Download Reliability and Safety Engineering 2nd Ed [2015] PDF

TitleReliability and Safety Engineering 2nd Ed [2015]
TagsReliability Engineering Quality Management Risk
File Size12.7 MB
Total Pages583
Table of Contents
                            Foreword
Preface
Acknowledgments
Contents
1 Introduction
	1.1 Need for Reliability and Safety Engineering
	1.2 Exploring Failures
	1.3 Improving Reliability and Safety
	1.4 Definitions and Explanation of Some Relevant Terms
		1.4.1 Quality
		1.4.2 Reliability
		1.4.3 Maintainability
		1.4.4 Availability
		1.4.5 Risk and Safety
		1.4.6 Probabilistic Risk Assessment/Probabilistic Safety Assessment
	1.5 Resources
	1.6 History
	1.7 Present Challenges and Future Needs for the Practice of Reliability and Safety Engineering
	References
2 Basic Reliability Mathematics
	2.1 Classical Set Theory and Boolean Algebra
		2.1.1 Operations on Sets
		2.1.2 Laws of Set Theory
		2.1.3 Boolean Algebra
	2.2 Concepts of Probability Theory
		2.2.1 Axioms of Probability
		2.2.2 Calculus of Probability Theory
		2.2.3 Random Variables and Probability Distributions
	2.3 Reliability and Hazard Functions
	2.4 Distributions Used in Reliability and Safety Studies
		2.4.1 Discrete Probability Distributions
			2.4.1.1 Binomial Distribution
			2.4.1.2 Poisson Distribution
			2.4.1.3 Hyper Geometric Distribution
			2.4.1.4 Geometric Distribution
		2.4.2 Continuous Probability Distributions
			2.4.2.1 Exponential Distribution
			2.4.2.2 Normal Distribution
			2.4.2.3 Lognormal Distribution
			2.4.2.4 Weibull Distribution
			2.4.2.5 Gamma Distribution
			2.4.2.6 Erlangian Distribution
			2.4.2.7 Chi-Square Distribution
			2.4.2.8 F-Distribution
			2.4.2.9 t-Distribution
		2.4.3 Summary
	2.5 Failure Data Analysis
		2.5.1 Nonparametric Methods
		2.5.2 Parametric Methods
			2.5.2.1 Identifying Candidate Distributions
			2.5.2.2 Estimating the Parameters of Distribution
			2.5.2.3 Goodness-of-Fit Tests
	References
3 System Reliability Modeling
	3.1 Reliability Block Diagram (RBD)
		3.1.1 Procedure for System Reliability Prediction Using RBD
		3.1.2 Different Types of Models
		3.1.3 Solving RBD
			3.1.3.1 Truth Table Method
			3.1.3.2 Cut-Set and Tie-Set Method
			3.1.3.3 Bounds Method
	3.2 Markov Models
		3.2.1 Elements of Markov Models
	3.3 Fault Tree Analysis
		3.3.1 Procedure for Carrying Out Fault Tree Analysis
		3.3.2 Elements of Fault Tree
		3.3.3 Evaluations of Fault Tree
		3.3.4 Case Study
	References
4 Reliability of Complex Systems
	4.1 Monte Carlo Simulation
		4.1.1 Analytical versus Simulation Approaches for System Reliability Modeling
		4.1.2 Elements of Monte Carlo Simulation
		4.1.3 Repairable Series and Parallel System
		4.1.4 Simulation Procedure for Complex Systems
			4.1.4.1 Case Study---AC Power Supply System of Indian NPP
		4.1.5 Increasing Efficiency of Simulation
	4.2 Dynamic Fault Tree Analysis
		4.2.1 Dynamic Fault Tree Gates
		4.2.2 Modular Solution for Dynamic Fault Trees
		4.2.3 Numerical Method
		4.2.4 Monte Carlo Simulation
			4.2.4.1 Case Study 1---Simplified Electrical (AC) Power Supply System of NPP
			4.2.4.2 Case Study 2---Reactor Regulation System (RRS) of NPP
	References
5 Electronic System Reliability
	5.1 Importance of Electronic Industry
	5.2 Various Components Used and Their Failure Mechanisms
		5.2.1 Resistors
		5.2.2 Capacitors
		5.2.3 Inductors
		5.2.4 Relays
		5.2.5 Semiconductor Devices
		5.2.6 Microcircuits (ICs)
	5.3 Reliability Prediction of Electronic Systems
		5.3.1 Parts Count Method
		5.3.2 Parts Stress Method
	5.4 PRISM
	5.5 Sneak Circuit Analysis (SCA)
		5.5.1 Definition of SCA
		5.5.2 Network Tree Production
		5.5.3 Topological Pattern Identification
	5.6 Case Study
		5.6.1 Total Failure Rate
	5.7 Physics of Failure Mechanisms of Electronic Components
		5.7.1 Physics of Failures
		5.7.2 Failure Mechanisms for Resistors
			5.7.2.1 Failure Due to Excessive Heating
			5.7.2.2 Failure Due to Metal Diffusion and Oxidation
		5.7.3 Failure Mechanisms for Capacitor
			5.7.3.1 Dielectric Breakdown
		5.7.4 MOS Failure Mechanisms
			5.7.4.1 Electro Migration (EM)
			5.7.4.2 Time Dependent Dielectric Breakdown
				AHI (Anode Hole Injection)
				Thermo-Chemical Model
				Anode Hydrogen Release (AHR)
