The robustness of a design has a major influence on how much the product's performance will vary and is of great concern to design, quality, and production engineers. While variability is always central to the definition of robustness, the concept does contain ambiguity, and although subtle, this ambiguity can have significant influence on the strategies used to combat variability, the way it is quantified and ultimately, the quality of the final design. In this contribution, the literature for robustness metrics was systematically reviewed. From the 108 relevant publications found, 38 metrics were determined to be conceptually different from one another. The metrics were classified by their meaning and interpretation based on the types of the information necessary to calculate the metrics. Four different classes were identified: (1) sensitivity robustness metrics; (2) size of feasible design space robustness metrics; (3) functional expectancy and dispersion robustness metrics; and (4) probability of compliance robustness metrics. The goal was to give a comprehensive overview of robustness metrics and guidance to scholars and practitioners to understand the different types of robustness metrics and to remove the ambiguities of the term robustness. By applying an exemplar metric from each class to a case study, the differences between the classes were further highlighted. These classes form the basis for the definition of four specific subdefinitions of robustness, namely the “robust concept,” “robust design,” “robust function,” and “robust product.”

References

References
1.
Taguchi
,
G.
,
Chowdhury
,
S.
, and
Wu
,
Y.
,
2005
,
Taguchi's Quality Engineering Handbook
,
Wiley
,
Hoboken, NJ
.
2.
Phadke
,
M. S.
,
1989
,
Quality Engineering Using Robust Design
,
Prentice Hall
,
Englewood Cliffs, NJ
.
3.
Ebro
,
M.
,
Howard
,
T. J.
, and
Rasmussen
,
J. J.
,
2012
, “
The Foundation for Robust Design: Enabling Robustness Through Kinematic Design and Design Clarity
,”
International Design Conference
,
DESIGN
, Vol.
DS 70
, pp.
817
826
.https://www.designsociety.org/publication/32050/the_foundation_for_robust_design_enabling_robustness_through_kinematic_design_and_design_clarity
4.
Gremyr
,
I.
,
Arvidsson
,
M.
, and
Johansson
,
P.
,
2003
, “
Robust Design Methodology: Status in the Swedish Manufacturing Industry
,”
Qual. Reliab. Eng. Int.
,
19
(
4
), pp.
285
293
.
5.
Thornton
,
A. C.
,
Donnelly
,
S.
, and
Ertan
,
B.
,
2000
, “
More Than Just Robust Design: Why Product Development Organizations Still Contend With Variation and Its Impact on Quality
,”
Res. Eng. Des.
,
12
(
3
), pp.
127
143
.
6.
Krogstie
,
L.
,
Ebro
,
M.
, and
Howard
,
T. J.
,
2014
, “
How to Implement and Apply Robust Design: Insights From Industrial Practice
,”
Total Qual. Manag. Bus. Excellence
,
26
(
11–12
), pp.
1
19
.
7.
Göhler
,
S. M.
,
Ebro
,
M.
, and
Howard
,
T. J.
,
2016
, “
Mechanisms and Coherences of Robust Design Methodology: A Robust Design Process Proposal
,”
Total Qual. Manage. Bus. Excellence
,
3363
, pp.
1
21
.
8.
Beyer
,
H.-G.
, and
Sendhoff
,
B.
,
2007
, “
Robust Optimization—A Comprehensive Survey
,”
Comput. Methods Appl. Mech. Eng.
,
196
(
33–34
), pp.
3190
3218
.
9.
Saltelli
,
A.
,
Ratto
,
M.
,
Andres
,
T.
,
Campolongo
,
F.
,
Cariboni
,
J.
,
Gatelli
,
D.
,
Saisana
,
M.
, and
Tarantola
,
S.
,
2008
,
Global Sensitivity Analysis: The Primer
,
Wiley
,
Chichester, UK
.
10.
Frey
,
C.
