachusetts Institute of TechnologyCambridgeUSA

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