Handling Multiple Method Detection Limit Estimates: Which Statistical Estimate Should Be Reported?

Method detection limits (MDLs) are used as figures of merit for trace and ultratrace measurement systems. They are typically used in the context of environmental regulation and product quality regulation in which, to be judged capable, a measurement system must provide an MDL that is at or below the regulatory limit or the product specification. Sometimes MDL requirements are stricter than this illustration. The focus of this paper is to develop an understanding of how the usage context of the reported MDL drives the selection of which statistical estimator to use when multiple MDL estimates are available. Selection of a specific MDL or DL estimation methodology is highly controversial and such controversy is driven by both data and measurement science and the financial and regulatory implications of higher or lower reported MDLs. MDLs used to be measured infrequently, often only once. Current automated systems allow a much broader understanding of the statistical behavior of MDLs over time to be developed by providing multiple estimates of MDLs. What should and can be done with such data? In practice, a mean or median MDL is commonly reported from the multiple MDL estimates. When is this appropriate? The issue of which MDL summary statistic to report, and why, will be developed both from the likely usage context of the MDL estimates and the real-world behavior of MDLs. In some common reporting contexts, use of an estimate of an upper-tail percentile from the MDL distribution is a more reasonable reporting MDL measure than use of an average or median.