Receiver operating characteristic-curve limits of detection

• Robust limits of detection using ROC-curves
• Readily used even with less well-behaved systems
• Easily extends to heteroscedastic systems

Using a simple UV LED-excited ruby fluorescence measurement system, we demonstrate that it is easily possible to obtain unbiased detection limits, despite the system deliberately having non-linear response function and non-Gaussian noise. Even when the noise precision model is heteroscedastic, but otherwise only roughly linear, the receiver operating characteristic (ROC) method readily yields results that are in accordance with a priori canonical specifications of false positives and false negatives at the detection limit. The present work demonstrates that obtaining unbiased detection limits is not abstruse and need not be mathematically complicated. Rather, detection limits continue to serve a useful purpose as part of the characterization of chemical measurement systems.