A Bayes approach for uncertainty bounds for a stochastic analysis of the Space Shuttle main engine

In this paper a Bayesian approach was presented to derive a time-dependent parametric probability function of a sudden critical structural failure of the Space Shuttle Main Engine Block I design, including uncertainty bounds at any given time. The probability function was assumed to have a Weibull form with parameters β and η. Under this assumption, both prior belief about this type of failure (based on a component based analysis) and the information available from the complex test data set of the SSME were used as input for the Bayesian update. The test data contains both actual failures and tests that were stopped before failure (`censored´), which made the process of examining the data set a challenging endeavor. The outcome of the Bayesian update formed the posterior belief in the parameters of the probability function. It was concluded that under the assumption of a Weibull distribution for a sudden critical structural failure, the uncertainty about the parameters is strongly diminished by combining the prior belief with the test data