pith. sign in

arxiv: 2210.14434 · v2 · pith:MNUJ4NQ5new · submitted 2022-10-26 · 📡 eess.SY · cs.SY

Functional requirements decomposition in set-based design

Minghui Sun , Zhaoyang Chen , Georgios Bakirtzis , Hassan Jafarzadeh , Cody Fleming This is my paper

Pith reviewed 2026-05-24 11:07 UTC · model grok-4.3

classification 📡 eess.SY cs.SY
keywords set-based designfunctional requirements decompositionhierarchical methodsystems engineeringdesign methodologyuncertainty reductionparallel abstraction
0
0 comments X

The pith

A four-step method decomposes functional requirements hierarchically for set-based design while preserving top-level consistency.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper presents a four-step method for decomposing functional requirements in set-based design. This approach supports hierarchical breakdown by systematically defining, reasoning about, and narrowing sets of design possibilities. It enables parallel abstraction of alternatives during early design stages. The method ensures that sub-requirements remain consistent with the top-level functional requirements, avoiding gaps or inconsistencies in the design process.

Core claim

We introduce a four-step method to decompose functional requirements for set-based design hierarchically. We systematically define, reason, and narrow the sets, breaking down the functional requirements into formal sub-requirements. This method allows parallel abstraction, ensuring the resulting system satisfies the top-level functional requirements.

What carries the argument

Four-step hierarchical decomposition method that defines, reasons about, and narrows sets to produce formal sub-requirements.

If this is right

  • Enables parallel exploration of multiple design alternatives early in the process.
  • Supports gradual uncertainty reduction during complex systems design.
  • Produces formal sub-requirements that maintain consistency with top-level ones.
  • Advances the design incrementally while satisfying original requirements.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The method could extend to other design approaches that involve hierarchical requirement breakdown.
  • Automation of the narrowing step might be possible through computational modeling of sets.
  • It could help detect requirement inconsistencies at earlier stages than current practices.
  • Testing on industrial case studies would reveal how well the parallel abstraction scales to large systems.

Load-bearing premise

Systematically defining, reasoning about, and narrowing sets of possibilities produces formal sub-requirements that preserve consistency with top-level functional requirements without introducing gaps or inconsistencies.

What would settle it

A case study applying the method where the resulting sub-requirements lead to a system design that fails to satisfy the original top-level functional requirements.

Figures

Figures reproduced from arXiv: 2210.14434 by Cody Fleming, Georgios Bakirtzis, Hassan Jafarzadeh, Minghui Sun, Zhaoyang Chen.

Figure 1
Figure 1. Figure 1: Graphical illustration of refinement. The green circles are the ranges defined in F R, and the brown circles are the ranges defined in F R0 . Note that a system satisfying the functional require￾ments is a special case of refinement. As implies by Eq. (2), the system can take all the values in R∗ x and pro￾vide the output values that are bounded within R∗ y , which satisfies the relationship of refinement … view at source ↗
Figure 2
Figure 2. Figure 2: Graphical illustration of composability. The green circles are the ranges defined in F Rj , and the brown circles are the ranges defined in F Rk [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: A two-level example system to describe the hierarchical [PITH_FULL_IMAGE:figures/full_fig_p007_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: {x 0} and {y 0} can be divided into six groups to reason about the design space and the performance space. The ranges of each group will be calculated differently in Section 5.4. For {x 0} and {y 0}, we use [PITH_FULL_IMAGE:figures/full_fig_p008_4.png] view at source ↗
Figure 5
Figure 5. Figure 5: The boundaries of F P S∗ . However, y 0 may also be the input variables of some sub-functions. Expanding the ranges of y 0 will inevitably lead to the expansion of the input ranges of some sub￾functions, which will in turn makes the system more dif￾ficult or expensive to implement. Therefore, there is an inherent tension between accommodating excessive un￾certainty and the level of difficulty in implementi… view at source ↗
Figure 6
Figure 6. Figure 6: The functional architecture for the top-level functional re [PITH_FULL_IMAGE:figures/full_fig_p012_6.png] view at source ↗
Figure 1
Figure 1. Figure 1: Continuous evolution of the reachable sets of [PITH_FULL_IMAGE:figures/full_fig_p019_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Discrete sampling of the continuous evolution of the [PITH_FULL_IMAGE:figures/full_fig_p019_2.png] view at source ↗
read the original abstract

