Bayesian model updating with summarized statistical and reliability data

The accuracy of model-based reliability analysis is affected by the uncertainty regarding the model parameters used to predict the behavior of the engineering system. The uncertainty in the model parameters can be reduced by combining prior knowledge about the parameters with observed data regarding system inputs and outputs. In some cases, the information about the observations is only available as abstracted data, where the original raw data have been reduced to a summarized representation. Common forms of abstracted data include summary statistics, such as the mean and variance for continuous variables and observed frequencies for discrete variables. In the context of reliability analysis, a common form of available information is summarized reliability data for various mechanical components (e.g., failure rates or failure probabilities) instead of detailed actual test data. This paper presents a methodology for updating the model parameters using these abstracted data forms through a Bayesian network. First, the concept of a statistics function is developed and linked to the abstracted data forms. The concept of arc reversal is then exploited to transform the Bayesian network to a form that can be used to incorporate the statistics function and thereby enable the updating of the model parameters. Several numerical examples are used to demonstrate the applicability and generality of the proposed method for several different forms of abstracted data.