In the area of system reliability analysis, dynamic and dependent behaviors such as multi-state, multi-phase, functional dependence, common cause failures, competing failures, standby sparing, and sequence dependence have been recognized as a significant contribution to problems in overall system reliability. However, with the incorporation of those behaviors, resulting dynamic system reliability models cannot be efficiently and accurately solved by existing state space based models such as Markov methods. In this presentation, an overview on various dynamic and dependent behaviors will be presented first. Efficient combinatorial approaches, in particular, decision diagrams will then be discussed for the reliability analysis of multi-state systems with illustration of examples from areas of computer systems, capacitated transmission networks, and MCNC benchmark circuits.

1. Efficient Combinatorial Models
for Reliability Analysis of
Complex Dynamic Systems (基
C l D i S t (基
于组合模型的复杂动态系统可
靠性分析)
Dr. Liudong Xing (邢留冬博士)
©2011 ASQ & Presentation Xing
Presented live on Nov 09th, 2011
http://reliabilitycalendar.org/The_Re
liability_Calendar/Webinars_
liability Calendar/Webinars ‐
_Chinese/Webinars_‐_Chinese.html

2. ASQ Reliability Division
ASQ Reliability Division
Chinese Webinar Series
Chinese Webinar Series
One of the monthly webinars
One of the monthly webinars
on topics of interest to
reliability engineers.
To view recorded webinar (available to ASQ Reliability
Division members only) visit asq.org/reliability
) /
To sign up for the free and available to anyone live
webinars visit reliabilitycalendar.org and select English
Webinars to find links to register for upcoming events
http://reliabilitycalendar.org/The_Re
liability_Calendar/Webinars_
liability Calendar/Webinars ‐
_Chinese/Webinars_‐_Chinese.html

3. Efficient Combinatorial Models for
Reliability Analysis of Complex Dynamic
Systems
(基于组合模型的复杂动态系统可靠性分析)
Presented by
Dr. Liudong Xing (邢留冬)
E-mail: lxing@umassd.edu
E mail: lxing@umassd edu
Electrical and Computer Engineering Dept.
University of Massachusetts
Dartmouth, MA, USA
www.massachusetts.edu
www massachusetts edu
ASQ Reliability Division Webinar Series

4. http://technicalhut.blogspot.com/2011/09/robo-earth-database-to-network-robots.html
http://www.0592en.com/class/trans/2011/1031/1406.html, http://www.metrolic.com/us-nuclear-power-plant-funds-remain-unused-168212/
http://www.geekwithlaptop.com/cloud-computing-takes-us-into-the-future-of-technology-chrome-os-leads-the-way, http://spie.org/x14634.xml?ArticleID=x14634 2
http://www.infrastructurist.com/2009/05/19/a-vibrant-us-train-industry-would-employ-more-people-than-car-makers-do-now/ -- Image Sources

5. Motivation
Computing and engineering systems are
evolving t
l i toward enabling much l
d bli h larger
collaboration & handling more complicated
missions.
The i
Th increasing complexity and scale im l
si m l xit d s l imply
that reliability problems will not only continue
to be a challenge but also require more
efficient models and solutions
3

6. @ This Talk --
Reliability Analysis of Complex Dynamic Systems
Evaluation Methods p
Complex Behavior
Analytical methods Multiple states (多状态)
o Combinatorial methods Multiple phases (多阶段)
(fault trees, decision Sequence dependence (顺序相依)
diagrams) Dynamic sparing (动态备用)
o State space-based Imperfect coverage (不完全覆盖)
methods (Markov models)
Common-cause failures (共因故障)
(共 障)
Simulation methods Functional dependence (功能相依)
Measurement-based Competing failures (竞争失效)
p g
Acknowledgment: US National Science Foundation (NSF)
No. 0614652 & 0832594 & 1112947 4

7. Agenda
Overview of complex b h i
O i f l behavior
Reliability and sensitivity analysis of multi-
multi
state systems
5

8. Multi-State (多状态)
System & components: more than two levels of
p
performance (or states) varying from perfect
p
operation to complete failure
Behaviors modeled: shared loads, performance
,p
degradation, imperfect coverage, multiple failure
modes, etc.
Applications: power systems, transmission networks,
communication networks circuits etc
networks, circuits,
Challenge:
o dependence among multiple states
6

