Incomplete component information may lead to wide bounds for system reliability prediction, making decisions difficult in the system design stage. The missing information is often the component dependence, which is a crucial source for the exact system reliability estimation. Component dependence exists due to the shared environment and operating conditions. But it is difficult for system designers to model component dependence because they may have limited information about component design details if outside suppliers designed and manufactured the components. This research intends to produce narrow system reliability bounds with a new way for system designers to consider the component dependence implicitly and automatically without knowing component design details. The proposed method is applicable for a wide range of applications where the time-dependent system stochastic load is shared by components of the system. Simulation is used to obtain the extreme value of the system load for a given period of time, and optimization is employed to estimate the system reliability bounds, which are narrower than those from the traditional method with independent component assumption and completely dependent component assumption. Examples are provided to demonstrate the proposed method.
Issue Section:
Research Papers
References
1.
Singh
, A.
, Mourelatos
, Z. P.
, and Li
, J.
, 2010
, “Design for Lifecycle Cost Using Time-Dependent Reliability
,” ASME J. Mech. Des.
, 132
(9
), p. 091008
.2.
Ditlevsen
, O.
, 1979
, “Narrow Reliability Bounds for Structural Systems
,” J. Struct. Mech.
, 7
(4
), pp. 453
–472
.3.
Cornell
, C. A.
, 1967
, “Bounds on the Reliability of Structural Systems
,” J. Struct. Div.
, 93
(1
), pp. 171
–200
.4.
Ramachandran
, K.
, 2004
, “System Reliability Bounds: A New Look With Improvements
,” Civ. Eng. Environ. Syst.
, 21
(4
), pp. 265
–278
.5.
Boole
, G.
, 1854
, Laws of Thought
(American Reprint of 1854 Edition), Dover
, New York
.6.
Choi
, S.-K.
, Grandhi
, R.
, and Canfield
, R. A.
, 2006
, Reliability-Based Structural Design
, Springer Science & Business Media
, Berlin.7.
Hohenbichler
, M.
, and Rackwitz
, R.
, 1983
, “First-Order Concepts in System Reliability
,” Struct. Saf.
, 1
(3
), pp. 177
–188
.8.
Kounias
, E. G.
, 1968
, “Bounds for the Probability of a Union, With Applications
,” Ann. Math. Stat.
, 39
(6
), pp. 2154
–2158
.9.
Hunter
, D.
, 1976
, “An Upper Bound for the Probability of a Union
,” J. Appl. Probab.
, 13
(3
), pp. 597
–603
.10.
Zhang
, Y. C.
, 1993
, “High-Order Reliability Bounds for Series Systems and Application to Structural Systems
,” Comput. Struct.
, 46
(2
), pp. 381
–386
.11.
Song
, J.
, and Der Kiureghian
, A.
, 2003
, “Bounds on System Reliability by Linear Programming
,” J. Eng. Mech.
, 129
(6
), pp. 627
–636
.12.
Domyancic
, L. C.
, and Millwater
, H. R.
, 2012
, “Advances in Bounding Techniques for Aircraft Structures
,” AIAA J.
, 50
(6
), pp. 1307
–1313
.13.
Cheng
, Y.
, and Du
, X.
, 2016
, “System Reliability Analysis With Dependent Component Failures During Early Design Stage—A Feasibility Study
,” ASME J. Mech. Des.
, 138
(5
), p. 051405
.14.
Zhang
, H.
, Dai
, H.
, Beer
, M.
, and Wang
, W.
, 2013
, “Structural Reliability Analysis on the Basis of Small Samples: An Interval Quasi-Monte Carlo Method
,” Mech. Syst. Signal Process.
, 37
(1–2
), pp. 137
–151
.15.
Utkin
, L. V.
, and Kozine
, I. O.
, 2002
, “Stress-Strength Reliability Models Under Incomplete Information
,” Int. J. Gen. Syst.
, 31
(6
), pp. 549
–568
.16.
Guo
, J.
, and Du
, X.
, 2010
, “Reliability Analysis for Multidisciplinary Systems With Random and Interval Variables
,” AIAA J.
, 48
(1
), pp. 82
–91
.17.
Gunawan
, S.
, and Papalambros
, P. Y.
, 2006
, “A Bayesian Approach to Reliability-Based Optimization With Incomplete Information
,” ASME J. Mech. Des.
