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Uncertainty quantification (UQ) is gaining in maturity and importance in engineering analysis. While historical engineering analysis and design methods have relied heavily on safety factors (SF) with built-in conservatism, modern approaches require detailed assessment of reliability to provide optimized and balanced designs. This paper presents methodologies that support the transition toward this type of approach. Fundamental concepts are described for UQ in general engineering analysis. These include consideration of the sources of uncertainty and their categorization. Of particular importance are the categorization of aleatory and epistemic uncertainties and their separate propagation through an UQ analysis. This familiar concept is referred to here as a “two-dimensional” approach, and it provides for the assessment of both the probability of a predicted occurrence and the credibility in that prediction. Unique to the approach presented here is the adaptation of the concept of a bounding probability box to that of a credible probability box. This requires estimates for probability distributions related to all uncertainties both aleatory and epistemic. The propagation of these distributions through the uncertainty analysis provides for the assessment of probability related to the system response, along with a quantification of credibility in that prediction. Details of a generalized methodology for UQ in this framework are presented, and approaches for interpreting results are described. Illustrative examples are presented.

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A unique numerical method has been developed for solving one-dimensional ablation heat transfer problems. This paper provides a comprehensive description of the method, along with detailed derivations of the governing equations. This methodology supports solutions for traditional ablation modeling including such effects as heat transfer, material decomposition, pyrolysis gas permeation and heat exchange, and thermochemical surface erosion. The numerical scheme utilizes a control-volume approach with a variable grid to account for surface movement. This method directly supports implementation of nontraditional models such as material swelling and mechanical erosion, extending capabilities for modeling complex ablation phenomena. Verifications of the numerical implementation are provided using analytical solutions, code comparisons, and the method of manufactured

Reliability of solid rocket motors has steadily increased since the beginning of solid propulsion systems. Increased reliability of solid rocket motors has produced a 100 percent success rate in orbital space launched rocket systems in the United States over the past 20 years. Historical failures have been attributed to different components of these systems including nozzles, propellant, cases, joints, propellant/liner/insulation bonds, and insulation. Attribution to improvements in testing, nondestructive evaluation (NDE), materials, manufacturing, processes, technology, and analytical tools is indicated for the increased reliability of these systems. This paper includes the following: 1) reviews of trends in historical reliability of solid rocket motors, 2) identification of historical failures modes and their implications to modern systems, and 3) a brief summary review of approaches that have been developed to improve reliability. Nomenclature