In this paper, we formalize the problem of partial barrier coverage, that is, the problem of using robot sensors (guards) to minimize the probability of undetected intrusion in a particular region by an intruder. We use ideas from noncooperative game theory together with previous results from complete barrier coverage - the problem of completely preventing undetected intrusion - to develop new methods that solve this problem for the specific case of bounded-range line-of-sight sensors in a two-dimensional polygonally-bounded region. Our solution constructs equilibrium strategies for the intruder and guards, and calculates the level of partial coverage.