Designing systems is typically uncertain and ambiguous at early stages. Set-based design supports alternative exploration and gradual uncertainty reduction during the early lifecycle, making it practical for complex systems design. In parallel, the functional requirements decomposition helps to advance the design incrementally. However, current literature on set-based design lacks formal guidance in how to decompose functional requirements. To bridge this gap, we introduce a four-step method to decompose functional requirements for set-based design hierarchically. We systematically define, reason, and narrow the sets, breaking down the functional requirements into formal sub-requirements. This method allows parallel abstraction, ensuring the resulting system satisfies the top-level functional requirements.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

3 major / 0 minor

Summary. The manuscript introduces a four-step method for hierarchically decomposing functional requirements in set-based design. The method consists of systematically defining, reasoning about, and narrowing sets of possibilities to produce formal sub-requirements, enabling parallel abstraction while claiming to ensure that the resulting system satisfies the original top-level functional requirements.

Significance. If the soundness of the decomposition could be established, the contribution would address a documented gap in set-based design literature by supplying procedural guidance for requirement breakdown under early-stage uncertainty. The approach aligns with incremental design principles and could support complex systems engineering workflows. No machine-checked proofs, reproducible examples, or falsifiable predictions are supplied in the current version.

major comments (3)
  1. [Abstract] Abstract: the assertion that the four-step process 'ensuring the resulting system satisfies the top-level functional requirements' is stated directly but rests on an unshown reasoning chain; no inductive invariant, consistency preservation lemma, or gap-analysis argument is supplied to justify that narrowing steps avoid inconsistencies or omissions.
  2. [Method (four-step decomposition)] Four-step method description: the central assumption that 'systematically define, reason, and narrow the sets' produces sub-requirements preserving consistency with top-level FRs is presented procedurally without a concrete worked example, counter-example check, or formal mapping that would demonstrate absence of gaps.
  3. [No dedicated validation or example section] Validation: the manuscript contains no case study, numerical illustration, or error analysis that would test whether decomposed sub-requirements actually entail the top-level requirements, leaving the satisfaction guarantee as an assertion rather than a derived property.

Simulated Author's Rebuttal

3 responses · 0 unresolved

We thank the referee for the constructive feedback highlighting the need for stronger justification of the method's claims. We address each major comment below and will revise the manuscript to incorporate examples and clarification where appropriate.

read point-by-point responses

  1. Referee: [Abstract] the assertion that the four-step process 'ensuring the resulting system satisfies the top-level functional requirements' is stated directly but rests on an unshown reasoning chain; no inductive invariant, consistency preservation lemma, or gap-analysis argument is supplied to justify that narrowing steps avoid inconsistencies or omissions.

    Authors: We agree the abstract states the claim without detailing the supporting chain. The method is constructed so that each narrowing step operates on sets that are subsets of the prior level's possibilities, thereby preserving top-level satisfaction by design. We will revise the abstract to use 'intended to ensure' and add a short paragraph in the method section outlining the consistency argument at a high level. revision: yes

  2. Referee: [Method (four-step decomposition)] the central assumption that 'systematically define, reason, and narrow the sets' produces sub-requirements preserving consistency with top-level FRs is presented procedurally without a concrete worked example, counter-example check, or formal mapping that would demonstrate absence of gaps.

    Authors: The manuscript presents the steps procedurally as the core contribution is the method. To address the lack of illustration, we will add a worked example section showing the four steps applied to a sample functional requirement, including how each narrowing maintains consistency with the parent requirement. revision: yes

  3. Referee: [No dedicated validation or example section] the manuscript contains no case study, numerical illustration, or error analysis that would test whether decomposed sub-requirements actually entail the top-level requirements, leaving the satisfaction guarantee as an assertion rather than a derived property.

