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NASA Bayesian Inference for Probabilistic Risk Analysis

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NASA Bayesian Inference for Probabilistic Risk Analysis NASA/SP-2009-569 Bayesian Inference for NASA Probabilistic Risk and Reliability Analysis Dr. Homayoon Dezfuli NASA Project Manager, NASA Headquarters, Washington, DC Dana Kelly Idaho National Laboratory, Idaho Falls, ID Dr. Curtis Smith Idaho National Laboratory, Idaho Falls, ID Kurt Vedros Idaho National Laboratory, Idaho Falls, ID William Galyean Idaho National Laboratory, Idaho Falls, ID National Aeronautics and Space Administration June 2009 NASA STI Program ... in Profile Since its founding, NASA has been dedicated • CONFERENCE PUBLICATION. Collected to the advancement of aeronautics and space papers from scientific and technical science. The NASA scientific and technical conferences, symposia, seminars, or other information (STI) program plays a key part in meetings sponsored or co-sponsored helping NASA maintain this important role. by NASA. The NASA STI program operates under the • SPECIAL PUBLICATION. Scientific, auspices of the Agency Chief Information Officer. technical, or historical information from It collects, organizes, provides for archiving, and NASA programs, projects, and missions, disseminates NASA’s STI. The NASA STI often concerned with subjects having program provides access to the NASA substantial public interest. Aeronautics and Space Database and its public interface, the NASA Technical Report Server, • TECHNICAL TRANSLATION. English- thus providing one of the largest collections of language translations of foreign scientific aeronautical and space science STI in the world. and technical material pertinent to Results are published in both non-NASA channels NASA’s mission. and by NASA in the NASA STI Report Series, which includes the following report types: Specialized services also include creating custom thesauri, building customized • TECHNICAL PUBLICATION. Reports of databases, and organizing and publishing completed research or a major significant research results. phase of research that present the results of NASA Programs and include extensive data For more information about the NASA STI or theoretical analysis. Includes compilations program, see the following: of significant scientific and technical data and information deemed to be of continuing • Access the NASA STI program home page reference value. NASA counterpart of peer- at http://www.sti.nasa.gov reviewed formal professional papers but has less stringent limitations on manuscript length • E-mail your question via the Internet to and extent of graphic presentations. [email protected] • TECHNICAL MEMORANDUM. Scientific and • Fax your question to the NASA STI Help technical findings that are preliminary or of Desk at 443-757-5803 specialized interest, e.g., quick release reports, working papers, and bibliographies • Phone the NASA STI Help Desk at that contain minimal annotation. Does not 443-757-5802 contain extensive analysis. • Write to: • CONTRACTOR REPORT. Scientific and NASA STI Help Desk technical findings by NASA-sponsored NASA Center for AeroSpace Information contractors and grantees. 7115 Standard Drive Hanover, MD 21076-1320 Foreword This NASA-HANDBOOK is published by the National Aeronautics and Space Administration (NASA) to provide a Bayesian foundation for framing probabilistic problems and performing inference on these problems. It is aimed at scientists and engineers and provides an analytical structure for combining data and information from various sources to generate estimates of the parameters of uncertainty distributions used in risk and reliability models. The overall approach taken in this document is to give both a broad perspective on data analysis issues and a narrow focus on the methods required to implement a comprehensive database repository. It is intended for use across NASA. Recent years have seen significant advances in the use of risk analysis at NASA. These advances are reflected both in the state of practice of risk analysis within projects, and in the status of several NASA requirements and procedural documents. Because risk and reliability models are intended to support decision processes, it is critical that inference methods used in these models be robust and technically sound. To this end, the Office of Safety and Mission Assurance (OSMA) undertook the development of this document. This activity, along with other ongoing OSMA-sponsored projects related to risk and reliability, supports the attainment of the holistic and risk-informed decision-making environment that NASA intends to adopt. This document is not intended to prescribe any technical procedure and/or software tool. The coverage of the technical topics is also limited with respect to (1) the historical genesis of Bayesian methods; (2) comparisons of “classical statistics” approaches with Bayesian ones; (3) the detailed mathematics of a particular method (unless needed to apply the method); and (5) a source of actual reliability or risk data/information. Additionally, this document is focused on hardware failures; excluded from the current scope are specific inference approaches for phenomenological, software, and human failures. As with many disciplines, there are bound to be differences in technical and implementation approaches. The authors acknowledge that these differences exist and to the extent practical these instances have been identified. The Bayesian Inference handbook assumes that probabilistic inference problems range from simple, well- supported cases to complex, multi-dimensional problems. Consequently, the approaches provided to evaluate these diverse sets of issues range from single-line spreadsheet formula approaches to Monte Carlo-based sampling methods. As such, the level of analyst sophistication should be commensurate with the issue complexity and the selected computational engine. To assist analysts in applying the inference principles, the document provides “call out” boxes to provide definitions, warnings, and tips. In addition, a hypothetical (but representative) system analysis and multiple examples are provided, as are methods to extend the analysis to accommodate real-world complications such as uncertain, censored, and disparate data. For most of the example problems, the Bayesian Inference handbook uses a modern computational approach known as Markov chain Monte Carlo (MCMC). Salient references provide the technical basis and mechanics of MCMC approaches. MCMC methods work for simple cases, but more importantly, they work efficiently on very complex cases. Bayesian inference tends to become computationally intensive when the analysis involves multiple parameters and correspondingly high-dimensional integration. MCMC methods were described in the early 1950s in research into Monte Carlo sampling at Los Alamos. Recently, with the advance of computing power and improved analysis algorithms, MCMC is increasingly being used for a variety of Bayesian inference problems. MCMC is effectively (although not literally) numerical (Monte Carlo) integration by way of Markov chains. Inference is performed by sampling from a target distribution (i.e., a specially constructed Markov chain, based upon the inference problem) until convergence (to the posterior distribution) is achieved. The MCMC approach may be implemented using I BAYESIAN INFERENCE FOR NASA PROBABILISTIC RISK AND RELIABILITY ANALYSIS custom-written routines or existing general purpose commercial or open-source software. In the Bayesian Inference document, an open-source program called OpenBUGS (commonly referred to as WinBUGS) is used to solve the inference problems that are described. A powerful feature of OpenBUGS is its automatic selection of an appropriate MCMC sampling scheme for a given problem. The approach that is taken in the document is to provide analysis “building blocks” that can be modified, combined, or used as-is to solve a variety of challenging problems. Not just for risk and reliability inference, MCMC methods are also being used for other U.S. Government activities (e.g., at the Food and Drug Administration, the Nuclear Regulatory Commission, National Institute of Standards and Technology, and the National Atmospheric Release Advisory Center). The MCMC approach used in the document is implemented via textual scripts similar to a macro-type programming language. Accompanying each script is a graphical diagram illustrating the elements of the script and the overall inference problem being solved. In a production environment, analysis could take place by running a script (with modifications keyed to the problem-specific information). Alternatively, other implementation approaches could include: (1) using an interface-driven front-end to automate an applicable script, (2) encapsulating an applicable script into a spreadsheet function call, or (3) creating an automated script-based inference engine as part of an information management system. In lieu of using the suggested MCMC-based analysis approach, some of the document’s inference problems could be solved using the underlying mathematics. However, this alternative numerical approach is limited because several of the inference problems are difficult to solve either analytically or via traditional numerical methods. As a companion activity to this handbook, a data repository and information management system is being planned by OSMA. The approaches described in the report will be considered in the development of the inference engine for this system. While not a risk or reliability data source itself, the Bayesian Inference document describes typical sources of generic and NASA-specific
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