Limits of detection and decision. Part 4

Probability density functions (PDFs) have been derived for a number of commonly used limit of detection definitions, including several variants of the Relative Standard Deviation of the Background–Background Equivalent Concentration (RSDB–BEC) method, for a simple linear chemical measurement system (CMS) having homoscedastic, Gaussian measurement noise and using ordinary least squares (OLS) processing. All of these detection limit definitions serve as both decision and detection limits, thereby implicitly resulting in 50% rates of Type 2 errors. It has been demonstrated that these are closely related to Currie decision limits, if the coverage factor, k, is properly defined, and that all of the PDFs are scaled reciprocals of noncentral t variates. All of the detection limits have well-defined upper and lower limits, thereby resulting in finite moments and confidence limits, and the problem of estimating the noncentrality parameter has been addressed. As in Parts 1–3, extensive Monte Carlo simulations were performed and all the simulation results were found to be in excellent agreement with the derived theoretical expressions. Specific recommendations for harmonization of detection limit methodology have also been made.