Abstract

With the increasing size and complexity of modern infrastructure networks rises the challenge of devising efficient and accurate methods for the reliability analysis of these systems. Special care must be taken in order to include any possible interdependencies between networks and to properly treat all uncertainties. This work presents a new approach for the reliability analysis of complex interconnected networks through Monte Carlo simulation and survival signature. Application of the survival signature is key in overcoming limitations imposed by classical analysis techniques and facilitating the inclusion of competing failure modes. The (inter)dependencies are modeled using vine copulas while the uncertainties are handled by applying probability boxes and imprecise copulas. The proposed method is tested on a complex scenario based on the IEEE reliability test system, proving its effectiveness and highlighting the ability to model complicated scenarios subject to a variety of dependent failure mechanisms.

References

1.
UN-OCHA
,
2013
, “
Philippines: Typhoon Haiyan Situation
,” UN OCHA, Mandaluyong, Phillipines, Report No. 19.
2.
Buldyrev
,
S. V.
,
Parshani
,
R.
,
Paul
,
G.
,
Eugene Stanley
,
H.
, and
Havlin
,
S.
,
2010
, “
Catastrophic Cascade of Failures in Interdependent Networks
,”
Nature
,
464
(
7291
), pp.
1025
1028
.10.1038/nature08932
3.
Leavitt
,
W. M.
, and
Kiefer
,
J. J.
,
2006
, “
Infrastructure Interdependency and the Creation of a Normal Disaster: The Case of Hurricane Katrina and the City of New Orleans
,”
Public Works Manage. Policy
,
10
(
4
), pp.
306
314
.10.1177/1087724X06289055
4.
Comfort
,
L. K.
, and
Haase
,
T. W.
,
2006
, “
Communication, Coherence, and Collective Action: The Impact of Hurricane Katrina on Communications Infrastructure
,”
Public Works Manage. Policy
,
10
(
4
), pp.
328
343
.10.1177/1087724X06289052
5.
Behrensdorf
,
J.
,
Brandt
,
S.
,
Broggi
,
M.
, and
Beer
,
M.
,
2017
, “
Numerically Efficient Reliability Analysis of Complex Interdependent Networks
,”
Safety and Reliability. Theory and Applications
,
M.
Cepin
and
R.
Bris
, eds.,
CRC Press
, London.
6.
Coolen
,
F. P. A.
, and
Coolen-Maturi
,
T.
,
2012
, “
Generalizing the Signature to Systems With Multiple Types of Components
,”
Complex Systems and Dependability
,
W.
Zamojski
,
J.
Mazurkiewicz
,
J.
Sugier
,
T.
Walkowiak
, and
J.
Kacprzyk
, eds.,
Springer
,
Berlin
, pp.
115
130
.
7.
Patelli
,
E.
,
Feng
,
G.
,
Coolen
,
F. P. A.
, and
Coolen-Maturi
,
T.
,
2017
, “
Simulation Methods for System Reliability Using the Survival Signature
,”
Reliab. Eng. Syst. Saf.
,
167
, pp.
327
337
.10.1016/j.ress.2017.06.018
8.
Schirmacher
,
D.
, and
Schirmacher
,
E.
,
2008
, “
Multivariate Dependence Modeling Using Pair-Copulas
,” Society of Actuaries: 2008 Enterprise Risk Management Symposium, Chicago, IL, Technical Report No.
2008-m-as08-1
.https://pdfs.semanticscholar.org/aaee/a3a5d2a2e37b952c89f88421751ba538d459.pdf
9.
Cherubini
,
U.
,
Luciano
,
E.
, and
Vecchiato
,
W.
,
2004
,
Copula Methods in Finance
,
Wiley
, Chichester, UK.
10.
Goodwin
,
B. K.
, and
Hungerford
,
A.
,
2014
, “
Copula-Based Models of Systemic Risk in us Agriculture: Implications for Crop Insurance and Reinsurance Contracts
,”
Am. J. Agric. Econ.
,
97
(
3
), pp.
879
896
.10.1093/ajae/aau086
11.
Zhang
,
L.
, and
Singh
,
V. P.
,
2006
, “
Bivariate Flood Frequency Analysis Using the Copula Method
,”
J. Hydrol. Eng.
,
11
(
2
), pp.
150
164
.10.1061/(ASCE)1084-0699(2006)11:2(150)
12.
Joe
,
H.
,
2014
, “
Dependence Modeling With Copulas
,”
Monographs on Statistics & Applied Probability
, Vol.
134
,
Chapman and Hall/CRC
, New York.
13.
Yan
,
J.
,
2006
, “
Multivariate Modeling With Copulas and Engineering Applications
,”
Springer Handbook of Engineering Statistics
,
Springer
, Berlin, pp.
973
990
.
14.
Ram
,
M.
, and
Singh
,
S. B.
