Technical Brief

Integration of Statistics- and Physics-Based Methods—A Feasibility Study on Accurate System Reliability Prediction

[+] Author and Article Information
Zhengwei Hu

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: zhmp7@mst.edu

Xiaoping Du

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 September 20, 2017; final manuscript received March 21, 2018; published online May 11, 2018. Assoc. Editor: Samy Missoum.

J. Mech. Des 140(7), 074501 (May 11, 2018) (7 pages) Paper No: MD-17-1638; doi: 10.1115/1.4039770 History: Received September 20, 2017; Revised March 21, 2018

Component reliability can be estimated by either statistics-based methods with data or physics-based methods with models. Both types of methods are usually independently applied, making it difficult to estimate the joint probability density of component states, which is a necessity for an accurate system reliability prediction. The objective of this study is to investigate the feasibility of integrating statistics- and physics-based methods for system reliability analysis. The proposed method employs the first-order reliability method (FORM) directly for a component whose reliability is estimated by a physics-based method. For a component whose reliability is estimated by a statistics-based method, the proposed method applies a supervised learning strategy through support vector machines (SVM) to infer a linear limit-state function that reveals the relationship between component states and basic random variables. With the integration of statistics- and physics-based methods, the limit-state functions of all the components in the system will then be available. As a result, it is possible to predict the system reliability accurately with all the limit-state functions obtained from both statistics- and physics-based reliability methods.

Copyright © 2018 by ASME
Your Session has timed out. Please sign back in to continue.


Cheng, Y. , Conrad, D. C. , and Du, X. , 2017, “ Narrower System Reliability Bounds With Incomplete Component Information and Stochastic Process Loading,” ASME J. Comput. Inf. Sci. Eng., 17(4), p. 041007. [CrossRef]
Lawless, J. , 1983, “ Statistical Methods in Reliability,” Technometrics, 25(4), pp. 305–316. [CrossRef]
Mahadevan, S. , 1997, “ Physics-Based Reliability Models,” Mechanical Engineering, Basel-Marcel Dekker, New York, pp. 197–232.
Chiralaksanakul, A. , and Mahadevan, S. , 2005, “ First-Order Approximation Methods in Reliability-Based Design Optimization,” ASME J. Mech. Des., 127(5), pp. 851–857. [CrossRef]
Zhao, Y. G. , and Ono, T. , 1999, “ A General Procedure for First/Second-Order Reliability Method (FORM/SORM),” Struct. Saf., 21(2), pp. 95–112. [CrossRef]
Du, X. , and Sudjianto, A. , 2004, “ First Order Saddlepoint Approximation for Reliability Analysis,” AIAA J., 42(6), pp. 1199–1207. [CrossRef]
Choi, S.-K. , Grandhi, R. , and Canfield, R. A. , 2006, Reliability-Based Structural Design, Springer Science & Business Media, London.
Song, J. , and Kang, W.-H. , 2009, “ System Reliability and Sensitivity Under Statistical Dependence by Matrix-Based System Reliability Method,” Struct. Saf., 31(2), pp. 148–156. [CrossRef]
Fiondella, L. , and Xing, L. , 2014, “ Reliability of Two Failure Mode Systems Subject to Correlated Failures,” Annual Reliability and Maintainability Symposium (RAMS), Colorado Springs, CO, Jan. 27–30, pp. 1–6.
Hu, Z. , and Du, X. , 2017, “ System Reliability Prediction With Shared Load and Unknown Component Design Details,” AI EDAM, 31(3), pp. 223–234.
Hu, Z. , and Du, X. , 2016, “ A Physics-Based Reliability Method for Components Adopted in New Series Systems,” Annual Reliability and Maintainability Symposium (RAMS), Tucson, AZ, Jan. 25–28, pp. 1–7.
Hu, Z. , and Du, X. , 2017, “ System Reliability Analysis With In-House and Outsourced Components,” Second International Conference on System Reliability and Safety (ICSRS), Milan, Italy, Dec. 20–22, pp. 146–150.
Basudhar, A. , Missoum, S. , and Sanchez, A. H. , 2008, “ Limit State Function Identification Using Support Vector Machines for Discontinuous Responses and Disjoint Failure Domains,” Probab. Eng. Mech., 23(1), pp. 1–11. [CrossRef]
Basudhar, A. , Dribusch, C. , Lacaze, S. , and Missoum, S. , 2012, “ Constrained Efficient Global Optimization With Support Vector Machines,” Struct. Multidiscip. Optim., 46(2), pp. 201–221. [CrossRef]
Rosenblatt, M. , 1952, “ Remarks on a Multivariate Transformation,” Ann. Math. Stat., 23(3), pp. 470–472. [CrossRef]
Hogg, R. V. , and Craig, A. T. , 1995, Introduction to Mathematical Statistics, 5th ed., Prentice Hall, Upper Saddle River, NJ.


Grahic Jump Location
Fig. 1

Marginal classifiers along with SVs

Grahic Jump Location
Fig. 2

Classification of training points using SVM

Grahic Jump Location
Fig. 3

A cantilever beam system

Grahic Jump Location
Fig. 4

A crank-slider system



Some tools below are only available to our subscribers or users with an online account.

Related Content

Customize your page view by dragging and repositioning the boxes below.

Related Journal Articles
Related eBook Content
Topic Collections

Sorry! You do not have access to this content. For assistance or to subscribe, please contact us:

  • TELEPHONE: 1-800-843-2763 (Toll-free in the USA)
  • EMAIL: asmedigitalcollection@asme.org
Sign In