    Authors: We acknowledge that the current version lacks any illustrative or validation example. We will add a dedicated section containing a concrete case study from a systems engineering application, demonstrating the decomposition steps and tracing how the sub-requirements entail the original top-level requirement. revision: yes

Circularity Check

0 steps flagged

No circularity: procedural method presented without equations, fits, or self-citation reductions

full rationale

The paper introduces a four-step procedural method for hierarchical functional requirements decomposition in set-based design. The abstract states that the method 'systematically define[s], reason[s], and narrow[s] the sets, breaking down the functional requirements into formal sub-requirements' and 'allows parallel abstraction, ensuring the resulting system satisfies the top-level functional requirements.' No equations, parameters, or fitted quantities appear. No self-citations are invoked to justify uniqueness or load-bearing premises. The central claim is an assertion about the method's properties rather than a derivation that reduces by construction to its inputs. This is a standard non-circular methodological contribution; any soundness gap is a correctness concern, not circularity.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The contribution is a procedural method rather than a mathematical derivation, so the ledger contains only standard domain assumptions about set-based design and hierarchical decomposition; no free parameters or invented entities are introduced in the abstract.

axioms (2)
  • domain assumption Set-based design supports alternative exploration and gradual uncertainty reduction during the early lifecycle.
    Invoked in the opening sentences as the foundation for why decomposition guidance is needed.
  • domain assumption Functional requirements decomposition advances the design incrementally.
    Stated as a parallel benefit that the new method is intended to support.

pith-pipeline@v0.9.0 · 5638 in / 1351 out tokens · 21409 ms · 2026-05-24T11:07:49.127149+00:00 · methodology

discussion (0)

Sign in with ORCID, Apple, or X to comment. Anyone can read and Pith papers without signing in.

Reference graph

Works this paper leans on

54 extracted references · 54 canonical work pages

  1. [1]

    Choice over uncertainty and ambiguity in techni- cal problem solving,

    Schrader, S., Riggs, W. M., and Smith, R. P., 1993, “Choice over uncertainty and ambiguity in techni- cal problem solving,” Journal of Engineering and Technology Management,10(1-2), pp. 73–99

    work page 1993

  2. [2]

    C., 1989, A theory of quantitative infer- ence for artifact sets applied to a mechanical design compiler Tech

    Ward, A. C., 1989, A theory of quantitative infer- ence for artifact sets applied to a mechanical design compiler Tech. rep., MASSACHUSETTS INST OF TECH CAMBRIDGE ARTIFICIAL INTELLI- GENCE LAB

    work page 1989

  3. [3]

    Quantitative set-based de- sign for complex system development,

    Shallcross, N. J., 2021, “Quantitative set-based de- sign for complex system development,” PhD thesis, University of Arkansas

    work page 2021

  4. [4]

    Set-based think- ing in the engineering design community and be- yond,

    Ghosh, S., and Seering, W., 2014, “Set-based think- ing in the engineering design community and be- yond,” In International Design Engineering Techni- cal Conferences and Computers and Information in Engineering Conference, V ol. 46407, American So- ciety of Mechanical Engineers, p. V007T07A040

    work page 2014

  5. [5]

    Literature review: exploring the role of set-based design in trade-off analytics,

    Specking, E. A., Whitcomb, C., Parnell, G. S., Go- erger, S. R., Pohl, E., and Kundeti, N. S. A., 2018, 14 “Literature review: exploring the role of set-based design in trade-off analytics,” Naval Engineers Journal, 130(2), pp. 51–62

    work page 2018

  6. [6]

    Toyota’s principles of set-based concurrent engi- neering,

    Sobek II, D. K., Ward, A. C., and Liker, J. K., 1999, “Toyota’s principles of set-based concurrent engi- neering,” MIT Sloan Management Review, 40(2), p. 67

    work page 1999

  7. [7]

    Set-based design: The state-of- practice and research opportunities,

    Shallcross, N., Parnell, G. S., Pohl, E., and Speck- ing, E., 2020, “Set-based design: The state-of- practice and research opportunities,” Systems En- gineering, 23(5), pp. 557–578

    work page 2020

  8. [8]

