TECHNICAL PAPERS: Gas Turbines: Structures and Dynamics

Confidence Interval Simulation for Systems of Random Variables

[+] Author and Article Information
Thomas A. Cruse1

 Air Force Research Laboratory, Wright-Patterson AFB, OH 45463Thomas.Cruse@wpafb.af.mil

Jeffrey M. Brown

 Air Force Research Laboratory, Propulsion Directorate, Wright-Patterson AFB, OH 45463Jeffrey.Brown@wpafb.af.mil

Note that we are using Bayesian terms in two different modes in this study: one is the notion of a Bayesian network where Markov chain properties derive from the direct use of Bayes’ theorem; second is the use of prior estimates for random variable distribution parameters that are subsequently updated to posterior distributions through another application of Bayes’ theorem.


Corresponding author. Professor of Mechanical Engineering, Vanderbilt University.

J. Eng. Gas Turbines Power 129(3), 836-842 (Oct 11, 2005) (7 pages) doi:10.1115/1.2718217 History: Received September 16, 2005; Revised October 11, 2005

Bayesian network models are seen as important tools in probabilistic design assessment for complex systems. Such network models for system reliability analysis provide a single probability of failure value whether the experimental data used to model the random variables in the problem are perfectly known or derive from limited experimental data. The values of the probability of failure for each of those two cases are not the same, of course, but the point is that there is no way to derive a Bayesian type of confidence interval from such reliability network models. Bayesian confidence (or belief) intervals for a probability of failure are needed for complex system problems in order to extract information on which random variables are dominant, not just for the expected probability of failure but also for some upper bound, such as for a 95% confidence upper bound. We believe that such confidence bounds on the probability of failure will be needed for certifying turbine engine components and systems based on probabilistic design methods. This paper reports on a proposed use of a two-step Bayesian network modeling strategy that provides a full cumulative distribution function for the probability of failure, conditioned by the experimental evidence for the selected random variables. The example is based on a hypothetical high-cycle fatigue design problem for a transport aircraft engine application.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

WinBUGS DAG for probabilistic HCF

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Figure 2

Comparison of probabilistic sensitivity factors

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Figure 3

DAG for the inner-loop response surface approximation

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Figure 4

Failure rate probability density function simulation results for sample size=11

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Figure 5

Convergence of failure rate with sample size

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Figure 6

Statistical importance factors for 95%-bound conditions



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