Alyson G. Wilson

Finding Near-Optimal Bayesian Experimental Designs via Genetic Algorithms

This article shows how a genetic algorithm can be used to find near-optimal Bayesia nexperimental designs for regression models. The design criterion considered is the expected Shannon information gain of the posterior distribution obtained from performing a given experiment compared with the prior distribution. Genetic algorithms are described and then applied to experimental design. The methodology is then illustrated with a wide range of examples: linear and nonlinear regression, single and multiple factors, and normal and Bernoulli distributed experimental data.

Bayesian networks for multilevel system reliability

Bayesian networks have recently found many applications in systems reliability; however, the focus has been on binary outcomes. In this paper we extend their use to multilevel discrete data and discuss how to make joint inference about all of the nodes in the network. These methods are applicable when system structures are too complex to be represented by fault trees. The methods are illustrated through four examples that are structured to clarify the scope of the problem.

A fully Bayesian approach for combining multilevel failure information in fault tree quantification and optimal follow-on resource allocation

Abstract This paper presents a fully Bayesian approach that simultaneously combines non-overlapping (in time) basic event and higher-level event failure data in fault tree quantification. Such higher-level data often correspond to train, subsystem or system failure events. The fully Bayesian approach also automatically propagates the highest-level data to lower levels in the fault tree. A simple example illustrates our approach. The optimal allocation of resources for collecting additional data from a choice of different level events is also presented. The optimization is achieved using a genetic algorithm.

Integrated Analysis of Computer and Physical Experiments

Scientific investigations frequently involve data from computer experiment(s) as well as related physical experimental data on the same factors and related response variable(s). There may also be one or more expert opinions regarding the response of interest. Traditional statistical approaches consider each of these datasets separately with corresponding separate analyses and fitted statistical models. A compelling argument can be made that better, more precise statistical models can be obtained if the combined data are analyzed simultaneously using a hierarchical Bayesian integrated modeling approach. However, such an integrated approach must recognize important differences, such as possible biases, in these experiments and expert opinions. We illustrate our proposed integrated methodology by using it to model the thermodynamic operation point of a top-spray fluidized bed microencapsulation processing unit. Such units are used in the food industry to tune the effect of functional ingredients and additives. An important thermodynamic response variable of interest, Y, is the steady-state outlet air temperature. In addition to a set of physical experimental observations involving six factors used to predictY, similar results from three different computer models are also available. The integrated data from the physical experiment and the three computer models are used to fit an appropriate response surface (regression) model for predicting Y.

Advances in Data Combination, Analysis and Collection for System Reliability Assessment

The systems that statisticians are asked to assess, such as nuclear weapons, infrastructure networks, supercomputer codes and munitions, have become increasingly complex. It is often costly to conduct full system tests. As such, we present a review of methodology that has been proposed for addressing system reliability with limited full system testing. The first approaches presented in this paper are concerned with the combination of multiple sources of information to assess the reliability of a single component. The second general set of methodology addresses the combination of multiple levels of data to determine system reliability. We then present developments for complex systems beyond traditional series/parallel representations through the use of Bayesian networks and flowgraph models. We also include methodological contributions to resource allocation considerations for system relability assessment. We illustrate each method with applications primarily encountered at Los Alamos National Laboratory.

Information integration for complex systems

This paper develops a framework to determine the performance or reliability of a complex system. We consider a case study in missile reliability that focuses on the assessment of a high fidelity launch vehicle intended to emulate a ballistic missile threat. In particular, we address the case of how to make a system assessment when there are limited full-system tests. We address the development of a system model and the integration of a variety of data using a Bayesian network.

Modern statistical and mathematical methods in reliability

# Competing Risk Modeling in Reliability (T Bedford) # Game-Theoretic and Reliability Methods in Counter-Terrorism and Security (V Bier) # Regression Models for Reliability Given the Usage Accumulation History (T Duchesne) # Bayesian Methods for Assessing System Reliability: Models and Computation (T Graves & M Hamada) # Dynamic Modeling in Reliability and Survival Analysis (E A Pena & E Slate) # End of Life Analysis (H Wynn et al.) # and other papers

A Bayesian Model for Integrating Multiple Sources of Lifetime Information

We present a Bayesian model for assessing the reliability of multicomponent systems. Novel features of this model are the natural manner in which lifetime data collected at either the component, subsystem, or system level are integrated with prior information at any level. The model allows pooling of information between similar components, the incorporation of expert opinion, and straightforward handling of censored data. The methodology is illustrated with two examples.

Statistical Engineering — Forming the Foundations

Editors: Christine M. Anderson-Cook, Lu Lu, Panelists: Gordon Clark, Stephanie P. DeHart, Roger Hoerl, Bradley Jones, R. Jock MacKay, Douglas Montgomery, Peter A. Parker, James Simpson, Ronald Snee, Stefan H. Steiner, Jennifer Van Mullekom, G. Geoff Vining, Alyson G. Wilson Los Alamos National Laboratory, Los Alamos, New Mexico Ohio State University, Columbus, Ohio DuPont, Roanoke, Virginia GE Global Research, Schenectady, New York SAS, Cary, North Carolina University of Waterloo, Waterloo, Ontario, Canada Arizona State University, Tempe, Arizona NASA, Langley, Virginia Eglin Air Force Base, Valparaiso, Florida Snee Associates, Newark, Delaware DuPont, Richmond, Virginia Virginia Tech, Blacksburg, Virginia Institute for Defense Analyses, Washington, DC INTRODUCTION

Bayesian Methods for Estimating System Reliability Using Heterogeneous Multilevel Information

We propose a Bayesian approach for assessing the reliability of multicomponent systems. Our models allow us to evaluate system, subsystem, and component reliability using multilevel information. Data are collected over time, and include binary, lifetime, and degradation data. We illustrate the methodology through two examples and discuss extensions. Supplementary materials are available online.