			5.7.4.3 Hot Carrier Injection
			5.7.4.4 Negative Bias Temperature Instability
		5.7.5 Field Programmable Gate Array
			5.7.5.1 Hierarchical Model
			5.7.5.2 Optimal Model
			5.7.5.3 Coarse Model
			5.7.5.4 Tile Based Model
	References
6 Software Reliability
	6.1 Introduction to Software Reliability
	6.2 Past Incidences of Software Failures in Safety Critical Systems
	6.3 The Need for Reliable Software
	6.4 Difference Between Hardware Reliability and Software Reliability
	6.5 Software Reliability Modeling
		6.5.1 Software Reliability Growth Models
		6.5.2 Black Box Software Reliability Models
		6.5.3 White Box Software Reliability Models
	6.6 How to Implement Software Reliability
	6.7 Emerging Techniques in Software Reliability Modeling---Soft Computing Technique
		6.7.1 Need for Soft Computing Methods
		6.7.2 Environmental Parameters
		6.7.3 Anil-Verma Model
	6.8 Future Trends of Software Reliability
	References
7 Mechanical Reliability
	7.1 Reliability Versus Durability
	7.2 Failure Modes in Mechanical Systems
		7.2.1 Failures Due to Operating Load
		7.2.2 Failure Due to Environment
	7.3 Reliability Circle
		7.3.1 Specify Reliability
		7.3.2 Design for Reliability
			7.3.2.1 Reliability Analysis and Prediction
			7.3.2.2 Stress-Strength Interference Theory
		7.3.3 Test for Reliability
			7.3.3.1 Degradation Data Analysis
		7.3.4 Maintain the Manufacturing Reliability
		7.3.5 Operational Reliability
	References
8 Structural Reliability
	8.1 Deterministic versus Probabilistic Approach in Structural Engineering
	8.2 The Basic Reliability Problem
		8.2.1 First Order Second Moment (FOSM) Method
		8.2.2 Advanced First Order Second Moment Method (AFOSM)
	8.3 First Order Reliability Method (FORM)
	8.4 Reliability Analysis for Correlated Variables
		8.4.1 Reliability Analysis for Correlated Normal Variables
		8.4.2 Reliability Analysis for Correlated Non-normal Variables
	8.5 Second Order Reliability Methods (SORM)
	8.6 System Reliability
		8.6.1 Classification of Systems
			8.6.1.1 Series System
			8.6.1.2 Parallel System
			8.6.1.3 Combined Series-Parallel Systems
		8.6.2 Evaluation of System Reliability
			8.6.2.1 Numerical Integration
			8.6.2.2 Bounding Techniques
			8.6.2.3 Approximate Methods
	References
9 Maintenance of Large Engineering Systems
	9.1 Introduction
	9.2 Peculiarities of a Large Setup of Machinery
	9.3 Prioritizing the Machinery for Maintenance Requirements
		9.3.1 Hierarchical Level of Machinery
		9.3.2 FMECA (Failure Mode Effect and Criticality Analysis)
			9.3.2.1 FMEA
			9.3.2.2 CA (Criticality Analysis)
			9.3.2.3 Criticality Ranking
				FMECA Summary
	9.4 Maintenance Scheduling of a Large Setup of Machinery
		9.4.1 Introduction
		9.4.2 Example
		9.4.3 Example---MOOP of Maintenance Interval Scheduling
		9.4.4 Use of NSGA II---Elitist Genetic Algorithm Program
		9.4.5 Assumptions and Result
	9.5 Decision Regarding Maintenance Before an Operational Mission
		9.5.1 Introduction
		9.5.2 The Model
		9.5.3 Assumptions
		9.5.4 Result
	9.6 Summary
	References
10 Probabilistic Safety Assessment
	10.1 Introduction
	10.2 Concept of Risk and Safety
	10.3 An Overview of Probabilistic Safety Assessment Tasks
	10.4 Identification of Hazards and Initiating Events
		10.4.1 Preliminary Hazard Analysis
		10.4.2 Master Logic Diagram (MLD)
	10.5 Event Tree Analysis
	10.6 Importance Measures
	10.7 Common Cause Failure Analysis
		10.7.1 Treatment of Dependent Failures
		10.7.2 The Procedural Framework for CCF Analysis
		10.7.3 Treatment of Common Cause Failures in Fault Tree Models
		10.7.4 Common Cause Failure Models
	10.8 Human Reliability Analysis
		10.8.1 HRA Concepts
		10.8.2 HRA Process, Methods, and Tools
			10.8.2.1 HRA Process
			10.8.2.2 HRA Methods
	References
11 Dynamic PSA
	11.1 Introduction to Dynamic PSA
		11.1.1 Need for Dynamic PSA
		11.1.2 Dynamic Methods for Risk Assessment
	11.2 Dynamic Event Tree Analysis
		11.2.1 Event Tree versus Dynamic Event Tree
		11.2.2 DET Approach---Steps Involved
		11.2.3 DET Implementation---Comparison Among Tools
	11.3 Example---Depleting Tank
		11.3.1 Description on Depleting Tank Problem
		11.3.2 Analytical Solution
		11.3.3 Discrete DET Solution
	11.4 DET Quantification of Risk---Practical Issues and Possible Solutions
