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Effective repetition count across independent calibration blocks accounts for dependence confined to each acquisition block rather than shared by every stored trace. Suppose block $j$ contains $n_j$ empty-interval indicator random variables, all with common probability $0<p<1$ and within-block correlation coefficient $\rho \ge 0$. Assume different blocks are independent. With $N={\sum }_j{n}_j$, summing within-block covariances givesMatching this to the variance of an average of independent indicators yieldsFor $K$ equal blocks of size $m$, this reduces to $N_{\mathrm{eff}}=Km/[1+(m-1)\rho ]$. The denominator involves the block size, not the total $Km$; the single-block expression in effective repetition count for detector intervals with shared drift must not be applied as though the same drift state affected every block.

For an original comparison, fix $N=120$ and $\rho =0.05$. One block gives $N_{\mathrm{eff}}=120/6.95\approx 17.27$. Six independent blocks of twenty give $N_{\mathrm{eff}}=120/1.95\approx 61.54$. Six very uneven blocks of sizes $(100,4,4,4,4,4)$ instead giveAll three designs store the same number of traces. The difference comes from how often the same fluctuating condition is reused. For fixed $N$, $K$, and positive $\rho$, minimizing ${\sum }_j{n}_j^2$ favors balanced blocks; this motivates optimal allocation of detector repetitions across calibration blocks when block-preparation costs also matter.

Independence must come from the physical acquisition model. Starting another file does not erase a shared clock, reference calibration, or slowly varying environmental influence. NIST's uncertainty law retains shared-input covariance explicitly.^[ref] If drift persists between nominal blocks, those cross-block terms must be added and the displayed formula changes. A cluster bootstrap likewise requires blocks that are suitable independent resampling units.

The effective repetition count for detector intervals with shared drift is the number of independent repetitions that would give the same variance for an average indicator as the actual dependent repetitions. In overdispersion of detector-interval counts under shared drift, let $X_i$ indicate an empty interval, with common probability $\overline{p}$ satisfying $0<\overline{p}<1$. If the covariance between distinct indicators is $v=\mathrm{Var}(p(H))$, their correlation coefficient isThe parent's law of total variance calculation therefore givesThis is an observable-specific variance equivalence, not a literal count of independent traces or a guarantee of confidence interval coverage. A different statistic or a different dependence pattern may require a different equivalence.

For an original feasible mixture, take $\overline{p}=0.1$ and $\rho =0.1$. These moments can arise when the block probability is $0$ with probability $9/19$ and $0.19$ with probability $10/19$: its variance is $0.009$. With $N=50$, the variance-inflation multiplier is $5.9$ andDoubling the repetitions to $100$ only raises $N_{\mathrm{eff}}$ to about $9.17$. For a fixed positive $\rho$, its large-$N$ limit is $1/\rho$, here $10$.

The experiment must therefore record which traces share a reference or drift state. Acquiring genuinely independent calibration blocks addresses a different limitation from oversampling one block; effective repetition count across independent calibration blocks depends on that grouping. A cluster bootstrap can preserve the observed within-block dependence when blocks are suitable independent resampling units. NIST's uncertainty law explicitly retains shared-input covariance, supporting the need to model reference reuse rather than discard it.^[ref]

Overdispersion of detector-interval counts under shared drift is excess count variability caused by a common experimental condition changing the chance of an interval outcome. Let $M$ count empty physical detector-width intervals among $N$ readings. Conditional on a block's calibration state $H$, suppose the readings are independent with empty probability $p(H)$, so $M\mid H\sim \mathrm{Binomial}(N,p(H))$.

Writing $\overline{p}=\mathbb{E}[p(H)]$, the law of total variance givesThe first term is the binomial variance using the mean probability. The second comes from sharing one fluctuating condition across the block. Individual indicators have covariance $\mathrm{Var}(p(H))$ across different readings, even though they are independent after conditioning on $H$.

For an original mixture example, suppose equally likely block conditions have empty probabilities $0.01$ and $0.09$. Then $\overline{p}=0.05$ and $\mathrm{Var}(p(H))=0.0016$. With $N=100$, the expected count is five, but its variance is $4.75+15.84=20.59$, with standard deviation about $4.54$. An independent binomial model with probability $0.05$ would give standard deviation only about $2.18$.

The effective repetition count for detector intervals with shared drift can consequently be much smaller than the number of stored traces. Repeating measurements within one unchanged calibration block does not supply the same information about drift as acquiring independent blocks. Record acquisition grouping and reference reuse before pooling interval categories.

The negative covariance of empty and positive detector-interval counts applies to a fixed-probability multinomial model. Shared drift adds cross-repetition dependence and can change that count covariance as well as each count's variance. In the example, the two probability states are stipulated; a physical model would relate them to the receiver's drift, variance-difference estimator and uncertainty calibration.

NIST retains shared influences in uncertainty propagation and explains that confidence interpretations depend on the assumed distributions.^[ref] Observed overdispersion can motivate checking the block model, but does not by itself identify which physical influence caused it.