1. Metrics for Developing Functional Requirements and Selecting Design Parameters in Axiomatic Design
Christopher A. Brown and Richard Henley
Mechanical Engineering Department
Worcester Polytechnic Institute,
Worcester, Massachusetts
USA

2. Objective
Evaluate the systematic use of metrics for developing design decompositions
Verify the quality of the design solutions

3. Lord Kelvin
“If you cannot measure it, you cannot improve it.”
How do you measure:
success in achieving the FRs?
value added during the design process?
quality of the design solution?
progress in a design review?

4. Rationale for Metrics Select the best FRs
Design solutions can be no better than their FRs.
Poor FRs limit the value of the design solution
no matter how well the axioms are applied after the FRs are developed.
Teach so that people learn and adopt AD
Failure of engineers to adopt AD often stems from difficulties with the formulation of good FRs

5. Value Chain The customer needs define the value
The best FRs provide the best value
DPs and PVs continue the value chain
Anything that does not contribute to the value chain can be eliminated
Useful for eliminating unnecessary expenses in existing products

6. State of the Art Verify CEME decompositions
Use themes, e.g., energy, time (Brown 2013)
Use metrics for FRs in order to establish that a decomposition is CEME (Henley 2015)
Sort out FRs from non-FRs and optimization and selection criteria (OCs or SCs )
FRs that begin with terms like maximize or minimize can be OCs or SCs (Thompson ICAD 2103)

7. State of the Art
Thompson (CIRP 2013) promotes a rigorous approach to considering the needs of customers and stakeholders.
identify several different stakeholder categories
develop a check list to generate CNs
associate with FRs possibly at different levels in the decomposition

8. Methods and techniques
philosophical and experiential
rooted in practice and teaching of AD
evolved during over 25 years of experience
consulting with industry on design problems.
advising capstone engineering design projects
teaching a project-oriented graduate course on axiomatic design of manufacturing

9. Perspectives 25 years ago Quantitative approach
small numbers of FR-DP pairs in spreadsheets (<100)
Based on Principles of Design (Suh 1990)
Rigorous use of design equations (FR = f(DP))
Matrix with partial derivatives
Evaluate semangularity and reangularity

10. Perspectives 12 years ago
Acclaro facilitates larger design and process matrices
Use of Xs and 0s replaces partial derivatives
Designs include thousands of FR-DP pairs
Size wins over metrics
Emphasis on verbal descriptions and assumed quantitative relationships
CEME by themes
Difficult to verify
Students resort to verification by declaration

11. Separate Function and Physical
Fundamental to Axiomatic Design
FRs cannot contain physical information
Maximize the solution space
The DP is the physical design solution
Common problem with beginning students…
FR provide bolt
DP bolt
State the FR to provide the largest possible space for the design solution
FR fasten parts
DP: bolt, rivet, screw, glue, clamp, press fit, or solder

12. Decomposition top down
Mutually exclusive - Collectively exhaustive

13. FRs must be CEME Collectively Exhaustive Mutually Exclusive
did you think of everything?
Axiom 2 probability of success in satisfying CNs
Mutually Exclusive
redundancy? overlap?
Axiom 1 independence
Orthogonally of the FRs 13

14. Translating tolerances: FRs to DPs
softer spring, k2 , results in a larger design range,
and lower information FR k1 k2
Breakage
FR tolerance
F F
nominal
Slip
F=kX DP
DP tolerance X  ΔX

15. Equations for the decomposition
Design
FRi = f(DPi , DPj , DPk …)
Parent-child
FRi = g(FRi.1, FRi.2, FRi.3 …)

16. Lead with metrics
Insist that students identify the metrics with the FRs and DPs at each step in the decomposition
FR0 fasten parts
What will you measure to see if it is successful?
What has value to the customer?
Load to separate
Displacement to separate
Work to separate
Combination?

17. Consider work to separate
Decompose FR0 – improve understanding of CNs
FR1 Control maximum load (L)
FR2 control initial stiffness (Si = Li/Xi)
FR3 control displacement before rupture (X)

18. Load – Displacement work = ∫Lds Load (L) Displacement (X)
Maximum allowable
nominal L
Tolerance
Minimum allowable
work = ∫Lds
Si = Li/Xi
X  ΔX
Displacement (X)

19. Metrics Candidates Product attribute Vector addition, orthogonal space
FR0 = (FR1² + FR2² + FR3² + …)½
Based on Axiom 2 (probability of success)
I = log (1/p)
Functional Metric p is probability of success in satisfying CN
Physical Metric p is probability of success in fulfilling FR
Process Metric…
Depends on value chain CN→FR→DP→PV

20. FRs versus OCs and SCs FR, binary value in achieving tolerance or not
Probability of achieving tolerance - FRs
Optimization and Selection criteria (OCs & SCs)
Proximity to preference

21. Conclusions Frequent challenges for students have been identified
The use of metrics has potential for addressing challenges
Continued work on teaching metrics

22. Thank you for your attention

23. Adaptive or responsive re-design
systematic application of adaptive re-design
systems that go beyond re-initialization [11. 12] to re-design,
as used in play calling for football [7] for
defining new DPs and possibly new metrics and FRs

24. Supposition Rigorous use of metrics will guide
the formulation of superior functional requirements (FRs), and
the selection of the best design parameters (DPs).

25. Zigzagging Decomposition1
FR 0
DP 0 2
FR 1
FR 2
DP 1
DP 2 3 4 5 6
FR 1.1
FR 1.2
FR 1.3
FR 2.1
FR 2.2
DP 1.1 DP
1.2
1.3
DP 2.1
DP 2.2 9… 8 7