,
Patil
,
S. R.
,
Frey
,
C. H.
, and
Patil
,
S. R.
,
2002
, “
Identification and Review of Sensitivity Analysis Methods
,”
Risk Anal.
,
22
(
3
), pp.
553
578
.
11.
Thornton
,
A. C.
,
2004
,
Variation Risk Management: Focusing Quality Improvements in Product Development and Production
,
Wiley
,
Hoboken, NJ
.
12.
Fowlkes
,
W. Y.
, and
Creveling
,
C. M.
,
1995
,
Engineering Methods for Robust Product Design
,
Addison-Wesley
,
Reading, MA
.
13.
Eifler
,
T.
,
Mathias
,
J.
,
Engelhardt
,
R.
,
Kloberdanz
,
H.
,
Bohn
,
A.
, and
Birkhofer
,
H.
,
2011
, “
Evaluation of Solution Variants in Conceptual Design by Means of Adequate Sensitivity Indices
,”
ICED 11
18th International Conference on Engineering Design—Impacting Society Through Engineering Design
, Vol.
9
, pp.
314
323
.https://www.designsociety.org/publication/30809/evaluation_of_solution_variants_in_conceptual_design_by_means_of_adequate_sensitivity_indices
14.
Zang
,
C.
,
Friswell
,
M. I.
, and
Mottershead
,
J. E.
,
2005
, “
A Review of Robust Optimal Design and Its Application in Dynamics
,”
Comput. Struct.
,
83
(
4–5
), pp.
315
326
.
15.
Murphy
,
T. E.
,
Tsui
,
K.-L.
, and
Allen
,
J. K.
,
2004
, “
A Review of Robust Design Methods for Multiple Responses
,”
Res. Eng. Des.
,
15
(
4
), pp.
201
215
.
16.
Robinson
,
T. J.
,
Borror
,
C. M.
, and
Myers
,
R. H.
,
2004
, “
Robust Parameter Design: A Review
,”
Qual. Reliab. Eng. Int.
,
20
(
1
), pp.
81
101
.
17.
Biolchini
,
J.
,
Mian
,
P. G.
,
Candida
,
A.
, and
Natali
,
C.
,
2005
, “
Systematic Review in Software Engineering
,” System Engineering and Computer Science Department COPPE/UFRJ, Technical Report ES, 679(05), 45.
18.
Hamby
,
D.
,
1995
, “
A Comparison of Sensitivity Analysis Techniques
,”
Health Phys.
,
68
(
2
), pp.
195
204
.
19.
Helton
,
J. C.
,
Johnson
,
J. D.
,
Sallaberry
,
C. J.
, and
Storlie
,
C. B.
,
2006
, “
Survey of Sampling-Based Methods for Uncertainty and Sensitivity Analysis
,”
Reliab. Eng. Syst. Saf.
,
91
(
10–11
), pp.
1175
1209
.
20.
Hutcheson
,
R. S.
, and
Mcadams
,
D. A.
,
2012
, “
Sensitivity Measures for Use During Conceptual Design
,”
Int. J. Des. Eng.
,
5
(
1
), pp.
1
20
.
21.
Chen
,
W.
,
Allen
,
J. K.
,
Tsui
,
K.-L.
, and
Mistree
,
F.
,
1996
, “
A Procedure for Robust Design: Minimizing Variations Caused by Noise Factors and Control Factors
,”
ASME J. Mech. Des.
,
118
(
4
), pp.
478
485
.
22.
Allen
,
J. K.
,
Seepersad
,
C.
,
Choi
,
H.
, and
Mistree
,
F.
,
2006
, “
Robust Design for Multiscale and Multidisciplinary Applications
,”
ASME J. Mech. Des.
,
128
(
4
), pp.
832
843
.
23.
Dantan
,
J. Y.
,
Gayton
,
N.
,
Qureshi
,
A. J.
,
Lemaire
,
M.
, and
Etienne
,
A.