,
2009
, “
Analysis of Reliability Characteristics of a Complex Engineering System Under Copula
,”
J. Reliab. Stat. Stud.
,
2
(
1
), pp.
91
102
.http://jrss.in.net/assets/29.pdf
15.
Beer
,
M.
,
Ferson
,
S.
, and
Kreinovich
,
V.
,
2013
, “
Imprecise Probabilities in Engineering Analyses
,”
Mech. Syst. Signal Process.
,
37
(
1–2
), pp.
4
29
.10.1016/j.ymssp.2013.01.024
16.
Nelson
,
R. B.
,
2007
,
An Introduction to Copulas
(Springer Series in Statistics),
Springer Science & Business Media
,
New York
.
17.
Sklar
,
M.
,
1959
, “
Fonctions de Repartition an Dimensions et Leurs Marges
,”
Publ. Inst. Statist. Univ. Paris
,
8
, pp.
229
231
.
18.
Mai
,
J.-F.
, and
Scherer
,
M.
,
2012
,
Simulating Copulas: Stochastic Models, Sampling Algorithms, and Applications
(Series in Quantitative Finance, Vol.
4
),
Imperial College Press
,
London
.
19.
Hofert
,
M.
, and
Mächler
,
M.
,
2011
, “
Nested Archimedean Copulas Meet R: The Nacopula Package
,”
J. Stat. Software
,
39
(
9
), pp.
1
20
.10.18637/jss.v039.i09
20.
Kurz
,
M.
,
2016
, “
Vinecopulamatlab Toolbox
,” New York, accessed July 1, 2019, https://github.com/MalteKurz/VineCopulaMatlab
21.
Watson
,
I. A.
,
1981
,
Review of Common Cause Failures
,
UKAEA
,
Abingdon, UK
.
22.
Hanks
,
B. J.
,
1998
, “
An Appreciation of Common Cause Failures in Reliability
,”
Proc. Inst. Mech. Eng., Part E
,
212
(
1
), pp.
31
35
.10.1243/0954408981529277
23.
Samaniego
,
F. J.
,
2007
,
System Signatures and Their Applications in Engineering Reliability
(International Series in Operations Research & Management Science, Vol.
110
),
Springer
, Berlin.
24.
Aslett
,
L. J. M.
,
2012
, “
Reliability Theory: Tools for Structural Reliability Analysis
,” accessed July 1, 2019, http://www.louisaslett.com
25.
Reed
,
S.
,
2017
, “
An Efficient Algorithm for Exact Computation of System and Survival Signatures Using Binary Decision Diagrams
,”
Reliab. Eng. Syst. Safe
,
165
, pp.
257
267
.10.1016/j.ress.2017.03.036
26.
Behrensdorf
,
J.
,
Brandt
,
S.
,
Broggi
,
M.
, and
Beer
,
M.
,
2018
, “
Efficient Approximation of the Survival Signature for Large Networks
,”
Sixth International Symposium on Reliability Engineering and Risk Management
, Singapore, May 31–June 1, Paper No. RR14.
27.
Ferson
,
S.
,
Kreinovich
,
V.
,
Grinzburg
,
L.
,
Myers
,
D.
, and
Sentz
,
K.
,
2015
, “
Constructing Probability Boxes and Dempster-Shafer Structures
,” Sandia National Laboratory, Albuquerque, NM, Report No.
SAND-2015-4166J
.https://pdfs.semanticscholar.org/b8cb/0e70fea24a3dcdfee967e39914a756eb6c6e.pdf
28.
Feng
,
G.
,
Patelli
,
E.
,
Beer
,
M.
, and
Coolen
,
F. P. A.
,
2016
, “
Imprecise System Reliability and Component Importance Based on Survival Signature
,”
Reliab. Eng. Syst. Saf.
,
150
, pp.
116
125
.10.1016/j.ress.2016.01.019
29.
Pelessoni
,
R.
,
Vicig
,
P.
,
Montes
,
I.
, and
Miranda
,
E.
,
2016
, “
Bivariate p-Boxes
,”
Int. J. Uncertainty, Fuzziness Knowl.-Based Syst.
,
24
(
2
), pp.
229
263
.10.1142/S0218488516500124
30.
Montes
,
I.
,
Miranda
,
E.
,
Pelessoni
,
R.
, and
Vicig
,
P.
,
2015
, “
Sklar's Theorem in an Imprecise Setting
,”
Fuzzy Sets Syst.
,
278
, pp.
48
66
.10.1016/j.fss.2014.10.007
31.
Grigg
,
C.
,
Wong
,
P.
,
Albrecht
,
P.
,
Allan
,
R.
,
Bhavaraju
,
M.
,
Billinton
,
R.
,
Chen
,
Q.
,
Fong
,
C.
,
Haddad
,
S.
,
Kuruganty
,
S.
,
Li
,
W.
,
Mukerji
,
R.
,
Patton
,
D.
,
Rau
,
N.
,
Reppen
,
D.
,
Schneider
,
A.
,
Shahidehpour
,
M.
, and
Singh
,
C.
,
1999
, “
The IEEE Reliability Test System-1996. A Report Prepared by the Reliability Test System Task Force of the Application of Probability Methods Subcommittee
,”
IEEE Trans. Power Syst.
,
14
(
3
), pp.
1010
1020
.10.1109/59.780914
32.
Gruber
,
L. F.
, and
Czado
,
C.
,
2018
, “
Bayesian Model Selection of Regular Vine Copulas
,”
Bayesian Anal.
,
13
(
4
), pp.
1111
1135
.10.1214/17-BA1089
You do not currently have access to this content.