9. Multi-Phase (多阶段)
A system supporting a mission characterized by
multiple, consecutive, and non-overlapping phases of
operation
System components subject to different stresses,
environmental conditions, and reliability requirements i
i t l diti s d li bilit i ts in
different phases
Applications: aerospace (aircraft, rockets, spacecraft),
nuclear power, airborne weapon systems, etc
Challenge:
o dynamics in system configuration, failure criteria, and
y y g , ,
component failure behavior
o s-dependencies across phases for a given component
7

10. Sequence Dependence (顺序相依)
The order that fault events occur is important to the
system reliability
Challenge: sequence-dependent system f l
h ll d d failure
criteria
Failure
F il
Primary:
P
Switch:
Sw
Standby:
P S Sw P
S
• Sw P: system fails Modeled using priority AND
•P Sw: system OK
y g
gate in fault tree analysis
y
8

11. Dynamic Sparing (动态备用)
λP
One module is on-line &
mponents
operational, and one or λS Hot
com
more modules serve as t
τ1 τ2
standby units.
λP
When the on-line module
components
λS Cold
experiences a fault and
the fault is detected, it is
c
t
τ1 τ2
removed and replaced with
λP
a standby unit.
omponents
αS λS Warm
Challenge: time/order-
dependent failure
co
t
τ1 τ2
behavior
9

12. I
Imperfect F lt C
f t Fault Coverage (不完全覆盖)
Imperfect detection, location or recovery of a
detection location,
component fault may cause an extensive damage to the
entire system, despite presentence of redundancies.
system redundancies
Extent of an uncovered fault damage can exhibit
multiple levels in hierarchical systems: if an
undetected error escapes from one level, it may be
covered at a higher level
level.
Challenge: multiple failure modes
10

13. Common Cause Failures (共因故障)
Common-Cause
Simultaneous failure of multiple components due to a
common cause
Challenge: multiple dependent component failures
External
Cause
Common
Cause
Global Effect on a
Failure
Internal Cause y y
System/Subsystem
(Propagated
Failure)
Selective Effect on
System Components
11

14. Functional Dependence (功能相依)
Occurrence of some event (trigger) causes other
components ( p n n components) to become
mp n n (dependent mp n n ) m
inaccessible or unusable
Cascading f il
C di failures: multiple f il
lti l failures i iti t d by th
initiated b the
trigger of one component in the system resulting in a
chain reaction ord i effect (
h i i domino ff (common i power
in
grids)
FDEP FDEP
A B C ......
12

15. Competing Failures (竞争失效)
Occur in systems subject to both functional
dependence (FDEP) and propagated failures (PF)
d d d d f il
PF has different consequences due to competition in
the time domain between trigger failure and failure
propagated from dependent components
components.
Trigger f
gg failure PF of dependent components: f
f p mp failure isolation
PF of dependent components Trigger failure: system fails
13

16. Agenda
Overview of complex behavior
Reliability and sensitivity analysis of multi-
l l l l
state systems (MSS)
y ( )
o Basic concepts
o MSS analysis methods
l h d
o Examples
E mp
14

17. MSS R li bilit
Reliability
MSS reliability at level d :
o probability that the system performance level is
greater than or equal to d.
MRd = P (ϕ ( x) ≥ d )
o φ( ) system structure function
(x): f
15

18. MSS S
Sensitivity M
iti it Measures
Quantify importance of components, and help
prioritize reliability improvement activities
Composite importance measures (CIM): evaluate
contribution of a m
f multi-state component as a whole to
mp
MSS reliability
o Example: Birnbaum or average of the Sum of Absolute
Deviation (SAD)
∑
ωi
j =1
P(ϕ ( x) < d | x i = bij ) − P(ϕ ( x) < d )
MI SAD
=
ωi −1
i
16

19. MSS A l i M th d (1)
Analysis Methods
Simulation-based methods
o computationally expensive and time-consuming
p y p g
o approximate results
o a complete new simulation must be performed when
parameter values change
State
St t space-based methods (M k models)
b d th d (Markov d l )
o more sever state explosion problem than analyzing binary
systems
Multi-state minimal path/cut vectors (MMPV/MMCV)
p
o doubly exponential complexity
17

20. MSS Analysis Methods (2)
Decision diagrams (决策图)-based methods
o Multi-state binary decision diagrams (MBDD)
o Logarithmically-encoded binary decision diagrams
Logarithmically encoded
(LBDD)
o Multi-state multi-valued decision diagrams (MMDD)
18

