Minimum detectable concentration in radiological scanning surveys, when the detector produces a continuous stream rather than discrete independent counts.
Scan MDC is the smallest residual radioactivity concentration a moving detector can reliably distinguish from background, at stated false-positive and false-negative probabilities. The classical derivation assumes independent counts in discrete intervals. Continuously collected data violates that assumption: the stream is serially correlated, so the effective number of independent observations is smaller than the raw count implies, and treating it as independent understates the false-positive rate.
The remedy is to derive critical levels on a differenced or smoothed version of the stream — generalized midpoint, moving-average, or exponentially weighted moving-average lag-k differencing — and to assess the bias and precision of the resulting limits by bootstrap rather than by normal approximation.
Static MDC has a clean structure. A background count is accumulated over a fixed interval, a critical level is set from the Poisson or normal-approximated background distribution, and the detection limit follows from the power requirement at a specified true concentration. Every observation is independent, and the interval is known in advance.
A scanning survey breaks each of those conditions. The detector is moving, so the time any point on the surface spends within the field of view is short and depends on scan speed. The surveyor's response is part of the measurement chain, which is why MARSSIM introduces a surveyor efficiency term. And with continuously collected data, adjacent observations overlap in the physical volume they interrogate, so they are correlated by construction.
The consequence matters practically. If a survey design assumes n independent observations when the effective number is materially smaller, the nominal false-positive rate is not the actual one — and a scanning survey that flags too often is abandoned by the people running it.
Background in a real survey is not constant. It drifts with geology, moisture, cosmic contribution and detector temperature. A critical level derived against a fixed background will chase that drift.
Lag-k differencing addresses this directly: each observation is compared against one k steps earlier, so any drift common to both cancels, while a localized elevation — which is what residual radioactivity produces — survives the difference. Three schemes behave differently:
Generalized midpoint differencing compares an observation against the midpoint of a surrounding window. It is symmetric, which reduces phase lag in locating the anomaly, but it uses information from both sides of the point and so is unavailable at the ends of a scan line.
Moving-average differencing smooths before differencing, trading resolution for variance reduction. The averaging window sets the trade: wider windows lower the noise floor and therefore the achievable MDC, but blur a small hot spot toward background.
Exponentially weighted moving-average (EWMA) differencing weights recent observations more heavily with geometrically decaying memory. It responds faster to a step change than a flat moving average of comparable variance, which suits the scanning case, where the signal genuinely is a step as the detector passes over an area.
The choice of scheme and of k is not cosmetic. It determines how much background variability is removed, how much signal is retained, and therefore what MDC is achievable at a given scan speed.
These are routinely conflated, and the conflation hides half the decision-error structure.
The critical level is the threshold applied to an observed measurement to decide whether activity is present. It is a property of the decision rule and controls the false-positive rate — how often clean ground is flagged.
The detection limit is the true concentration that would be detected with a specified probability, conventionally 95 percent. It is a property of the measurement system's capability and controls the false-negative rate — how often real contamination is missed.
Reporting a single number as "the MDC" without saying which quantity it is, and at what error rates, describes an incomplete decision. Under differencing the distinction sharpens further, because the critical level applies to the differenced statistic while the concentration of interest lives on the original scale.
Once the stream is differenced or smoothed, the sampling distribution of the derived critical level has no convenient closed form. Serial correlation, the smoothing weights and the differencing lag all enter, and normal approximations understate the variability of the result.
Bootstrap resampling of the differenced stream gives a direct estimate of both the bias and the precision of the critical level and of the MDC that follows from it. That is what converts a derived limit into a defensible one: a regulator can be shown not only the number but how stable it is under resampling of the data that produced it.
MRP Group authored the statistical methodology content for the Section 9 revision of NUREG-1507, the U.S. Nuclear Regulatory Commission report covering minimum detectable concentrations with typical radiation survey instrumentation, as a subcontractor to SC&A, Inc. The work covered derivation of critical levels and detection limits under the differencing schemes above, a simulation study extending prior PNNL work, bootstrap bias and precision assessment, and a gamma walkover field application. It was conducted in multi-author tracked-change review alongside NRC and contractor reviewers, with coordination toward integration into the Visual Sample Plan (VSP) software.
Related presentation: Bland JS, Parody RJ. "A priori minimum detectable concentration (MDC) for continuously collected data (CCD)," 25 September 2025.
The smallest residual radioactivity concentration a moving detector can reliably distinguish from background, at specified false-positive and false-negative probabilities. It differs from static MDC because the detector is in motion, the observation window over any point is brief and speed-dependent, and the surveyor's decision process forms part of the measurement system.
Adjacent observations interrogate overlapping physical volumes and are correlated by construction. The effective number of independent observations is smaller than the raw count, so an independence assumption understates the false-positive rate — the survey flags clean ground more often than the design predicts.
The lag sets how much background drift is removed against how much localized signal survives. Too small and drift passes through; too large and a small anomaly is differenced away along with the drift. The right choice depends on scan speed, detector response time and the spatial scale of the contamination you need to detect — which is why it belongs in the survey design, not in post-processing.
The critical level is the threshold applied to an observed measurement to decide whether activity is present; it controls the false-positive rate. The detection limit is the true concentration that would be detected with a specified probability, typically 95 percent; it controls the false-negative rate. The critical level is a property of the decision rule, the detection limit a property of the measurement system's capability. Reporting one without the other describes only half the decision-error structure.
Under serial correlation and smoothing, the sampling distribution of the derived critical level has no convenient closed form, and normal approximations understate its variability. Bootstrap resampling of the differenced stream gives a direct estimate of the bias and precision of the critical level and of the resulting MDC, which is what allows the derived limits to be defended rather than merely asserted.
The structure does. Any continuously monitored process where a localized excursion must be distinguished from drifting background raises the same problem — the correlation structure of the stream determines the achievable detection limit, and the smoothing scheme is a design choice with consequences for both error rates. Statistical process control faces the identical trade-off in choosing between Shewhart, CUSUM and EWMA charts.
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