Confidence Interval Simulation for Systems of Random Variables

Abstract

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.