21. An Illustrative Example
A Ill t ti E l
Each board has 4 states B1
P1 M1
o Bii,4 (both P & M are functional)
4
Bus
o Bi,3 (M is functional, P is down)
B2
o Bii,2 (P is functional, M is down)
2 P2 M2
o Bi,1 (both P & M are down)
The system has 3 states
o S3 (at least one P & both M are
functional)
f i l)
o S2 (at least one P & exactly one
M are functional)
o S1 (no P or M is functional)
19

22. MBDD
4 Boolean variables to encode 4 board states
o (B1,1, B1,2, B1,3, B1,4) for board B1
o (B2,1, B2,2, B2,3, B2,4) for board B2
, , ,3 ,
Board State B1,1 Board State B1,2 Board State B1,3 Board State B1,4
o numerous variables;
o special operations to handle state dependencies in model
generation and evaluation
X. Zang, D.Wang, H. Sun, and K. S. Trivedi, “A BDD-based algorithm for analysis of multistate systems
with multistate components,” IEEE Trans. Computers, vol. 52, no. 12, pp. 1608–1618, Dec. 2003 20

23. LBDD
2 auxiliary Boolean variables to encode 4 board states
y
o (v1, v2) for board B1
o (w1, w2) for board B1
v1 v2 B1 states 1,3
0 0 B1,1 v1
0 1 B1,2
0
1
v2
0
1
1 0 B1,3
1
1
1 1 B1,4
o binary logic; no dependence among fewer auxiliary variables
o state encoding and decoding are needed
A. Shrestha and L. Xing, “A Logarithmic Binary Decision Diagrams-Based Method for Multistate Systems
Analysis,” IEEE Trans. Reliability, Vol. 57, No. 4, pp. 595-606, Dec. 2008.
21

24. MMDD
1 multi-valued variable per multi-state component
multi valued multi state
o (B1) for board B1
o (B2) for board B2
B1 B1 B1 B1
1 4 1 4 1 4 1 4
2 3 2 3 2 3 2 3
1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1
Board State B1,1 Board State B1,2 Board State B1,3 Board State B1,4
o no dependence among multi-valued variables
o straightforward model generation and evaluation
L. Xing and Y. Dai, “A New Decision Diagram Based Method for Efficient Analysis on Multi-State Systems,”
IEEE Trans. Dependable and Secure Computing, vol. 6, no. 3, pp. 161-174, Jul.-Sep. 2009.
S. V. Amari, L. Xing, A. Shrestha, J. Akers, and K. S. Trivedi, “Performability Analysis of Multi-State
Computing Systems Using Multi-Valued Decision Diagrams,” IEEE Trans. on Computers, vol. 59, no. 10, pp.
1419-1433, 2010. 22

25. MFT
Example Computer System
MBDD, LBDD, MMDD
1
4
0
3
1
0
0
1
MBDD LBDD MMDD
23

26. Performance Comparison
Microelectronics Center of North Carolina
(MCNC) BBenchmarks
h k
o model size
o # recursive calls
o top-down recursive evaluation ti
t d i l ti time
o bottom-up evaluation time
A. Shrestha, L. Xing, and Y. Dai, “Decision Diagram-Based Methods, and Complexity Analysis for Multistate
Systems,” IEEE Trans. Reliability, vol. 59, no. 1, pp. 145-161, Mar. 2010. 24

27. Name Inpu Outp Product
t u Terms
t
MCNC Benchmarks
N B h k 5xp1
9sym
7
9
10
1
75
87
alu2 10 8 68
alu4 14 8 1028
Originally designed for b12 15 9 431
Boolean switching functions bw 5 28 87
clip 9 5 167
con1 7 2 9
Adapted to form MSS with
p inc 7 9 34
multistate components mdiv7 8 10 256
misex1 8 7 32
y p
o Each binary output ≡ a misex2 25 18 29
system state misex3c 14 14 305
o A group of binary inputs ≡
g p y p postal 8 1 25
rd53
d 3 5 3 32
multistate component rd73 7 3 141
o E.g., 4 binary inputs form 16- rd84 8 4 256
state components sao2 10 4 58
sn74181 14 8 1132
squar5 5 8 32
xor5 5 1 16
Z5xp1 7 10 128
25
Z9sym 9 1 420

