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A Bayesian forecasting model is developed to quantify uncertainty about the postflight state of a field-joint primary O-ring (not damaged or damaged), given the O-ring temperature at the time of launch of the space shuttle Challenger in 1986. The crux of this problem is the enormous extrapolation that must be performed: 23 previous shuttle flights were launched at temperatures between 53 degrees F and 81 degrees F, but the next launch is planned at 31 degrees F. The fundamental advantage of the Bayesian model is its theoretic structure, which remains correct over the entire sample space of the predictor and that affords flexibility of implementation. A novel approach to extrapolating the input elements based on expert judgment is presented; it recognizes that extrapolation is equivalent to changing the conditioning of the model elements. The prior probability of O-ring damage can be assessed subjectively by experts following a nominal-interacting process in a group setting. The Bayesian model can output several posterior probabilities of O-ring damage, each conditional on the given temperature and on a different strength of the temperature effect hypothesis. A lower bound on, or a value of, the posterior probability can be selected for decision making consistently with expert judgment, which encapsulates engineering information, knowledge, and experience. The Bayesian forecasting model is posed as a replacement for the logistic regression and the nonparametric approach advocated in earlier analyses of the Challenger O-ring data. A comparison demonstrates the inherent deficiency of the generalized linear models for risk analyses that require forecasting an event conditional on a predictor value outside the sampling interval, and combining empirical evidence with expert judgment.

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This paper develops a method for finding a robust test plan, which consists of a mixture of full system and subsystem tests, to estimate the reliability of a system given that the model for the system reliability is flawed. A robust test plan is developed by trading off the number of full system and subsystem tests to minimize the mean-squared error (MSE) of the maximum likelihood estimate (MLE) of system reliability. The MSE is decomposed into the variance of the MLE and a bias from incorrectly specifying the model that relates the subsystem reliabilities to the full system reliability (series, parallel, other). The variance of the MLE is based on the inverse Fisher Information. The bias is due to the modeling error. A demonstration of the test plan determination is given for a hypothetical system by trading off between the MSE (estimation accuracy), the degree of modeling error, and the cost of doing system and subsystem tests. A Pareto frontier can be identified, as illustrated in the paper.