,
2013
, “
Tolerance Analysis Approach Based on the Classification of Uncertainty (Aleatory/Epistemic)
,”
Procedia CIRP
,
10
, pp.
287
293
.
24.
Suh
,
N. P.
,
2001
,
Axiomatic Design: Advances and Applications
,
Oxford University Press
,
New York
.
25.
Howard
,
T. J.
,
Ebro
,
M.
,
Eifler
,
T.
,
Petersen
,
S.
,
Göhler
,
S. M.
,
Christiansen
,
A.
, and
Rafn
,
A.
,
2014
, “
The Variation Management Framework (VMF) for Robust Design
,”
1st International Symposium on Robust Design
, Kobenhavn, Denmark, Aug. 14–15.http://orbit.dtu.dk/fedora/objects/orbit:134955/datastreams/file_13747761-ba04-4c70-807b-d6de0d463e74/content
26.
Dai
,
Z.
,
Scott
,
M. J.
, and
Mourelatos
,
Z. P.
,
2003
, “
Incorporating Epistemic Uncertainty in Robust Design
,”
ASME
Paper No. DETC2003/DAC-48713.
27.
Hu
,
Z.
,
Du
,
X.
,
Kolekar
,
N. S.
, and
Banerjee
,
A.
,
2013
, “
Robust Design With Imprecise Random Variables and Its Application in Hydrokinetic Turbine Optimization
,”
Eng. Optim.
,
46
(
3
), pp.
393
419
.
28.
The Guardian
,
2010
, “
Toyota's Sticky Accelerator Problem
,” accessed Feb. 23, 2016, http://www.theguardian.com/business/interactive/2010/feb/04/toyotaautomotive-industry
29.
Mahalanobis
,
P. C.
,
1936
, “
On the Generalised Distance in Statistics
,”
Proc. Natl. Inst. Sci. India
,
12
(
1
), pp. pp.
49
55
.
30.
Frey
,
D. D.
,
Jahangir
,
E.
, and
Engelhardt
,
F.
,
2000
, “
Computing the Information Content of Decoupled Designs
,”
Res. Eng. Des.—Theory, Appl. Concurrent Eng.
,
12
(
2
), pp.
90
102
.
31.
Lasserre
,
J. B.
,
1983
, “
An Analytical Expression and an Algorithm for the Volume of a Convex Polyhedron in Rn
,”
J. Optim. Theory Appl.
,
39
(
3
), pp.
363
377
.
32.
Hamby
,
D. M.
,
1994
, “
A Review of Techniques for Parameter Sensitivity Analysis of Environmental Models
,”
Environ. Monit. Assess.
,
32
(
2
), pp.
135
154
.
33.
Minto
,
B.
,
2009
,
The Pyramid Principle: Logic in Writing and Thinking
,
Pearson Education
,
London
.
34.
Pahl
,
G.
,
Beitz
,
W.
,
Feldhusen
,
J.
, and
Grote
,
K.-H.
,
2007
,
Engineering Design: A Systematic Approach
,
Springer Science & Business Media
,
London
.
35.
Matthiassen
,
B.
,
1997
, “
Design for Robustness and Reliability: Improving the Quality Consciousness in Engineering Design
,”
Technical University of Denmark
,
Kongens Lyngby, Denmark
.
36.
Chakhunashvili
,
A.
,
Johansson
,
P.
, and
Bergman
,
B.
,
2004
, “
Variation Mode and Effect Analysis
,”
Reliability and Maintainability, 2004 Annual Symposium
-
RAMS
, IEEE, Jan. 26–29, pp.
364
369
.
37.
Johannesson
,
P.
,
Bergman
,
B.
,
Svensson
,
T.
,
Arvidsson
,
M.
,
Lönnqvist
,
Å.
,
Barone
,
S.
, and
De Maré
,
J.
,
2013
, “
A Robustness Approach to Reliability
,”
Qual. Reliab. Eng. Int.
,
29
(
1
), pp.
17
32
.
38.
Ebro
,
M.