28. Model Size
M d l Si
WMBDD > WLBDD > WMMDD
26

29. 10
100
1000
10000
100000
1000000
xor5
rd53
squar5
con1
misex1
postal
rd73
inc
bw
rd84
Top-down
5xp1
Z9sym
Z5xp1
9sym
clip
mdiv7
RMBDD > RMMDD > RLBDD
MBDD
sao2
misex2
alu2
LBDD
b12
# of Top down Recursive Calls
misex3c
sn74181
alu4
MMDD
27

30. Top-down R
T d Recursive E l ti Time
si Evaluation Ti
TMBDD > TLBDD > TMMDD
(in ms, time for decoding states is included for LBDD)
MBDD LBDD MMDD
1000
100
10
1
0.1
0.01
v7
2
1
bw
sq 3
73
84
1
r5
u2
u4
m n1
Z9 1
m o2
r5
c
al
p
m
x1
m x2
ym
sn 3c
xp
5
18
in
p
b1
cli
st
sy
xo
ua
di
co
sa
al
al
rd
rd
rd
5x
ise
ise
x
9s
Z5
po
74
m
ise
28

31. 0 01
0.01
0.1
1
10
100
xo
r5
rd
5
po 3
st
al
co
n1
rd
7
sq 3
ua
Z9 r 5
B tt
sy
m m
ise
x1
rd
84
5x
p1
9s
ym
in
c
sa
o
Z5 2
xp
1
bw
m
ise
x2
al
TMBDD > TLBDD > TMMDD
u2
MBDD
b1
2
E l ti Ti
cli
p
m
Bottom-up Evaluation Time
m div7
LBDD
ise
x
sn 3c
74
18
1
al
u4
MMDD
29

32. S mm
Summary
LBDD is a tradeoff that transforms multi-
state domain into an equivalent auxiliary
q y
binary domain, but offers reduced system
model size than MBDD
MBDD.
In general, MMDD is more efficient than
MBDD and LBDD.
30

33. AT
Transmission N t
smissi Network
k
2
The system must 1
3
supply a demand >= 3
l d d s
5
7 t
units from s to t. 4
6
Component Transmission Capacity State Probability
1 0 1 2 3 4 0.10 0.05 0.15 0.35 0.35
2 0 1 2 - - 0.10 0.05 0.85 - -
3 0 1 2 - - 0.10
0 10 0.05 0.85
0 05 0 85 - -
4 0 1 2 3 - 0.20 0.10 0.45 0.25 -
5 0 1 2 - - 0.10 0.05 0.85 - -
6 0 1 2 - - 0 10
0.10 0 05 0 85
0.05 0.85 - -
7 0 1 2 3 4 0.15 0.15 0.05 0.45 0.20
A. Shrestha, L. Xing, D. W. Coit, “An Efficient Multi-State Multi-Valued Decision Diagram-Based Approach
for Multi-State System Sensitivity Analysis,” IEEE Trans. Reliability, vol. 59, no. 3, pp. 581-592, Sept. 2010. 31

34. x1
MMDD-based
3, 4
1 2
0
x2 x2 x2
0 1, 2
0
1
2 0 1 2
Analysis Results
x3 x3 x3 x3 x3
0 1, 2 0
0 1, 2 2
1
0 2
1
0 1
2 1, 2
x4 x4 x4 3
3 2, 3 1, 2, 3 s 7 t
0
0, 1, 2 0, 1
5
x5 x5 2 x5
2 0 4
1 0
0 1 1, 2
6
x6 x6 1, 2
MRd =3 = P (ϕ ( x) ≥ 3)
0
2
0, 1 x7
0, 1, 2 3, 4
= 0.54541524
0 1
Rank j Birnbaum MAD MMAW MMFV
1 7 0.5559039984 0.3817906706 1.4199334287 0.4199334287
2 1 0.1750166234 0.1036475213 1.1140024163 0.1140024163
3 4 0.1011335000 0.0723422213 1.0795695635 0.0795695635
4 2 0.0622255969 0.0219048863 1.0240932917 0.0240932917
5 3 0.0622255969
0 0622255969 0.0219048863
0 0219048863 1.0240932917
1 0240932917 0.0240932917
0 0240932917
6 5 0.0169283156 0.0060528488 1.0066575580 0.0066575580
7 6 0.0169283156 0.0060528488 1.0066575580 0.0066575580 32