		11.4.1 Challenges in Direct Quantification of Risk with DET
		11.4.2 Uncertainties and Dynamics in Risk Assessment
	References
12 Applications of PSA
	12.1 Objectives of PSA
	12.2 PSA of Nuclear Power Plant
		12.2.1 Description of PHWR
		12.2.2 PSA of Indian NPP (PHWR Design)
			12.2.2.1 Dominating Initiating Events
			12.2.2.2 Reliability Analysis
			12.2.2.3 Accident Sequence Identification
			12.2.2.4 Event Trees
			12.2.2.5 Dominating Accident Sequences
			12.2.2.6 Risk Importance Measures
	12.3 Technical Specification Optimization
		12.3.1 Traditional Approaches for Technical Specification Optimization
			12.3.1.1 Measures Applicable for AOT Evaluations
			12.3.1.2 Measures Applicable for STI Evaluations
		12.3.2 Advanced Techniques for Technical Specification Optimization
			12.3.2.1 Mathematical Modeling of Problem
			12.3.2.2 Genetic Algorithm (GA) as Optimization Method
			12.3.2.3 Case Studies: Test Interval Optimization for Emergency Core Cooling System of PHWR
	12.4 Risk Monitor
		12.4.1 Necessity of Risk Monitor?
		12.4.2 Different Modules of Risk Monitor
		12.4.3 Applications of Risk Monitor
	12.5 Risk Informed In-Service Inspection
		12.5.1 RI-ISI Models
			12.5.1.1 ASME/WOG Model
			12.5.1.2 EPRI Model
			12.5.1.3 Comparison of RI-ISI Models
		12.5.2 ISI and Piping Failure Frequency
			12.5.2.1 In-Service Inspection
			12.5.2.2 Models for Including ISI Effect on Piping Failure Frequency
			12.5.2.3 Case Study
			12.5.2.4 Using Three-State Markov Model
			12.5.2.5 Using Four-State Markov Model
	References
13 Uncertainty Analysis in Reliability/Safety Assessment
	13.1 Mathematical Models and Uncertainties
	13.2 Uncertainty Analysis: An Important Task of PRA/PSA
	13.3 Methods of Characterising Uncertainties
		13.3.1 The Probabilistic Approach
		13.3.2 Interval and Fuzzy Representation
		13.3.3 Dempster-Shafer Theory Based Representation
	13.4 Bayesian Approach
	13.5 Expert Elicitation Methods
		13.5.1 Definition and Uses of Expert Elicitation
		13.5.2 Treatment of Expert Elicitation Process
		13.5.3 Methods of Treatment
	13.6 Uncertainty Propagation
		13.6.1 Method of Moments
			13.6.1.1 Consideration of Correlation Using Method of Moments
		13.6.2 Monte Carlo Simulation
			13.6.2.1 Latin Hypercube Sampling
		13.6.3 Interval Analysis
		13.6.4 Fuzzy Arithmetic
	References
14 Advanced Methods in Uncertainty Management
	14.1 Uncertainty Analysis with Correlated Basic Events
		14.1.1 Dependency: Common Cause Failures versus Correlated Epistemic Parameters
		14.1.2 Methodology for PSA Based on Monte Carlo Simulation with Nataf Transformation
		14.1.3 Case Study
			14.1.3.1 Case A: Effect of Correlation Alone: No CCF Modeled in Fault Tree
			14.1.3.2 Case B: Effect of Correlation Combined with CCF Modeling
	14.2 Uncertainty Importance Measures
		14.2.1 Probabilistic Approach to Ranking Uncertain Parameters in System Reliability Models
			14.2.1.1 Correlation Coefficient Method
			14.2.1.2 Variance Based Method
		14.2.2 Method Based on Fuzzy Set Theory
		14.2.3 Application to a Practical System
	14.3 Treatment of Aleatory and Epistemic Uncertainties
		14.3.1 Epistemic and Aleatory Uncertainty in Reliability Calculations
		14.3.2 Need to Separate Epistemic and Aleatory Uncertainties
		14.3.3 Methodology for Uncertainty Analysis in Reliability Assessment Based on Monte Carlo Simulation
			14.3.3.1 Methodology
	14.4 Dempster-Shafer Theory
		14.4.1 Belief and Plausibility Function of Real Numbers
		14.4.2 Dempster's Rule of Combination
		14.4.3 Sampling Technique for the Evidence Theory
	14.5 Probability Bounds Approach
		14.5.1 Computing with Probability Bounds
		14.5.2 Two-Phase Monte Carlo Simulation
		14.5.3 Uncertainty Propagation Considering Correlation Between Variables
	14.6 Case Study to Compare Uncertainty Analysis Methods
		14.6.1 Availability Assessment of MCPS Using Fault Tree Analysis
		14.6.2 Uncertainty Propagation in MCPS with Different Methods
			14.6.2.1 Interval Analysis
			14.6.2.2 Fuzzy Arithmetic
			14.6.2.3 Monte Carlo Simulation
			14.6.2.4 Dempster-Shafer Theory
			14.6.2.5 Probability Bounds Analysis
		14.6.3 Observations from Case Study
	References
Appendix
Index
                        