    Survey on set-based design (sbd) quantitative methods,

    Dullen, S., Verma, D., Blackburn, M., and Whit- comb, C., 2021, “Survey on set-based design (sbd) quantitative methods,” Systems Engineering, 24(5), pp. 269–292

    work page 2021

  9. [9]

    De- sign margins: a hidden issue in industry,

    Eckert, C., Isaksson, O., and Earl, C., 2019, “De- sign margins: a hidden issue in industry,” Design Science, 5

    work page 2019

  10. [10]

    Bayesian network clas- sifiers and design flexibility metrics for set-based, multiscale design with materials design applica- tions,

    Matthews, J., Klatt, T., Seepersad, C. C., Haberman, M., and Shahan, D., 2014, “Bayesian network clas- sifiers and design flexibility metrics for set-based, multiscale design with materials design applica- tions,” In International Design Engineering Techni- cal Conferences and Computers and Information in Engineering Conference, V ol. 46322, American So- ci...

    work page 2014

  11. [11]

    Enhanced function-means modeling sup- porting design space exploration,

    M ¨uller, J. R., Isaksson, O., Landahl, J., Raja, V ., Panarotto, M., Levandowski, C., and Raudberget, D., 2019, “Enhanced function-means modeling sup- porting design space exploration,” AI EDAM, 33(4), pp. 502–516

    work page 2019

  12. [12]

    Combining set-based concur- rent engineering and function—means modelling to manage platform-based product family design,

    Raudberget, D. S., Michaelis, M. T., and Johan- nesson, H., 2014, “Combining set-based concur- rent engineering and function—means modelling to manage platform-based product family design,” In 2014 IEEE International Conference on Industrial Engineering and Engineering Management, IEEE, pp. 399–403

    work page 2014

  13. [13]

    Set-based concurrent engineering for early phases in platform development,

    Levandowski, C., Raudberget, D., and Johannesson, H., 2014, “Set-based concurrent engineering for early phases in platform development,” In Moving Integrated Product Development to Service Clouds in the Global Economy. IOS Press, pp. 564–576

    work page 2014

  14. [14]

    Creating dynamic requirements through iteratively prototyping critical functionalities,

    Kriesi, C., Blindheim, J., Bjelland, Ø., and Steinert, M., 2016, “Creating dynamic requirements through iteratively prototyping critical functionalities,” Pro- cedia CIRP ,50, pp. 790–795

    work page 2016

  15. [15]

    Integrating model-based sys- tem engineering with set-based concurrent engineer- ing principles for reliability and manufacturability analysis of mechatronic products,

    Borchani, M. F., Hammadi, M., Ben Yahia, N., and Choley, J.-Y ., 2019, “Integrating model-based sys- tem engineering with set-based concurrent engineer- ing principles for reliability and manufacturability analysis of mechatronic products,” Concurrent En- gineering, 27(1), pp. 80–94

    work page 2019

  16. [16]

    A framework for pro- ducibility and design for manufacturing require- ments in a system engineering context,

    Vallhagen, J., Isaksson, O., S ¨oderberg, R., and W¨armefjord, K., 2013, “A framework for pro- ducibility and design for manufacturing require- ments in a system engineering context,” Procedia CIRP ,11, pp. 145–150

    work page 2013

  17. [17]

    Capturing the industrial require- ments of set-based design for conga framework,

    Al-Ashaab, A., Golob, M. M., Noriega, M. P., Torri- ani, M. F., Alvarez, M. P., Beltran, M. A., Busachi, M. A., Ex-Ignotis, M. L., Rigatti, M. C., Sharma, M. S., et al., 2013, “Capturing the industrial require- ments of set-based design for conga framework,” Advances in Manufacturing Technology XXVII, p. 3

    work page 2013

  18. [18]

    Architectural design of complex systems using set-based concur- rent engineering,

    Ammar, R., Hammadi, M., Choley, J.-Y ., Barkallah, M., Louat, J., and Haddar, M., 2017, “Architectural design of complex systems using set-based concur- rent engineering,” In 2017 IEEE International Sys- tems Engineering Symposium (ISSE), IEEE, pp. 1– 7

    work page 2017

  19. [19]

