V. Bram Lillard

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....

Recasting gunfire data from binomial (hit/miss) to continuous (time-to-kill) allows us to draw statistical conclusions with tactical implications from free-play,live-fire surface gunnery events. Our analysis provided the Navy with suggestions forimprovements to its tactics and the employment of its weapons. A censored analysisenabled us to do so, where other methods fell short. Suggested Citation Ashwell, Benjamin A, V Bram Lillard, and George M Khoury. Improved Surface Gunnery Analysis with Continuous Data....

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....

This document was prepared to support Dr. Lillard’s visit to the NavalPostgraduate School where he will provide a guest lecture to students in the T&Ecourse. The briefing covers three primary themes: 1) evaluation of military systemson the basis of requirements and KPPs alone is often insufficient to determineeffectiveness and suitability in combat conditions, 2) statistical methods are essentialfor developing defensible and rigorous test designs, 3) operational testing is often theonly means to discover critical performance shortcomings....

Binomial metrics like probability-to-detect or probability-to-hit typically do not provide the maximum information from testing. Using continuous metrics such as time to detect provide more information, but do not account for non-detects. Censored data analysis allows us to account for both pieces of information simultaneously. Suggested Citation Lillard, V Bram. Censored Data Analysis Methods for Performance Data: A Tutorial. IDA Document NS D-5811. Alexandria, VA: Institute for Defense Analyses, 2016....

The current fiscal climate demands now, more than ever, that test and evaluation(T&E) provide relevant and credible characterization of system capabilities andshortfalls across all relevant operational conditions as efficiently as possible. Indetermining the answer to the question, “How much testing is enough?” it isimperative that we use a scientifically defensible methodology. Design ofExperiments (DOE) has a proven track record in Operational Test andEvaluation (OT&E) of not only quantifying how much testing is enough, but alsowhere in the operational space the test points should be placed....

Binomial metrics like probability-to-detect or probability-to-hit typically provide operationally meaningful and easy to interpret test outcomes. However, they are information-poor metrics and extremely expensive to test. The standard power calculations to size a test employ hypothesis tests, which typically result in many tens to hundreds of runs. In addition to being expensive, the test is most likely inadequate for characterizing performance over a variety of conditions due to the inherently large statistical uncertainties associated with binomial metrics....

In today’s fiscal environment, efficient and effective testing is essential. Often, military system requirements are defined using probability of success as the primary measure of effectiveness – for example, a system must complete its mission 80 percent of the time; or the system must detect 90 percent of targets. The traditional approach to testing these probability-based requirements is to execute a series of trials and then total the number of successes; the ratio of successes to number of trails provides an intuitive measure of the probability of success....