Bayesian

This presentation documents the work of IDA 2024 Summer Associate Emma Mitchell. The work presented details an R Shiny application developed to provide a user-friendly software tool for researchers to use in planning for and analyzing system reliability. Specifically, the presentation details how one can plan for a reliability test using Bayesian Reliability Assurance test methods. Such tests utilize supplementary data and information, including reliability models, prior test results, expert judgment, and knowledge of environmental conditions, to plan for reliability testing, which in turn can often help in reducing the required amount of testing....

To improve test planning for evaluating system reliability, we propose the use of Bayesian methods to incorporate supplementary data and reduce testing duration. Furthermore, we recommend Bayesian methods be employed in the analysis phase to better quantify uncertainty. We find that when using Bayesian Methods for test planning we can scope smaller tests and using Bayesian methods in analysis results in a more precise estimate of reliability – improving uncertainty quantification....

As operational testing becomes increasingly integrated and research questions become more difficult to answer, IDA’s Test Science team has found Bayesian models to be powerful data analysis methods. Analysts and decision-makers should understand the differences between this approach and the conventional way of analyzing data. It is also important to recognize when an analysis could benefit from the inclusion of prior information—what we already know about a system’s performance—and to understand the proper way to incorporate that information....

A challenging aspect ofa system reliability assessment is integratingmultiple sources of information, such as component, subsystem, and full-system data,along with previous test data or subject matter expert (SME) opinion. A powerfulfeature of Bayesian analyses is the ability to combine these multiple sources of dataand variability in an informed way to perform statistical inference. This feature isparticularly valuable in assessing system reliability where testing is limited and only asmall number of failures (or none at all) are observed....

The use of Bayesian statistics and experimental design as tools to scope testing and analyze data related to defense has increased in recent years. Planning a test using experimental design will allow testers to cover the operational space while maximizing the information obtained from each run. Understanding which factors can affect a detector’s performance can influence military tactics, techniques and procedures, and improve a commander’s situational awareness when making decisions in an operational environment....

This briefing provides an example of some of the nuanced issues in reliability estimation in operational testing. The statistical models are motivated by an example of the Paladin Integrated Management (PIM). We demonstrate how to use a Bayesian approach to reliability estimation that uses data from all phases of testing. Suggested Citation Browning, Caleb, Laura Freeman, Alyson Wilson, Kassandra Fronczyk, and Rebecca Dickinson. “Estimating System Reliability from Heterogeneous Data.” Presented at the Conference on Applied Statistics in Defense, George Mason University, October 2015....

This paper shows how Bayesian methods are ideal for the assessment of complex system reliability assessments. Several examples illustrate the methodology. Suggested Citation Freeman, Laura J, and Kassandra Fronczyk. “Improving Reliability Estimates with Bayesian Statistics.” ITEA Journal of Test and Evaluation 37, no. 4 (June 2015). Paper:

This presentation is a presentation for the Army Conference on Applied Statistics. The presentation covers a brief introduction to land warfare problems, and devises a methodology using Bayes Theorem to estimate parameters of interest. Two examples are given, a simple one using independent Bernoulli Trials, and a more complex one using correlated Red and Blue casualty data in a Loss Exchange Ratio and a hierarchical model. The presentation demonstrates that the Bayesian approach is successful in both examples at reducing the variance of the estimated parameters, potentially reducing the cost of devising a complex test program....