    Towards a correct by construction design of complex systems: The mbss approach,

    Yvars, P.-A., and Zimmer, L., 2022, “Towards a correct by construction design of complex systems: The mbss approach,” Procedia CIRP ,109, pp. 269– 274

    work page 2022

  20. [20]

    The transformation of product development process into lean environment using set-based concurrent engi- neering: A case study from an aerospace industry,

    Al-Ashaab, A., Golob, M., Attia, U. M., Khan, M., Parsons, J., Andino, A., Perez, A., Guzman, P., Onecha, A., Kesavamoorthy, S., et al., 2013, “The transformation of product development process into lean environment using set-based concurrent engi- neering: A case study from an aerospace industry,” Concurrent Engineering, 21(4), pp. 268–285

    work page 2013

  21. [21]

    Set-based concurrent engineering model for automotive elec- tronic/software systems development,

    Al-Ashaab, A., Howell, S., Usowicz, K., Her- nando Anta, P., and Gorka, A., 2009, “Set-based concurrent engineering model for automotive elec- tronic/software systems development,” In Pro- ceedings of the 19th CIRP Design Conference– Competitive Design, Cranfield University Press

    work page 2009

  22. [22]

    An indus- trial trial of a set-based approach to collaborative de- sign,

    Madhavan, K., Shahan, D., Seepersad, C. C., Hlavinka, D. A., and Benson, W., 2008, “An indus- trial trial of a set-based approach to collaborative de- sign,” In International Design Engineering Techni- cal Conferences and Computers and Information in Engineering Conference, V ol. 43253, pp. 737–747

    work page 2008

  23. [23]

    Hierarchi- cal design of negative stiffness metamaterials using a bayesian network classifier,

    Matthews, J., Klatt, T., Morris, C., Seepersad, C. C., Haberman, M., and Shahan, D., 2016, “Hierarchi- cal design of negative stiffness metamaterials using a bayesian network classifier,” Journal of Mechani- cal Design, 138(4)

    work page 2016

  24. [24]

    Requirements management for the design of en- ergy efficient buildings,

    Jansson, G., Schade, J., and Olofsson, T., 2013, “Requirements management for the design of en- ergy efficient buildings,” Journal of Information Technology in Construction (ITcon), 18, pp. 321– 337

    work page 2013

  25. [25]

    Bayesian 15 networks for set-based collaborative design,

    Shahan, D., and Seepersad, C. C., 2009, “Bayesian 15 networks for set-based collaborative design,” In In- ternational Design Engineering Technical Confer- ences and Computers and Information in Engineer- ing Conference, V ol. 49026, pp. 303–313

    work page 2009

  26. [26]

    A serious game for introducing set-based concur- rent engineering in industrial practices,

    Kerga, E., Rossi, M., Taisch, M., and Terzi, S., 2014, “A serious game for introducing set-based concur- rent engineering in industrial practices,” Concurrent Engineering, 22(4), pp. 333–346

    work page 2014

  27. [27]

    An interval- based constraint satisfaction (ibcs) method for de- centralized, collaborative multifunctional design,

    Panchal, J. H., Gero Fern ´andez, M., Paredis, C. J., Allen, J. K., and Mistree, F., 2007, “An interval- based constraint satisfaction (ibcs) method for de- centralized, collaborative multifunctional design,” Concurrent Engineering, 15(3), pp. 309–323

    work page 2007

  28. [28]

    Using set-based design to in- form system requirements and evaluate design de- cisions,

    Parnell, G. S., Specking, E., Goerger, S., Cilli, M., and Pohl, E., 2019, “Using set-based design to in- form system requirements and evaluate design de- cisions,” In INCOSE International Symposium, V ol. 29, Wiley Online Library, pp. 371–383

    work page 2019

  29. [29]

    Quantitative set-based design to inform design teams,

    Specking, E., Shallcross, N., Parnell, G. S., and Pohl, E., 2021, “Quantitative set-based design to inform design teams,” Applied Sciences, 11(3), p. 1239

    work page 2021

  30. [30]