35. Conclusion
Dy m
Dynamic and dependent behavior has been recognized
p g
as a significant contribution to problems in complex
reliability.
system reliability
o Multiple states (多状态), Multiple phases (多阶段), Sequence
dependence (顺序相依), Dynamic sparing (动态备用),
序相依 动态备
Imperfect coverage (不完全覆盖), Common-cause failures (共
因故障), F
因故障) Functional dependence (功能相依) C
ti ld d (功能相依), Competing
ti
failures (竞争失效), etc...
Decision diagrams (决策图) are state-of-the-art
combinatorial models for efficient reliability analysis
f ff y y
of complex systems.
33

36. References: Multi State (多状态)
Multi-State
o G. Levitin, L. Podofillini, and E. Zio, “Generalised importance measures for multi-state elements based on
, , , p
performance level restrictions,” Reliability Engineering & System Safety, vol. 82, no. 3, pp. 287–298, 2003.
o A. Lisnianski and G. Levitin, Multi-State System Reliability: Assessment, Optimization, and Applications, vol. 6:
Series of Quality, Reliability, and Engineering Statistics, World Scientific, 2003.
o J E R i
J. E. Ramirez-Marquez and D W C it “A Monte-Carlo simulation approach for approximating multi-state two-
M d D. W. Coit, M t C l i l ti hf i ti lti t t t
terminal reliability,” Reliability Engineering & System Safety, vol. 87, no. 2, pp. 253-264, Feb. 2005.
o J. Huang and M. J. Zuo, “Dominant multi-state systems,” IEEE Trans. Reliability, vol. 53, no. 3, pp. 362–368, Sep.
2004.
o X. Zang, D.Wang, H. Sun, and K. S. Trivedi, “A BDD-based algorithm for analysis of multistate systems with
multistate components,” IEEE Trans. Computers, vol. 52, no. 12, pp. 1608–1618, Dec. 2003.
o W. C. Yeh, “A fast algorithm for searching all multi-state minimal cuts,” IEEE Trans. Reliability, vol. 57, no. 4, pp.
581–588, Dec 2008
581 588 Dec. 2008.
o L. Xing and Y. Dai, “A New Decision Diagram Based Method for Efficient Analysis on Multi-State Systems,”
IEEE Trans. Dependable and Secure Computing, vol. 6, no. 3, pp. 161-174, Jul.-Sep. 2009.
o S. V. Amari, L. Xing, A. Shrestha, J. Akers, and K. S. Trivedi, “Performability Analysis of Multi-State Computing
g y y p g
Systems Using Multi-Valued Decision Diagrams,” IEEE Trans. on Computers, Vol. 59, No. 10, pp. 1419-1433,
October 2010.
o A. Shrestha and L. Xing, “A Logarithmic Binary Decision Diagrams-Based Method for Multistate Systems
Analysis,
Analysis ” IEEE Trans Reliability Vol 57 No 4 pp 595-606 December 2008.
Trans. Reliability, Vol. 57, No. 4, pp. 595-606, 2008
o A. Shrestha, L. Xing, and Y. Dai, “Decision Diagram-Based Methods, and Complexity Analysis for Multistate
Systems,” IEEE Trans. Reliability, vol. 59, no. 1, pp. 145-161, Mar. 2010.
o etc...
34

