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Research Papers: Design Automation

System Reliability Analysis With Dependent Component Failures During Early Design Stage—A Feasibility Study

[+] Author and Article Information
Yao Cheng

Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
258A Toomey Hall,
400 West 13th Street,
Rolla, MO 65409-0500
e-mail: ycbm7@mst.edu

Xiaoping Du

Professor
Department of Mechanical
and Aerospace Engineering,
Missouri University of Science and Technology,
272 Toomey Hall,
400 West 13th Street,
Rolla, MO 65409-0500
e-mail: dux@mst.edu

1Corresponding author.

Contributed by the Design Automation Committee of ASME for publication in the JOURNAL OF MECHANICAL DESIGN. Manuscript received May 8, 2015; final manuscript received October 15, 2015; published online April 6, 2016. Assoc. Editor: Nam H. Kim.

J. Mech. Des 138(5), 051405 (Apr 06, 2016) (12 pages) Paper No: MD-15-1360; doi: 10.1115/1.4031906 History: Received May 08, 2015; Revised October 15, 2015

It is desirable to predict product reliability accurately in the early design stage, but the lack of information usually leads to the use of independent component failure assumption. This assumption makes the system reliability prediction much easier, but may produce large errors since component failures are usually dependent after the components are put into use within a mechanical system. The bounds of the system reliability can be estimated, but are usually wide. The wide reliability bounds make it difficult to make decisions in evaluating and selecting design concepts, during the early design stage. This work demonstrates the feasibility of considering dependent component failures during the early design stage with a new methodology that makes the system reliability bounds much narrower. The following situation is addressed: the reliability of each component and the distribution of its load are known, but the dependence between component failures is unknown. With a physics-based approach, an optimization model is established so that narrow bounds of the system reliability can be generated. Three examples demonstrate that it is possible to produce narrower system reliability bounds than the traditional reliability bounds, thereby better assisting decision making during the early design stage.

