Sample size determination for estimation of sensor detection probabilities based on a test variable

Abstract

In this thesis, we study procedures and required sample sizes for estimating the probability of detection as a function of range to target for sensor systems as evaluated by the U.S. Army Yuma Proving Ground. First, we examine the problem within the context of a binomial experiment in order to improve the current estimation method used by the U.S. Army Yuma Proving Ground. Specifically, we evaluate the coverage probabilities and lengths of widely used confidence intervals for a binomial proportion and report the required sample sizes for some specified goals. Although the required sample sizes turn out to be impracticably large, we provide the U.S. Army Yuma Proving Ground with a better understanding of the usual confidence intervals and variability inherent in their current estimation scheme. Second, we show that confidence intervals for a probability of detection as a function of range based on the fit of a simple linear logistic regression model perform much better than the usual confidence intervals for a binomial proportion. Using an empirical approach based on a controlled set of simulations, we then determine the required sample size within the experimental region of interest.