    Iteration in en- gineering design: inherent and unavoidable or prod- uct of choices made?,

    Costa, R., and Sobek, D. K., 2003, “Iteration in en- gineering design: inherent and unavoidable or prod- uct of choices made?,” In International Design Engi- neering Technical Conferences and Computers and Information in Engineering Conference, V ol. 37017, pp. 669–674

    work page 2003

  31. [31]

    Exchanging preliminary information in concurrent engineering: Alternative coordination strategies,

    Terwiesch, C., Loch, C. H., and Meyer, A. D., 2002, “Exchanging preliminary information in concurrent engineering: Alternative coordination strategies,” Organization Science, 13(4), pp. 402–419

    work page 2002

  32. [32]

    Strategies for overlapping dependent de- sign activities,

    Bogus, S. M., Molenaar, K. R., and Diekmann, J. E., 2006, “Strategies for overlapping dependent de- sign activities,” Construction Management and Eco- nomics, 24(8), pp. 829–837

    work page 2006

  33. [33]

    Set-based requirements, technology, and de- sign development for ssn (x),

    Parker, M., Garner, M., Arcano, J., and Doerry, N., 2017, “Set-based requirements, technology, and de- sign development for ssn (x),” Warship 2017: Sub- marines & UUVs, 14-15 June 2017

    work page 2017

  34. [34]

    A set-based design approach for the design of high-performance wave energy converters,

    Trueworthy, A. M., DuPont, B. L., Maurer, B. D., and Cavagnaro, R. J., 2019, “A set-based design approach for the design of high-performance wave energy converters,” In Proceedings of the 13th Eu- ropean Tidal and Wave Energy Conference, Naples, Italy, pp. 1–6

    work page 2019

  35. [35]

    Scalable set-based design optimization and remanufacturing for meeting changing requirements,

    Al Handawi, K., Andersson, P., Panarotto, M., Isaksson, O., and Kokkolaras, M., 2021, “Scalable set-based design optimization and remanufacturing for meeting changing requirements,” Journal of Me- chanical Design, 143(2)

    work page 2021

  36. [36]

    Lessons learned from the application of enhanced function-means modelling,

    M ¨uller, J., Siiskonen, M., and Malmqvist, J., 2020, “Lessons learned from the application of enhanced function-means modelling,” In Proceedings of the Design Society: DESIGN Conference, V ol. 1, Cam- bridge University Press, pp. 1325–1334

    work page 2020

  37. [37]

    Dynamic plat- form modeling for concurrent product-production reconfiguration,

    Landahl, J., Jiao, R. J., Madrid, J., S ¨oderberg, R., and Johannesson, H., 2021, “Dynamic plat- form modeling for concurrent product-production reconfiguration,” Concurrent Engineering, 29(2), pp. 102–123

    work page 2021

  38. [38]

    Modularization in concept development us- ing functional modeling.,

    Levandowski, C., M ¨uller, J. R., and Isaksson, O., 2016, “Modularization in concept development us- ing functional modeling.,” In ISPE TE, pp. 117– 126

    work page 2016

  39. [39]

    Using plm and trade-off curves to sup- port set-based convergence of product platforms,

    Levandowski, C., Forslund, A., Johannesson, H., et al., 2013, “Using plm and trade-off curves to sup- port set-based convergence of product platforms,” In DS 75-4: Proceedings of the 19th International Conference on Engineering Design (ICED13), De- sign for Harmonies, V ol. 4: Product, Service and Systems Design, Seoul, Korea, 19-22.08. 2013, pp. 199–208

    work page 2013

  40. [40]

    Adapting to changes in design requirements using set-based design,

    McKenney, T. A., Kemink, L. F., and Singer, D. J., 2011, “Adapting to changes in design requirements using set-based design,” Naval Engineers Journal, 123(3), pp. 67–77

    work page 2011

  41. [41]

    Set- based design space exploration enabled by dynamic constraint analysis,

    Kizer, J. R., and Mavris, D. N., 2014, “Set- based design space exploration enabled by dynamic constraint analysis,” In Proceedings of the 29th Congress of the International Council of the Aero- nautical Sciences, ICAS

    work page 2014

  42. [42]