, and
Howard
,
T. J.
,
2016
, “
Robust Design Principles for Reducing Variation in Functional Performance
,”
J. Eng. Des.
, pp.
1
18
.
39.
Göhler
,
S. M.
, and
Howard
,
T. J.
,
2015
, “
The Contradiction Index—A New Metric Combining System Complexity and Robustness for Early Design Stages
,”
ASME
Paper No. DETC2015-47255.
40.
Charzyńska
,
A.
,
Nalȩcz
,
A.
,
Rybiński
,
M.
, and
Gambin
,
A.
,
2012
, “
Sensitivity Analysis of Mathematical Models of Signaling Pathways
,”
Biotechnologia
,
93
(
3
), pp.
291
308
.
41.
Han
,
J. S.
, and
Kwak
,
B. M.
,
2004
, “
Robust Optimization Using a Gradient Index: MEMS Applications
,”
Struct. Multidiscip. Optim.
,
27
(
6
), pp.
469
478
.
42.
Bhattacharjya
,
S.
, and
Chakraborty
,
S.
,
2011
, “
Improved Robust Design Optimisation of Structures
,”
Proc. ICE—Eng. Comput. Mech.
,
164
(
1
), pp.
47
57
.
43.
Sobol
, I
. M.
,
2001
, “
Global Sensitivity Indices for Nonlinear Mathematical Models and Their Monte Carlo Estimates
,”
Math. Comput. Simul.
,
55
(
1–3
), pp.
271
280
.
44.
Cukier
,
R. I.
,
Levine
,
H. B.
, and
Shuler
,
K. E.
,
1978
, “
Nonlinear Sensitivity Analysis of Multiparameter Model Systems
,”
J. Comput. Phys.
,
26
(
1
), pp.
1
42
.
45.
Manache
,
G.
, and
Melching
,
C. S.
,
2008
, “
Identification of Reliable Regression- and Correlation-Based Sensitivity Measures for Importance Ranking of Water-Quality Model Parameters
,”
Environ. Model. Software
,
23
(
5
), pp.
549
562
.
46.
Lee
,
M. C. W.
,
Kelly
,
D. W.
,
Degenhardt
,
R.
, and
Thomson
,
R. S.
,
2010
, “
A Study on the Robustness of Two Stiffened Composite Fuselage Panels
,”
Compos. Struct.
,
92
(
2
), pp.
223
232
.
47.
Kwag
,
S.
, and
Ok
,
S.-Y.
,
2013
, “
Robust Design of Seismic Isolation System Using Constrained Multi-Objective Optimization Technique
,”
KSCE J. Civ. Eng.
,
17
(
5
), pp.
1051
1063
.
48.
Caro
,
S.
,
Bennis
,
F.
, and
Wenger
,
P.
,
2005
, “
Tolerance Synthesis of Mechanisms: A Robust Design Approach
,”
ASME J. Mech. Des.
,
127
(
1
), pp.
86
94
.
49.
Caro
,
S.
,
Bennis
,
F.
, and
Wenger
,
P.
,
2005
, “
Comparison of Robustness Indices and Introduction of a Tolerance Synthesis Method for Mechanisms
,”
Can. Congr. Appl. Mech.
, pp.
3
4
.https://hal.archives-ouvertes.fr/hal-00465501/
50.
Ting
,
K.-L. L.
, and
Long
,
Y.
,
1996
, “
Performance Quality and Tolerance Sensitivity of Mechanisms
,”
ASME J. Mech. Des.
,
118
(
1
), pp.
144
150
.
51.
Li
,
M.
,
Azarm
,
S.
, and
Boyars
,
A.
,
2006
, “
A New Deterministic Approach Using Sensitivity Region Measures for Multi-Objective Robust and Feasibility Robust Design Optimization
,”
ASME J. Mech. Des.
,
128
(
4
), pp.
874
883
.
52.
Eslamnour
,
B.
, and
Ali
,
S.
