Thomas Johnson

A vulnerability assessment of a combat vehicle uses modeling and simulation (M&S) to predict the vehicle’s vulnerability to a given enemy attack. The system-level output of the M&S is the probability that the vehicle’s mobility is degraded as a result of the attack. The M&S models this system-level phenomenon by decoupling the attack scenario into a hierarchy of sub-systems. Each sub-system addresses a specific scientific problem, such as the fracture dynamics of an exploded munition, or the ballistic resistance provided by the vehicle’s armor....

M&S validation is critical for ensuring credible weapon system evaluations. System-level evaluations of Armored Fighting Vehicles (AFV) rely on the Advanced Joint Effectiveness Model (AJEM) and Full-Up System Level (FUSL) testing to assess AFV vulnerability. This report reviews and improves upon one of the primary methods that analysts use to validate AJEM, called the Component Damage Vector (CDV) Method. The CDV Method compares vehicle components that were damaged in FUSL testing to simulated representations of that damage from AJEM....

Fragmentation analysis is a critical piece of the live fire test and evaluation (LFT&E) of the lethality and vulnerability aspects of warheads. But the traditional methods for data collection are expensive and laborious. New optical tracking technology is promising to increase the fidelity of fragmentation data, and decrease the time and costs associated with data collection. However, the new data will be complex, three-dimensional “fragmentation clouds,” possibly with a time component as well, and there will be a larger number of individual data points....

Circular prediction regions are used in ballistic testing to express the uncertainty in shot accuracy. We compare two modeling approaches for estimating circular prediction regions for the miss distance of a ballistic projectile. The miss distance response variable is bivariate normal and has a mean and variance that can change with one or more experimental factors. The first approach fits a heteroskedastic linear model using restricted maximum likelihood, and uses the Kenward-Roger statistic to estimate circular prediction regions....

Engineers use reliability experiments to determine the factors that drive product reliability, build robust products, and predict reliability under use conditions. This article uses recent testing of a Howitzer to illustrate the challenges in designing reliability experiments for complex, repairable systems. We leverage lessons learned from current research and propose methods for designing an experiment for a complex, repairable system. Suggested Citation Freeman, Laura J., Rebecca M. Medlin, and Thomas H....

Advances in computational power have allowed both greater fidelity and more extensive use of such models. Numerous complex military systems have a corresponding model that simulates its performance in the field. In response, the DoD needs defensible practices for validating these models. Design of Experiments and statistical analysis techniques are the foundational building blocks for validating the use of computer models and quantifying uncertainty in that validation. Recent developments in uncertainty quantification have the potential to benefit the DoD in using modeling and simulation to inform operational evaluations....

This handbook focuses on methods for data-driven validation to supplement the vast existing literature for Verification, Validation, and Accreditation (VV&A) and the emerging references on uncertainty quantification (UQ). The goal of this handbook is to aid the test and evaluation (T&E) community in developing test strategies that support model validation (both external validation and parametric analysis) and statistical UQ. Suggested Citation Wojton, Heather, Kelly M Avery, Laura J Freeman, Samuel H Parry, Gregory S Whittier, Thomas H Johnson, and Andrew C Flack....

An operational test is resource-limited and must therefore rely on both live test data and modeling and simulation (M&S) data to inform a full evaluation. For the Joint Air-to-Ground Missile (JAGM) system, we needed to create a test design that accomplished dual goals, characterizing missile performance across the operational space and supporting rigorous validation of the M&S. Our key question is which statistical techniques should be used to compare the M&S to the live data?...

Acceptance Sampling by Variables (ASbV) is a statistical testing technique used in Personal Protective Equipment programs to determine the quality of the equipment in First Article and Lot Acceptance Tests. This article intends to remedy the lack of existing references that discuss the similarities between ASbV and certain techniques used in different sub-disciplines within statistics. Understanding ASbV from a statistical perspective allows testers to create customized test plans, beyond what is available in MIL-STD-414....

The purpose of survivability testing is to provide decision makers with relevant, credible evidence about the survivability of an aircraft that is conveyed with some degree of certainty or inferential weight. In developing an experiment to accomplish this goal, a test planner faces numerous questions What critical issue or issues are being address? What data are needed to answer the critical issues? What test conditions should be varied? What is the most economical way of varying those conditions?...

Reliability tests determine which factors drive system reliability. Often, the reliability or failure time data collected in these tests tend to follow distinctly non- normal distributions and include censored observations. The experimental design should accommodate the skewed nature of the response and allow for censored observations, which occur when systems under test do not fail within the allotted test time. To account for these design and analysis considerations, Monte Carlo simulations are frequently used to evaluate experimental design properties....

The complex, multifunctional nature of defense systems, along with the wide variety of system types, demands a structured but flexible analytical process for testing systems. This chapter summarizes commonly used techniques in defense system testing and specific challenges imposed by the nature of defense system testing. It highlights the core statistical methodologies that have proven useful in testing defense systems. Case studies illustrate the value of using statistical techniques in the design of tests and analysis of the resulting data....

Statistical literature refers to a type of error that is committed by giving the right answer to the wrong question. If a test design is adequately scoped to address an irrelevant objective, one could say that a Type III error occurs. In this paper, we focus on a specific Type III error that on some occasions test planners commit to reduce test size and resources. Suggested Citation Johnson, Thomas H., Rebecca M....

Statistical power is a useful measure for assessing the adequacy of anexperimental design prior to data collection. This paper proposes an approach referredto as the signal-to-noise transformation method (SNRx), to approximate power foreffects in a generalized linear model. The contribution of SNRx is that, with a coupleassumptions, it generates power approximations for generalized linear model effectsusing F-tests that are typically used in ANOVA for classical linear models.Additionally, SNRx follows Ohlert and Whitcomb’s unified approach for sizing aneffect, which allows for intuitive effect size definitions, and consistent estimates ofpower....

A sensitivity experiment is a special type of experimental design that is used when the response variable is binary and the covariate is continuous. Armor protection and projectile lethality tests often use sensitivity experiments to characterize a projectile’s probability of penetrating the armor. In this mini-tutorial we illustrate the challenge of modeling a binary response with a limited sample size, and show how sensitivity experiments can mitigate this problem. We review eight different single covariate sensitivity experiments and present a comparison of these designs using simulation....

This paper summarizes sensitivity test methods commonly employed in the Department of Defense. A comparison study shows that modern methods such as Neyer’s method and Three-Phase Optimal Design are improvements over historical methods. Suggested Citation Johnson, Thomas H., Laura Freeman, Janice Hester, and Jonathan L. Bell. “A Comparison of Ballistic Resistance Testing Techniques in the Department of Defense.” IEEE Access 2 (2014): 1442–55. https://doi.org/10.1109/ACCESS.2014.2377633. Paper:

This guide provides both a general explanation of power analysis and specific guidance to successfully interface with two software packages, JMP and Design Expert (DX). Suggested Citation Freeman, Laura J., Thomas H. Johnson, and James R. Simpson. “Power Analysis Tutorial for Experimental Design Software:” Fort Belvoir, VA: Defense Technical Information Center, November 1, 2014. https://doi.org/10.21236/ADA619843. Paper: