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.