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Research Papers

Toward the Effect of Dependent Distribution Parameters on Reliability Prediction

[+] 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 Computers and Information Division of ASME for publication in the JOURNAL OF COMPUTING AND INFORMATION SCIENCE IN ENGINEERING. Manuscript received October 7, 2017; final manuscript received January 22, 2018; published online March 19, 2018. Editor: Satyandra K. Gupta.

J. Comput. Inf. Sci. Eng 18(2), 021008 (Mar 19, 2018) (10 pages) Paper No: JCISE-17-1211; doi: 10.1115/1.4039193 History: Received October 07, 2017; Revised January 22, 2018

Random variables are commonly encountered in engineering applications, and their distributions are required for analysis and design, especially for reliability prediction during the design process. Distribution parameters are usually estimated using samples. In many applications, samples are in the form of intervals, and the estimated distribution parameters will also be in intervals. Traditional reliability methodologies assume independent interval distribution parameters, but as shown in this study, the parameters are actually dependent since they are estimated from the same set of samples. This study investigates the effect of the dependence of distribution parameters on the accuracy of reliability analysis results. The major approach is numerical simulation and optimization. This study demonstrates that the independent distribution parameter assumption makes the estimated reliability bounds wider than the true bounds. The reason is that the actual combination of the distribution parameters may not include the entire box-type domain assumed by the independent interval parameter assumption. The results of this study not only reveal the cause of the imprecision of the independent distribution parameter assumption, but also demonstrate a need of developing new reliability methods to accommodate dependent distribution parameters.

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Figures

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Fig. 1

Box domain of the mean and standard deviation

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Fig. 2

Distribution parameters with six interval samples

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Fig. 3

Dependent relationship between distribution parameters with different number of intervals: (a) 1 interval, (b) 2 intervals, (c) 3 intervals, (d) 4 intervals, (e) 5 intervals, (f) 7 intervals, (g) 8 intervals, and (h) 9 intervals

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Fig. 4

A bending stress applied on a beam

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Fig. 5

Probability of failure with respect to the number of interval samples

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Fig. 6

Dependent distribution parameters of Sy

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Fig. 7

A load applied to a simply supported beam

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Fig. 8

Dependent distribution parameters of E

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Fig. 9

Dependent distribution parameters of p

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Fig. 10

A cantilever tube

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Fig. 11

Dependent mean and standard deviation of F1

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