Publications

Abstract not provided.

Abstract not provided.

This paper develops Classical and Bayesian methods for quantifying the uncertainty in reliability for a system of mixed series and parallel components for which both go/no-go and variables data are available. Classical methods focus on uncertainty due to sampling error. Bayesian methods can explore both sampling error and other knowledge-based uncertainties. To date, the reliability community has focused on qualitative statements about uncertainty because there was no consensus on how to quantify them. This paper provides a proof of concept that workable, meaningful quantification methods can be constructed. In addition, the application of the methods demonstrated that the results from the two fundamentally different approaches can be quite comparable. In both approaches, results are sensitive to the details of how one handles components for which no failures have been seen in relatively few tests.

The purpose of this project was to investigate the use of Bayesian methods for the estimation of the reliability of complex systems. The goals were to find methods for dealing with continuous data, rather than simple pass/fail data; to avoid assumptions of specific probability distributions, especially Gaussian, or normal, distributions; to compute not only an estimate of the reliability of the system, but also a measure of the confidence in that estimate; to develop procedures to address time-dependent or aging aspects in such systems, and to use these models and results to derive optimal testing strategies. The system is assumed to be a system of systems, i.e., a system with discrete components that are themselves systems. Furthermore, the system is 'engineered' in the sense that each node is designed to do something and that we have a mathematical description of that process. In the time-dependent case, the assumption is that we have a general, nonlinear, time-dependent function describing the process. The major results of the project are described in this report. In summary, we developed a sophisticated mathematical framework based on modern probability theory and Bayesian analysis. This framework encompasses all aspects of epistemic uncertainty and easily incorporates steady-state and time-dependent systems. Based on Markov chain, Monte Carlo methods, we devised a computational strategy for general probability density estimation in the steady-state case. This enabled us to compute a distribution of the reliability from which many questions, including confidence, could be addressed. We then extended this to the time domain and implemented procedures to estimate the reliability over time, including the use of the method to predict the reliability at a future time. Finally, we used certain aspects of Bayesian decision analysis to create a novel method for determining an optimal testing strategy, e.g., we can estimate the 'best' location to take the next test to minimize the risk of making a wrong decision about the fitness of a system. We conclude this report by proposing additional fruitful areas of research.

This paper presents the conceptual framework that is being used to define quantification of margins and uncertainties (QMU) for application in the nuclear weapons (NW) work conducted at Sandia National Laboratories. The conceptual framework addresses the margins and uncertainties throughout the NW life cycle and includes the definition of terms related to QMU and to figures of merit. Potential applications of QMU consist of analyses based on physical data and on modeling and simulation. Appendix A provides general guidelines for addressing cases in which significant and relevant physical data are available for QMU analysis. Appendix B gives the specific guidance that was used to conduct QMU analyses in cycle 12 of the annual assessment process. Appendix C offers general guidelines for addressing cases in which appropriate models are available for use in QMU analysis. Appendix D contains an example that highlights the consequences of different treatments of uncertainty in model-based QMU analyses.

Current work on the Integrated Stockpile Evaluation (ISE) project is evidence of Sandia's commitment to maintaining the integrity of the nuclear weapons stockpile. In this report, we undertake a key element in that process: development of an analytical framework for determining the reliability of the stockpile in a realistic environment of time-variance, inherent uncertainty, and sparse available information. This framework is probabilistic in nature and is founded on a novel combination of classical and computational Bayesian analysis, Bayesian networks, and polynomial chaos expansions. We note that, while the focus of the effort is stockpile-related, it is applicable to any reasonably-structured hierarchical system, including systems with feedback.

This research effort focuses on methodology for quantifying the effects of model uncertainty and discretization error on computational modeling and simulation. The work is directed towards developing methodologies which treat model form assumptions within an overall framework for uncertainty quantification, for the purpose of developing estimates of total prediction uncertainty. The present effort consists of work in three areas: framework development for sources of uncertainty and error in the modeling and simulation process which impact model structure; model uncertainty assessment and propagation through Bayesian inference methods; and discretization error estimation within the context of non-deterministic analysis.