Document Text Contents
Page 1

Springer Series in Reliability Engineering

Ajit Kumar Verma
Srividya Ajit
Durga Rao Karanki

Reliability
and Safety
Engineering
Second Edition

Page 2

Springer Series in Reliability Engineering

Series editor

Hoang Pham, Piscataway, USA

Page 291

Gradient length = 5213.730167

A ¼

1:2e� 5 �1:6e� 4 3:4e� 5 2:8e� 4
�1:6e� 4 �2:5e� 3 �2:4e� 3 �0:081
3:4e� 5 �2:4e� 3 �2:3e� 3 4:7e� 3
2:8e� 4 �0:081 4:7e� 3 �0:044

2
6664

3
7775

B ¼
1:2e� 5 �1:6e� 4 3:4e� 5
�1:6e� 4 �2:5e� 3 �2:4e� 3
3:4e� 5 �2:4e� 3 �2:3e� 3

2
64

3
75

k ¼ 1:4e� 4 �1:3e� 4 �4:8e� 3½ �0
w ¼ bUð�bÞ � uð�bÞ ¼ �0:04037

x ¼
Yn�1
i¼1

1þ bkið Þ�0:5 ¼ 1:00328

y ¼
Yn�1
i¼1

1þ ð1þ bð ÞkiÞ�0:5 ¼ 1:00571

z ¼ Real
Yn�1
i¼1

1þ ðiþ bð ÞkiÞ�0:5
!

