Skip to Main Content
We describe a hierarchical Bayesian model for assessing the early reliability of complex systems, for which sparse or no system level failure data are available, except that which exists for comparable systems developed by different categories of manufacturers. Novel features of the model are the inclusion of a "quality" index to allow separate treatment for systems produced by "experienced" & "inexperienced" manufacturers. We show how this index can be employed to distinguish the behavior of systems produced by each category of manufacturer for the first few applications, with later pooling of outcomes from both categories of manufacturers after the first few uses (i.e., after inexperienced manufacturers gain experience). We demonstrate how this model, together with suitable informative priors, can reproduce the reliability growth in the modeled systems. Estimation of failure probabilities (and associated uncertainties) for early launches of new space vehicles is used to illustrate the methodology. Disclaimer-This paper is provided solely to illustrate how hierarchical Bayesian methods can be applied to estimate systems reliability (including uncertainties) for newly introduced complex systems with sparse or nonexistent system level test data. The example problem considered (i.e. estimating failure probabilities of new launch vehicles) is employed solely for illustrative purposes. The authors have made numerous assumptions & approximations throughout the document in order to demonstrate the central techniques. The specific methodologies, results, and conclusions presented in this paper are neither approved nor endorsed by the United States Air Force or the Federal Aviation Administration.