,
2009
, “
Measuring Robustness of Computing Systems
,”
Simul. Model. Pract. Theory
,
17
(
9
), pp.
1457
1467
.
53.
Gunawan
,
S.
, and
Azarm
,
S.
,
2004
, “
Non-Gradient Based Parameter Sensitivity Estimation for Single Objective Robust Design Optimization
,”
ASME J. Mech. Des.
,
126
(
3
), pp.
395
402
.
54.
Kang
,
Z.
, and
Bai
,
S.
,
2013
, “
On Robust Design Optimization of Truss Structures With Bounded Uncertainties
,”
Struct. Multidiscip. Optim.
,
47
(
5
), pp.
699
714
.
55.
Frey
,
D. D.
,
1999
, “
Application of Wavelets and Mahalanobis Distances to Robust Design of an Image Classification System
,”
ASI's 17th Annual Taguchi Methods Symposium
, pp.
198
209
.
56.
Zhu
,
J.
, and
Ting
,
K.-L. L.
,
2001
, “
Performance Distribution Analysis and Robust Design
,”
ASME J. Mech. Des.
,
123
(
1
), pp.
11
17
.
57.
Lamberti
,
P.
, and
Tucci
,
V.
,
2007
, “
Interval Approach to Robust Design
,”
COMPEL Int. J. Comput. Math. Electr. Electron. Eng.
,
26
(
20
, pp.
280
292
.
58.
Du
,
X.
,
Sudjianto
,
A.
, and
Chen
,
W.
,
2004
, “
An Integrated Framework for Optimization Under Uncertainty Using Inverse Reliability Strategy
,”
ASME J. Mech. Des.
,
126
(
4
), pp.
562
570
.
59.
Ren
,
X.
, and
Rahman
,
S.
,
2013
, “
Robust Design Optimization by Polynomial Dimensional Decomposition
,”
Struct. Multidiscip. Optim.
,
48
(
1
), pp.
127
148
.
60.
Chen
,
W.
, and
Yuan
,
C.
,
1999
, “
A Probabilistic-Based Design Model for Achieving Flexibility in Design
,”
ASME J. Mech. Des.
,
121
(
1
), pp.
77
83
.
61.
Jin
,
Y.
, and
Sendhoff
,
B.
,
2003
, “
Trade-Off Between Performance and Robustness: An Evolutionary Multiobjective Approach
,”
International Conference on Evolutionary Multi-Criterion Optimization
,
Springer Berlin
,
Heidelberg
, pp.
237
251
.
62.
Cheng
,
Q.
,
Xiao
,
C.
,
Zhang
,
G.
,
Gu
,
P.
, and
Cai
,
L.
,
2013
, “
An Analytical Robust Design Optimization Methodology Based on Axiomatic Design Principles
,”
Qual. Reliab. Eng. Int.
,
30
(
7
), pp.
1059
1073
.
63.
Otto
,
N.
, and
Antonsson
,
E. K.
,
1994
, “
Design Parameter Selection in the Presence of Noise
,”
Res. Eng. Des.
,
6
(
4
), pp.
234
246
.
64.
Du
,
X.
,
2012
, “
Toward Time-Dependent Robustness Metrics
,”
ASME J. Mech. Des.
,
134
(
1
), p.
011004
.
65.
Chen
,
W.
,
Simpson
,
T. W.
,
Allen
,
J. K.
, and
Mistree
,
F.
,
1999
, “
Satisfying Ranged Sets of Design Requirements Using Design Capability Indices as Metrics
,”
Eng. Optim.
,
31
(
5
), pp.
615
639
.
66.
Heidari
,
A.
,
Yoon
,
Y.-J.
,
Son
,
H.
, and
Choi
,
H.-J.
,
2012
, “
Simulation Based Design of Disk Resonator Biosensors Under Fabrication Uncertainty
,”
ASME J. Mech. Des.
,
134
(
4
), p.
041005
.
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