Background
Chemical measurement systems and their errors
The response, net response and content domains
Traditional limits of detection
Modern limits of detection
Receiver operating characteristics
Statistics of an ideal model CMS
If only the true intercept is unknown
If only the true slope is unknown
If the true intercept and true slope are both unknown
If only the population standard deviation is unknown
If only the true slope is known
If only the true intercept is known
If all three parameters are unknown
Bootstrapped detection limits in a real CMS
Four relevant considerations
Neyman-Pearson hypothesis testing
Heteroscedastic noises
Limits of quantitation
The sampled step function
The sampled rectangular pulse
The sampled triangular pulse
The sampled Gaussian pulse
Parting considerations.