37. References: Multi-Phase (多阶段)
Multi Phase
o J. D. Esary and H. Ziehms, “Reliability analysis of phased missions,” in Reliability and Fault Tree Analysis, R. E. Barlow,
J. B. Fussell, and N. D Si
J B F ll d N D. Singpurwalla, Edi
ll Editors., pp. 213–236, 1975
213 236
o A. K. Somani, J. A. Ritcey, and S. H. L. Au, "Computationally Efficient Phased-Mission Reliability Analysis for Systems
with Variable Configurations," IEEE Trans. Reliability, Vol. 41, No. 4, pp. 504-511, 1992.
o Y. Ma and K.S. Trivedi, "An algorithm for reliability analysis of phased mission systems, Reliability Engineering &
An phased-mission systems,"
System Safety, Vol. 66, pp. 157–170, 1999.
o A. Bondavalli, S. Chiaradonna, F. D. Giandomenico, and I. Mura, “Dependability modeling and evaluation of multiple-
phased systems using DEEM,” IEEE Trans. Reliability, Vol. 53, No. 4, pp. 509–522, Dec. 2004.
o M. K. Smotherman and K. Zemoudeh, “A non-homogeneous Markov model for phased-mission reliability analysis,” IEEE
Trans. Reliability, Vol. 38, No. 5, pp. 585–590, Dec. 1989.
o L. Xing and J. B. Dugan, “Analysis of Generalized Phased Mission System Reliability, Performance and Sensitivity,”
IEEE Trans. Reliability, vol. 51, no. 2, pp 199-211, Jun. 2002.
y, , , pp. ,
o L. Xing and J. B. Dugan, “A Separable TDD-Based Analysis of Generalized Phased-Mission Reliability,” IEEE Trans.
Reliability, vol. 53, no. 2, pp. 174-184, Jun. 2004.
o L. Xing, “Reliability Evaluation of Phased-Mission Systems with Imperfect Fault Coverage and Common-Cause Failures,”
IEEE T Trans. on R li bili vol. 56, no. 1, pp. 58-68, M 2007
Reliability, l 56 1 58 68 Mar. 2007.
o A. Shrestha and L. Xing, “Improved Modular Reliability Analyses of Hybrid Phased Mission Systems,” Journal of Risk
and Reliability, Vol. 222, No. 4, 2008, pp. 507-520
o A. Shrestha, L. Xing, and Y.S. Dai, “Reliability Analysis of Multi State Phased Mission Systems with Unordered and
Reliability Multi-State Phased-Mission
Ordered States,” IEEE Trans. Systems, Man, and Cybernetics, Part A: Systems & Humans , Vol. 41, No. 4, pp. 625-636, 2011.
o S. V. Amari and L. Xing, "Reliability Analysis of k-out-of-n Systems with Phased-Mission Requirements," International
Journal of Performability Engineering, Vol. 7, No. 6, pp. 595-600, Nov. 2011.
o etc...
35

38. References: Sequence Dependence
(顺序相依)
o J. B. Dugan, S. J. Bavuso, and M. A. Boyd, “Dynamic fault-tree models for fault-tolerant computer systems,” IEEE
Trans. on Reliability, vol. 41, no. 3, pp. 363-377, S 1992
l bl l 41 3 363 3 Sep. 1992.
o W. Long, T. Zhang, Y. Lu, and M. Oshima, “On the quantitative analysis of sequential failure logic using Monte
Carlo method for different distributions,” Proc. of Probabilistic Safety Assessment & Management, pp. 391-396, 2002.
o T Yuge and S. Yanagi “Quantitative analysis of a fault tree with priority AND gates,” Reliability Engineering &
T. S Yanagi, Quantitative gates
System Safety, vol. 93, no. 11, pp. 1577-1583, Nov. 2008.
o L. Xing, A. Shrestha, and Y. Dai, "Exact Combinatorial Reliability Analysis of Dynamic Systems with Sequence-
Dependent Failures," Reliability Engineering & System Safety, Vol. 96, No. 10, pp. 1375-1385, October 2011.
o etc...
36

39. References: Dynamic Sparing (动态备用)
o J. B. Dugan, S. J. Bavuso, and M. A. Boyd, “Dynamic fault-tree models for fault-tolerant computer systems,”
IEEE Trans. Reliability, vol. 41, no. 3, pp. 363-377, Sep. 1992.
o J She and M. G P h “R li bili of a k
J. Sh d M G. Pecht, “Reliability f k-out-of-n W
f Warm-Standby S
S db System,” IEEE T
” Trans. R l b l
Reliability, vol. 41,
l 41
no. 1, pp. 72-75, Mar. 1992
o D. Liu, C. Zhang, W. Xing, R. Li, and H. Li, “Quantification of Cut Sequence Set for Fault Tree Analysis,”
HPCC2007, Lecture Notes in Computer Science, no. 4782, pp 755-765, Springer-Verlag, 2007.
, p , , pp. , p g g,
o L. Xing, O. Tannous, and J. B. Dugan, "Reliability Analysis of Non-Repairable Cold-Standby Systems Using
Sequential Binary Decision Diagrams," IEEE Trans. Systems, Man, and Cybernetics, Part A: Systems and
Humans, in Press, DOI: 10.1109/TSMCA.2011.2170415
O. Tannous, L Xing, R. P
o O T L. Xi R Peng, M Xi and S.H, N "R d d
M. Xie, d S H Ng, "Redundancy All ti f S i P ll l Warm-
Allocation for Series-Parallel W
Standby Systems," Proc. of the IEEE International Conference on Industrial Engineering and Engineering
Management, Singapore, Dec. 2011
o P. Boddu and L. Xing, "Optimal Design of Heterogeneous Series-Parallel Systems with Common-Cause
Failures," International Journal of Performability Engineering, Special Issue on Performance and Dependability
Modeling of Dynamic Systems, Vol. 7, No. 5, pp. 455-466, Sep. 2011.
o O. Tannous, L. Xing, and J. B. Dugan, “Reliability Analysis of Warm Standby Systems using Sequential
BDD, Proc.
BDD ” Proc of the 57th Annual Reliability & Maintainability Symposium, Jan 2011.
Symposium Jan. 2011
o etc...
37