    A hy- brid agent approach for set-based conceptual ship design,

    Parsons, M. G., and Singer, D. J., 1999, “A hy- brid agent approach for set-based conceptual ship design,”

    work page 1999

  43. [43]

    Determining feasibility re- silience: Set based design iteration evaluation through permutation stability analysis,

    Ross, J. E., 2017, “Determining feasibility re- silience: Set based design iteration evaluation through permutation stability analysis,” PhD thesis, The University of Southern Mississippi

    work page 2017

  44. [44]

    Product development resilience through set-based design,

    Rapp, S., Chinnam, R., Doerry, N., Murat, A., and Witus, G., 2018, “Product development resilience through set-based design,” Systems Engineering, 21(5), pp. 490–500

    work page 2018

  45. [45]

    A model for quantifying system evolvability based on excess and capacity,

    Tackett, M. W., Mattson, C. A., and Ferguson, S. M., 2014, “A model for quantifying system evolvability based on excess and capacity,” Journal of Mechani- cal Design, 136(5), p. 051002

    work page 2014

  46. [46]

    Design space exploration for quantifying a system model’s feasible domain,

    LARSON, B. J., and MATTSON, C. A., 2012, “Design space exploration for quantifying a system model’s feasible domain,” Journal of mechanical design, 134(4)

    work page 2012

  47. [47]

    Integrating requirements de- velopment and decision analysis,

    Buede, D. M., 1997, “Integrating requirements de- velopment and decision analysis,” In 1997 IEEE In- ternational Conference on Systems, Man, and Cy- 16 bernetics. Computational Cybernetics and Simula- tion, V ol. 2, IEEE, pp. 1574–1579

    work page 1997

  48. [48]

    Com- putations with imprecise parameters in engineering design: background and theory,

    Wood, K. L., and Antonsson, E. K., 1989, “Com- putations with imprecise parameters in engineering design: background and theory,”

    work page 1989

  49. [49]

    Novel space- based design methodology for preliminary engineer- ing design,

    Nahm, Y .-E., and Ishikawa, H., 2006, “Novel space- based design methodology for preliminary engineer- ing design,” The International Journal of Advanced Manufacturing Technology,28(11), pp. 1056–1070

    work page 2006

  50. [50]

    Set-based design of mechanical systems with design robustness integrated,

    Qureshi, A. J., Dantan, J.-Y ., Bruyere, J., and Bigot, R., 2014, “Set-based design of mechanical systems with design robustness integrated,” International Journal of Product Development,19(1/2/3), pp. 64– 89

    work page 2014

  51. [51]

    Arch- comp21 category report: Continuous and hybrid systems with nonlinear dynamics.,

    Geretti, L., Sandretto, J. A. D., Althoff, M., Benet, L., Chapoutot, A., Collins, P., Duggirala, P. S., Forets, M., Kim, E., Linares, U., et al., 2021, “Arch- comp21 category report: Continuous and hybrid systems with nonlinear dynamics.,” In ARCH@ ADHS, pp. 32–54

    work page 2021

  52. [52]

    J., and Murray, R

    Astr ¨om, K. J., and Murray, R. M., 2010, Feed- back systems: an introduction for scientists and en- gineers Princeton university press

    work page 2010

  53. [53]

    Cora 2016 manual,

    Althoff, M., and Kochdumper, N., 2016, “Cora 2016 manual,” TU Munich, 85748

    work page 2016

  54. [54]

    The second toyota paradox: How de- laying decisions can make better cars faster,

    Ward, A., Liker, J. K., Cristiano, J. J., Sobek, D. K., et al., 1995, “The second toyota paradox: How de- laying decisions can make better cars faster,” Sloan management review,36, pp. 43–43. APPENDIX A Proof of Property 3. Let FR be the composite of {FR 1,FR 2,..,FR n}. Replace one FR i with FR′ i (i = 1 , 2...n). According to Property 2, {FR 1,FR 2,..,F...

    work page 1995