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Research Papers

Validation and Adjustment of Prior and Data for Bayesian Reliability Analysis in Engineering Design

[+] Author and Article Information
Zhaofeng Huang

Yan Jin

Department of Aerospace and Mechanical Engineering,  University of Southern California Los Angels, CA 90089yjin@usc.edu

J. Mech. Des 133(5), 051003 (Jun 06, 2011) (12 pages) doi:10.1115/1.4003841 History: Received May 14, 2010; Revised February 19, 2011; Published June 06, 2011; Online June 06, 2011

Bayesian reliability analysis (BRA) technique has been actively used in reliability assessment for engineered systems. However, there are two key controversies surrounding the BRA: the reasonableness of the prior and the consistency among all data sets. These issues have been debated in Bayesian analysis for many years. As we observed, they have not been resolved satisfactorily. These controversies have seriously hindered the applications of BRA as a useful reliability analysis tool to support engineering design. In this paper, a Bayesian reliability analysis methodology with a prior and data validation and adjustment scheme (PDVAS) is developed to address these issues. As the part of the PDVAS development, a consistency measure is first defined that judges the level of consistency among all data sets including the prior. The consistency measure is then used to adjust either the prior or the data or both to the extent that the prior and the data are statistically consistent. This prior and data validation and adjustment scheme is developed for Binomial sampling with Beta prior, called Beta-Binomial Bayesian model. The properties of the scheme are presented and discussed that provides some insights of PDVAS. Various forms of the adjustment formulas are shown, and a selection framework of a specific formula, based on engineering design and analysis knowledge, is established. Several illustrative examples are presented, which show the reasonableness, effectiveness, and usefulness of PDVAS. General discussion of the scheme is offered to enhance the Bayesian reliability analysis in engineering design for reliability assessment.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Figure 1

Traditional Bayesian analysis flow

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Figure 2

Bayesian result as a weighted average of prior and data set

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Figure 3

Modified Bayesian analysis flow with addition of prior and data validation and adjustment step

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Figure 4

Bayesian updating prior and data adjustment algorithm

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Figure 5

Details of the data adjustment step

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Figure 6

Potential candidate functions for SDA

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A family of beta curves as potential SDA functions

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Figure 8

SDA curves for the data in Table 1

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Figure 9

Linear SDA curve

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Figure 10

Mean comparisons of PDVAS and traditional Bayesian for example 1

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Figure 11

Variance comparisons of PDVAS and traditional Bayesian for example 1

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Figure 12

Mean comparisons of PDVAS and traditional Bayesian for example 2

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Figure 13

Variance comparisons of PDVAS and traditional Bayesian for example 2

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Figure 14

Mean comparisons of PDVAS and traditional Bayesian for example 3

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Figure 15

Variance comparisons of PDVAS and traditional Bayesian for example 3

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Figure 16

Means of PDVAS posteriors from 100 different update sequences

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Figure 17

Variances of PDVAS posteriors from 100 different update sequences

Tables

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