, 128
(4
), pp. 909
–918
.18.
Ditlevsen
, O.
, 1979
, “Generalized Second Moment Reliability Index
,” J. Struct. Mech.
, 7
(4
), pp. 435
–451
.19.
Hasofer
, A. M.
, and Lind
, N. C.
, 1974
, “Exact and Invariant Second-Moment Code Format (For Reliability Analysis in Multivariate Problems)
,” J. Eng. Mech. Div.
, 100
(1), pp. 111
–121
.20.
Der Kiureghian
, A.
, and Liu
, P.-L.
, 1986
, “Structural Reliability Under Incomplete Probability Information
,” J. Eng. Mech.
, 112
(1
), pp. 85
–104
.21.
Ditlevsen
, O.
, and Madsen
, H. O.
, 1996
, Structural Reliability Methods
, Wiley
, New York
.22.
Høyland
, A.
, and Rausand
, M.
, 2009
, System Reliability Theory: Models and Statistical Methods
, Wiley
, New York.23.
Xie
, M.
, and Lai
, C. D.
, 1996
, “Reliability Analysis Using an Additive Weibull Model With Bathtub-Shaped Failure Rate Function
,” Reliab. Eng. Syst. Saf.
, 52
(1
), pp. 87
–93
.24.
Cordeiro
, G. M.
, Ortega
, E. M. M.
, and Nadarajah
, S.
, 2010
, “The Kumaraswamy Weibull Distribution With Application to Failure Data
,” J. Franklin Inst.
, 347
(8
), pp. 1399
–1429
.25.
Hu
, Z.
, and Du
, X.
, 2013
, “A Sampling Approach to Extreme Value Distribution for Time-Dependent Reliability Analysis
,” ASME J. Mech. Des.
, 135
(7
), p. 071003
.26.
Spanos
, P. D.
, Beer
, M.
, and Red-Horse
, J.
, 2007
, “Karhunen–Loève Expansion of Stochastic Processes With a Modified Exponential Covariance Kernel
,” J. Eng. Mech.
, 133
(7
), pp. 773
–779
.27.
Cho
, H.
, Venturi
, D.
, and Karniadakis
, G. E.
, 2013
, “Karhunen–Loève Expansion for Multi-Correlated Stochastic Processes
,” Probab. Eng. Mech.
, 34
, pp. 157
–167
.28.
Levy
, B. C.
, 2008
, Principles of Signal Detection and Parameter Estimation
, Springer Science & Business Media
, Berlin.29.
Betz
, W.
, Papaioannou
, I.
, and Straub
, D.
, 2014
, “Numerical Methods for the Discretization of Random Fields by Means of the Karhunen–Loève Expansion
,” Comput. Methods Appl. Mech. Eng.
, 271
, pp. 109
–129
.30.
Li
, C.-C.
, and Der Kiureghian
, A.
, 1993
, “Optimal Discretization of Random Fields
,” J. Eng. Mech.
, 119
(6
), pp. 1136
–1154
.31.
Daniels
, H. E.
, 1954
, “Saddlepoint Approximations in Statistics
,” Ann. Math. Stat.
, 25
(4
), pp. 631
–650
.32.
Huzurbazar
, S.
, 1999
, “Practical Saddlepoint Approximations
,” Am. Stat.
, 53
(3
), pp. 225
–232
.33.
Du
, X.
, and Sudjianto
, A.
, 2004
, “First Order Saddlepoint Approximation for Reliability Analysis
,” AIAA J.
, 42
(6
), pp. 1199
–1207
.34.
Du
, X.
, 2010
, “System Reliability Analysis With Saddlepoint Approximation
,” Struct. Multidiscip. Optim.
, 42
(2
), pp. 193
–208
.35.
Fisher
, R. A.
, 1930
, “Moments and Product Moments of Sampling Distributions
,” Proc. London Math. Soc.
, s2-30
(1
), pp. 199
–238
.36.
Dao-Thien
, M.
, and Massoud
, M.
, 1974
, “On the Relation Between the Factor of Safety and Reliability
,” J. Eng. Ind.
, 96
(3
), pp. 853
–857
.37.
Vose
, D.
, 1996
, Quantitative Risk Analysis: A Guide to Monte Carlo Simulation Modelling
, Wiley
, New York.Copyright © 2017 by ASME
You do not currently have access to this content.