¼ 1:00327

Wð�bÞ ¼ uð�bÞ
Uð�bÞ ¼ 1:81707

pfFORM ¼ Uð�1:35597Þ ¼ 0:08756
pfSORM ðBreitungÞ ¼ Uð�bÞx ¼ 0:08784

pfSORM ðHohenbichlerÞ ¼ Uð�bÞ
Yn�1
i¼1

ð1þ kiWðbÞÞ�0:5 ¼ 0:08794

pfSORM ðTvedtÞ ¼ Uð�bÞxþ wðx� yÞ þ ð1þ bÞwðx� zÞ ¼ 0:08794
pfSORM ðexactÞ ¼ 0:08794

Example 7 The state of stress at most critical point is written in terms of principle
stresses as:

r1 ¼ 600P2 þ 9P1
r2 ¼ 400P2 þ 18P1
r3 ¼ �18P1

8.5 Second Order Reliability Methods (SORM) 277

Page 292

The limit state function (Von Mises theory) is

gðXÞ ¼ r2y � r21 þ r22 þ r23 � r1r2 � r2r3 � r1r3
� �

Distribution parameters of random variables are given in Table 8.7. Find reli-
ability index and failure probability?

where P1, P2, and σy are applied loads in lbs and yield strength of material used
respectively.

Solution: From FORM iteration scheme (Calculations in Table 8.8),

u�i ¼ ð
@g
@ui

Þ
P

ui
@g
@ui

� gðuiÞP ð@[email protected]Þ2
pf ¼ Uð�bÞ ¼ 2:731e - 4

Table 8.7 Parameters of
random variables

Variables Distribution Mean Std. Deviation

P1 Normal 150 30

P2 Normal 6 3

ry Normal 16,000 1600

Table 8.8 Calculations

Iter. Number 1 2 3 4 5

u�P1 0 0.8547 1.327 1.3448 1.3401

u�P2 0 1.3432 2.1504 2.2058 2.2002

u�ry 0 −2.985 −2.4117 −2.2966 −2.3053

g 1.96E8 1.46E7 −2.00E6 2.33E4 2.43E1
@g

@uP1
−1.47E7 −2.0E7 −2.28E7 −2.29E7 −2.29E7

@g
@uP2

−2.30E7 −3.2E7 −3.73E7 −3.76E7 −3.76E7

@g
@ury

5.12E7 3.59E7 3.89E7 3.94E7 3.94E7

auP1 −0.2527 −0.38 −0.389 −0.3876 −0.3877

auP2 −0.3971 −0.616 −0.6381 −0.6364 −0.6364

aury 0.8823 0.6904 0.6644 0.6668 0.6668

β 3.383 3.493 3.4566 3.457 3.457

278 8 Structural Reliability

Page 582

O
Operational reliability, 252, 395
Operator action tree, 369
OR gate, 113, 146, 158
Orthogonal transformation, 269, 272

P
Parallel model, 79
Part failure rate, 167
Parts count method, 165
Parts stress method, 165, 166
Patriot, 186
Physics of failures, 172
Plausibility, 466, 527, 529, 549
Poisson distribution, 37, 469, 470
Possibility transformations, 490
Power factor, 167
Power stress factor, 167
Power system functional zones, 398
Power system reliability, 13
Preliminary hazard analysis, 340, 341
Pressurised heavy water reactor, 398
Priority AND gate, 149
PRISM, 165, 167
Probabilistic risk assessment, 7, 10, 335, 532
Probabilistic safety assessment, 7, 136, 335,

375, 412
Probability bounds, 467, 532, 540, 550
Probability density function, 29, 30, 40, 56,

132, 463, 468, 498, 516, 549
Probability of detection, 297, 436, 437, 456
Probability of load curtailment
Probability plot, 64
Probability theory, 19, 24, 465
Process compliance index, 200, 204, 207, 210
Project risk index, 200, 201, 203, 210

Q
Quality, 3–5, 166, 199, 227, 229, 238, 243,

250, 552
Quality control, 2, 3, 8, 222, 238, 250
Quality factor, 166, 167, 238
Quality function deployment, 4, 228

R
Randomness, 459, 496, 508, 525, 539
Random number, 126, 127, 197, 199, 483, 484,

499, 530
Random samples, 57, 126, 483, 498, 499
Random variable, 5, 28, 29, 31, 32, 34, 39, 44,

53, 57, 61, 126, 140, 242, 258, 262,
271, 388, 483, 496, 498, 520

Rasmussen’s decision making model, 367
Reactor process system, 397

Reactor protection system, 344, 397, 509
Reactor regulation system, 118, 501, 542
Relays, 49, 163, 309
Reliability, 1–5, 8, 10–13, 31, 34, 41, 44, 49,