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References

Cross, N. , 2008, Engineering Design Methods: Strategies for Product Design, Wiley, Hoboken, NJ.
Pahl, G. , and Beitz, W. , 2013, Engineering Design: A Systematic Approach, Springer Science & Business Media, New York.
Hsu, W. , and Woon, I. M. , 1998, “ Current Research in the Conceptual Design of Mechanical Products,” Comput.-Aided Des., 30(5), pp. 377–389. [CrossRef]
Lewis, E. E. , and Lewis, E. , 1987, Introduction to Reliability Engineering, Wiley, New York.
Marini, V. K. , 2013, “ Information About Robustness, Reliability and Safety in Early Design Phases,” Ph.D. thesis, Department of Management Engineering, Technical University of Denmark, Lyngby, Denmark.
Parnell, G. S. , Driscoll, P. J. , and Henderson, D. L. , 2011, Decision Making in Systems Engineering and Management, Wiley, Hoboken, NJ.
Ormon, S. W. , Cassady, C. R. , and Greenwood, A. G. , 2002, “ Reliability Prediction Models to Support Conceptual Design,” IEEE Trans. Reliab., 51(2), pp. 151–157. [CrossRef]
Nachtmann, H. , and Chimka, J. R. , 2003, “ Fuzzy Reliability in Conceptual Design,” IEEE Annual Reliability and Maintainability Symposium, pp. 360–364.
Huang, Z. , and Jin, Y. , 2009, “ Extension of Stress and Strength Interference Theory for Conceptual Design-For-Reliability,” ASME J. Mech. Des., 131(7), p. 071001. [CrossRef]
Dhingra, A. K. , 1992, “ Optimal Apportionment of Reliability and Redundancy in Series Systems Under Multiple Objectives,” IEEE Trans. Reliab., 41(4), pp. 576–582. [CrossRef]
Li, X. , and Chen, J. , 2004, “ Aging Properties of the Residual Life Length of k-out-of-n Systems With Independent but Non-Identical Components,” Appl. Stochastic Models Bus. Ind., 20(2), pp. 143–153. [CrossRef]
Volkanovski, A. , Čepin, M. , and Mavko, B. , 2009, “ Application of the Fault Tree Analysis for Assessment of Power System Reliability,” Reliab. Eng. Syst. Saf., 94(6), pp. 1116–1127. [CrossRef]
Park, C. , Kim, N. H. , and Haftka, R. T. , 2015, “ The Effect of Ignoring Dependence Between Failure Modes on Evaluating System Reliability,” Struct. Multidiscip. Optim., 52(2), pp. 251–268. [CrossRef]
Humphreys, P. , and Jenkins, A. , 1991, “ Dependent Failures Developments,” Reliab. Eng. Syst. Saf., 34(3), pp. 417–427. [CrossRef]
Zhang, T. , and Horigome, M. , 2001, “ Availability and Reliability of System With Dependent Components and Time-Varying Failure and Repair Rates,” IEEE Trans. Reliab., 50(2), pp. 151–158. [CrossRef]
Pozsgai, P. , Neher, W. , and Bertsche, B. , 2002, “ Models to Consider Dependence in Reliability Calculation for Systems Consisting of Mechanical Components,” 3rd International Conference on Mathematical Methods in Reliability, Trondheim, Norwegen, pp. 539–542.
Neil, M. , Tailor, M. , Marquez, D. , Fenton, N. , and Hearty, P. , 2008, “ Modelling Dependable Systems Using Hybrid Bayesian Networks,” Reliab. Eng. Syst. Saf., 93(7), pp. 933–939. [CrossRef]
Marriott, C. , and Bate, P. , 2010, “ Dependent Failure Assessment in the Development of a Defuelling Facility for Nuclear Submarines,” 5th IET International Conference on System Safety, pp. 1–6.
Youn, B. D. , and Wang, P. , 2009, “ Complementary Intersection Method for System Reliability Analysis,” ASME J. Mech. Des., 131(4), p. 041004. [CrossRef]
Nguyen, T. H. , Song, J. , and Paulino, G. H. , 2010, “ Single-Loop System Reliability-Based Design Optimization Using Matrix-Based System Reliability Method: Theory and Applications,” ASME J. Mech. Des., 132(1), p. 011005. [CrossRef]
Wang, P. , Hu, C. , and Youn, B. D. , 2011, “ A Generalized Complementary Intersection Method (GCIM) for System Reliability Analysis,” ASME J. Mech. Des., 133(7), p. 071003. [CrossRef]
Kahn, J. , Linial, N. , and Samorodnitsky, A. , 1996, “ Inclusion-Exclusion: Exact and Approximate,” Combinatorica, 16(4), pp. 465–477. [CrossRef]
Boole, G. , 1854, Laws of Thought, American Reprint of 1854 edition, Dover, New York.
Choi, S.-K. , Grandhi, R. , and Canfield, R. A. , 2006, Reliability-Based Structural Design, Springer Science & Business Media, New York.
Hohenbichler, M. , and Rackwitz, R. , 1983, “ First-Order Concepts in System Reliability,” Struct. Saf., 1(3), pp. 177–188. [CrossRef]
Kounias, E. G. , 1968, “ Bounds for the Probability of a Union, With Applications,” Ann. Math. Stat., 39(6), pp. 2154–2158. [CrossRef]
Hunter, D. , 1976, “ An Upper Bound for the Probability of a Union,” J. Appl. Probab., 13(3), pp. 597–603. [CrossRef]
Ditlevsen, O. , 1979, “ Narrow Reliability Bounds for Structural Systems,” J. Struct. Mech., 7(4), pp. 453–472. [CrossRef]
Zhang, Y. C. , 1993, “ High-Order Reliability Bounds for Series Systems and Application to Structural Systems,” Comput. Struct., 46(2), pp. 381–386. [CrossRef]
Song, J. , and Der Kiureghian, A. , 2003, “ Bounds on System Reliability by Linear Programming,” J. Eng. Mech., 129(6), pp. 627–636. [CrossRef]
Ramachandran, K. , 2004, “ System Reliability Bounds: A New Look With Improvements,” Civ. Eng. Environ. Syst., 21(4), pp. 265–278. [CrossRef]
Domyancic, L. C. , and Millwater, H. R. , 2012, “ Advances in Bounding Techniques for Aircraft Structures,” AIAA J., 50(6), pp. 1307–1313. [CrossRef]
Høyland, A. , and Rausand, M. , 2009, System Reliability Theory: Models and Statistical Methods, Wiley, Hoboken, NJ.
Rausand, M. , and Høyland, A. , 2004, System Reliability Theory: Models, Statistical Methods, and Applications, Wiley, Hoboken, NJ.
Du, X. , and Huang, B. , 2007, “ Reliability-Based Design Optimization With Equality Constraints,” Int. J. Numer. Methods Eng., 72(11), pp. 1314–1331. [CrossRef]
Noh, Y. , Choi, K. K. , and Lee, I. , 2010, “ Identification of Marginal and Joint CDFs Using Bayesian Method for RBDO,” Struct. Multidiscip. Optim., 40(1–6), pp. 35–51. [CrossRef]
Hu, Z. , Du, X. , Kolekarb, N. S. , and Banerjee, A. , 2014, “ Robust Design With Imprecise Random Variables and Its Application in Hydrokinetic Turbine Optimization,” Eng. Optim., 46(3), pp. 393–419. [CrossRef]
Guo, J. , and Du, X. , 2010, “ Reliability Analysis for Multidisciplinary Systems With Random and Interval Variables,” AIAA J., 48(1), pp. 82–91. [CrossRef]

Figures

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Fig. 2

A speed reducer system

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Fig. 3

System reliability bounds of two designs

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Fig. 4

Simplified free-body diagram of component i

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Fig. 5

Three different components sharing same load

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Fig. 6

Simplified free-body diagram of component 1

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Fig. 7

Bounds of probabilities of system failure

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Fig. 8

Bounds of probabilities of system failure

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Fig. 9

Two components sharing different loads

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Fig. 10

Simplified free-body diagrams of design concept 1

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Fig. 11

Simplified free-body diagrams of design concept 2

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Fig. 12

Bounds of probabilities of system failure

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