This paper addresses issues that arise in measurement system analysis of a binary measurement system if the measurand is a hybrid between a dichotomy and a continuum. A case study is presented, which illustrates methods to assess the error rates of binary measurements with such a hybrid measurand. The case study concerns pass/fail inspection of laptop screens for scratches, where the measurand is the presence or absence of scratches. If a scratch is present, the measurand corresponds with a continuum of scratch sizes, but if no scratch is present, the measurand corresponds with a point. It is argued that if the measurand is a hybrid, a standard logistic regression model is not suitable to estimate the characteristic curve relating the reject probability with the measurand. Several alternative specifications for the characteristic curve are introduced and compared. We conclude that many of the methods currently used for assessment of a binary measurement system with a hybrid measurand are unsuited. This is a remarkable conclusion, given the frequent occurrence in industry of leak tests, inspections for defects, and other binary measurement systems with a hybrid measurand. Copyright © 2011 John Wiley & Sons, Ltd.