40. References: Imperfect Coverage (不完全覆盖)
o S. V. Amari, J. B. Dugan, and R. B. Misra, “A separable method for incorporating imperfect coverage in combinatorial
model,” IEEE Trans. on Reliability, vol. 48, no. 3, pp. 267–274, Sep. 1999.
o S. V. Amari, J. B. Dugan, and R. B. Misra, “Optimal reliability of systems subject to imperfect fault-coverage,” IEEE
Trans. on Reliability, vol. 48, no. 3, pp. 275 284, Sep. 1999.
275–284,
o G. Levitin and S. V. Amari, “Multi-state systems with static performance dependent fault coverage,” Journal of Risk and
Reliability, vol. 222, pp. 95-103, 2008.
o G. Levitin and S. V. Amari, “Multi-state systems with multi-fault coverage,” Reliability Engineering & System Safety, vol.
93, pp. 1730-1739, 2008.
o S. A. Doyle, J. B. Dugan, and A. Patterson-Hine, “A Combinatorial Approach to Modeling Imperfect Coverage,” IEEE
Transactions on Reliability, pp. 87-94, March 1995.
o J B Dugan “Fault Trees and Imperfect Coverage,” IEEE Transactions on Reliability vol 38, no. 2, pp. 177 - 185 June
J. B. Dugan, Fault Coverage Reliability, vol. 38 no 2 pp 185,
1989.
o L. Xing and J. B. Dugan, “Dependability Analysis of Hierarchical Systems with Modular Imperfect Coverage,” Proc. of the
19th International System Safety Conference, Huntsville, Alabama, Sep. 2001
o L. Xing, “Reliability Evaluation of Phased-Mission Systems with Imperfect Fault Coverage and Common-Cause Failures,”
IEEE Trans. on Reliability, vol. 56, no. 1, pp. 58-68, Mar. 2007.
o L. Xing and A. Shrestha, “Reliability Evaluation of Distributed Computer Systems Subject to Imperfect Coverage and
Dependent Common Cause Failures , Journal of Computer Sciences, Special Issue on Reliability and Autonomic Management,
Common-Cause Failures”,
vol. 2, no. 6, pp. 473-479, 2006.
o A. Shrestha, L. Xing, and S. V. Amari, “Reliability and Sensitivity Analysis of Imperfect Coverage Multi-State Systems,”
Proc. of The 56th Annual Reliability & Maintainability Symposium, San Jose, CA, USA, 2010.
o etc...
38