52, 59, 61, 72, 75, 78, 80, 82, 84, 89,
92, 99, 107, 123, 124, 126, 133, 137,
141, 153, 161, 165, 167, 172, 181, 183,
184, 187–190, 192, 199, 201, 216,
226–230, 313, 330, 403, 409, 439, 448,
462, 473, 484, 498, 508, 509, 511, 525

Reliability apportionment, 230
Reliability block diagram, 75, 123, 134, 302
Reliability circle, 226, 228
Reliability index, 259–262, 272, 404
Reliability test, 227, 245, 246, 248
Residual defect density, 202
Resistors, 161, 162, 167, 174, 175
Risk, 6, 10, 11, 204, 335, 336, 340, 382, 391,

411, 413, 415, 422, 424, 425, 428, 434,
449, 455, 472

Risk assessment, 7, 10, 11, 340, 390, 532
Risk estimation, 340
Risk-informed decision making, 412, 422
Risk informed in-service inspection, 426, 427,

455
Risk management, 340, 395, 427
Risk matrix, 431, 434, 449, 455
Risk monitor, 422–424, 426
Rosenblatt transformation, 269, 270, 279, 286
Rule based actions, 367, 405

S
Safety, 1, 2, 4, 7, 11, 118, 227, 257, 282,

307, 338, 344, 378, 403, 411, 419, 427,
434, 476

Safety margin, 243, 261, 283
Safety systems, 1, 4, 342, 344, 378, 391, 405,

424, 519
Second order reliability methods, 271
Semiconductor devices, 163
SEQ gate, 142, 146, 151, 157
Series model, 78
Series system, 1, 4, 342, 344, 378, 391, 405,

424, 519
Severity index, 243, 303
SHARP methodology, 368
Skill based action, 367, 405
Slip
Sneak circuit analysis, 169
Soft computing, 201
Software reliability, 11, 183, 184, 188, 189,

191, 192, 215
Software reliability growth models, 190, 191
Spare gate, 142, 147, 154

570 Index

Page 583

Standby redundancy, 84
State space method, 101, 146, 154
State time diagrams, 127, 148
Station blackout, 133, 151, 153–155, 409, 410
Steady state genetic algorithm, 418
Stochastic uncertainty, 459, 496, 517
Strength, 185, 222, 224, 234, 242–244,

290, 510
Stress, 185, 222, 224, 234, 242–244, 290, 510
Structural reliability, 10, 13, 436, 451
Subjective uncertainty, 459, 517
System average interruption duration index
System average interruption frequency index

T
Taylor series, 476, 478, 479
t- distribution, 58
Technical specification, 6, 104, 335, 398, 412,

427, 520
Technique for human error rate prediction

(THERP), 369, 370, 372
Temperature factor, 167
Tensile-yield-strength, 222
Test interval, 6, 13, 395, 412, 416, 420
Therac 25, 185
Three state markov model, 440, 448
Tie-set, 89
Time to failure, 5, 31, 42, 49, 94, 132, 148,

150, 484, 519, 524, 525
Time to repair, 6, 126, 132, 137, 148, 444, 519,

524
Total probability theorem, 26, 27
Transfer in gate, 112
Transfer out gate, 112
Transmission facility

Transmission system
Truth table method, 88
Two-phase Monte Carlo, 537, 539

U
Unavailability, 85, 118, 125, 134, 136, 137,

153, 364, 404, 414, 416, 422, 438, 490,
502, 506, 507, 543, 549

Uncertainty, 7, 13, 15, 257, 459, 461, 464, 476,
486, 496, 508, 511, 518, 532, 540, 541,
549, 552

Uncertainty analysis, 13, 340, 444, 462, 495,
508, 540

Uncertainty importance measure, 508–510, 515
Uncertainty management, 463
Uncertainty propagation, 107, 463, 476, 482,

488, 496, 498, 502, 508, 541, 552
Undeveloped event, 110
Unimodal bounds, 285, 289, 290

V
Variability, 222, 251, 459, 461, 490, 496,

517, 552
Variance, 30, 35, 42, 50, 137, 206, 207, 260,

478, 510, 551
Variance based techniques, 510
Venn diagram, 19, 25
Voting gate, 119, 141

W
Wear out, 2, 164, 189, 415
Weibull analysis, 252
Weibull distribution, 8, 49, 52, 247, 252–254
White box models, 192

Index 571

Similer Documents