41. References: C
R f Common-Cause Failures (共因故障)
C F il
o J. K. Vaurio, "Common cause failure probabilities in standby safety system fault tree analysis with testing—scheme
and timing dependencies," Reliability Engineering & System Safety, Vol. 79, No. 1, pp. 43-57, January 2003.
o S. Mitra, N. R. Saxena, and E. J. McCluskey, “Common-Mode Failures in Redundant VLSI Systems: A Survey,”
IEEE Trans on Reliability Vol 49 No 3 pp 285-295 September 2000.
Trans. Reliability, Vol. 49, No.3, pp. 285-295. 2000
o J. K. Vaurio, “An Implicit Method for Incorporating Common-Cause Failures in System Analysis,” IEEE Trans. on
Reliability, Vol. 47, No.2, pp. 173-180, 1998.
o K. N. Fleming, A. Mosleh, and A. P. Kelly, “On the analysis of dependent failures in risk assessment and reliability
evaluation ” Nuclear Safety, vol 24, pp. 637–657, 1983.
evaluation,” Safety vol. 24 pp 637 657 1983
o Z. Tang, H. Xu, and J. B. Dugan, "Reliability analysis of phased mission systems with common cause failures,"
Proceedings of Annual Reliability and Maintainability Symposium, pp. 313- 318, January 2005.
o K.N. Fleming, A. Mosleh, “Common-cause data analysis and implications in system modeling,” Proceeding of
International Topical Meeting on Probabilistic S f M h d & A li i
I i lT i lM i P b bili i Safety Methods Applications, V l 1 pp. 3/1 3/12 February 1985.
Vol. 1. 3/1-3/12, F b 1985
o G. Levitin, L. Xing, H. Ben-Haim, and Y. Dai, "Multi-state Systems with Selective Propagated Failures and
Imperfect Individual and Group Protections," Reliability Engineering and System Safety, in Press.
o G. Levitin and L. Xing, "Reliability and Performance of Multi state Systems with Propagated Failures Having
Reliability Multi-state
Selective Effect," Reliability Engineering and System Safety, vol. 95, no. 6, pp. 655-661, June 2010.
o L. Xing, P. Boddu, Y. Sun, and W. Wang, “Reliability Analysis of Static and Dynamic Fault-Tolerant Systems
subject to Probabilistic Common-Cause Failures,” Journal of Risk and Reliability, vol. 224, no. 1, pp.43-53, 2010 .
o L. Xing, A. Shrestha, L. Meshkat, and W. Wang, “Incorporating Common-Cause Failures into the Modular
Hierarchical Systems Analysis,” IEEE Trans. on Reliability, vol. 58, no. 1, pp. 10-19, Mar. 2009
o L. Xing and S. V. Amari, “Effective Component Importance Analysis for the Maintenance of Systems with
Common Cause Failures,” Intl. Jnl. of Reliability, Quality and Safety Engineering, vol. 14, no. 5, pp 459-478, 2007.
, f y, Q y f y g g, , , pp. ,
o etc...
39

42. References: Functional Dependence (功能相依)
& Competing Failures (竞争失效)
o J. B. Dugan, S. J. Bavuso, and M. A. Boyd, “Dynamic fault-tree models for fault-tolerant computer systems,” IEEE
Trans. on Reliability, vol. 41, no. 3, pp. 363-377, Sep. 1992.
o W. Li and H. Pham, “An inspection-maintenance model for systems with multiple competing processes,” IEEE
i d h i i i d lf ih li l i
Transactions on Reliability, 54(2), pp. 318-327, 2005.
o H. Pham and D. M. Malon, “Optimal design of systems with competing failure modes,” IEEE Transactions on
Reliability, 43(2), pp. 251 – 254, 1994.
o C. Bunea and T. A. Mazzuchi, “Competing failure modes in accelerated life testing,” Journal of Statistical Planning
and Inference, 136(5), pp. 1608-1620, 2006.
o A. Xu and Y. Tang , “Objective Bayesian analysis of accelerated competing failure models under Type-I censoring,”
Computational Statistics & Data Analysis, 55(10), pp. 2830-2839, 2011
o L. Xing, J. B. Dugan, and B. A. Morrissette, “Efficient Reliability Analysis of Systems with Functional Dependence
Loops,” Maintenance and Reliability, pp. 65-69, No. 3/2009, 2009.
o L. Xing, B. A. Morrissette , and J. B. Dugan, “Efficient Analysis of Imperfect Coverage Systems with Functional
Efficient
Dependence,” Proc. of the 56th Annual Reliability & Maintainability Symposium, San Jose, CA, USA, Jan. 2010.
o L. Xing and G. Levitin, "Combinatorial Algorithm for Reliability Analysis of Multi-State Systems with Propagated
Failures and Failure Isolation Effect," IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and
Humans , Vol. 41, No. 6, pp. 1156-1165, November 2011.
o L. Xing and G. Levitin, "Combinatorial Analysis of Systems with Competing Failures Subject to Failure Isolation and
Propagation Effects," Reliability Engineering and System Safety, Vol. 95, No. 11, pp. 1210-1215, November 2010.
o etc...
40

43. Thank You!
h k !
谢谢!
41