= Effective repetition count across independent calibration blocks
<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> $\rho\ge0$. Assume different blocks are independent. With $N=\sum_jn_j$, summing within-block <covariances> gives
$$
\operatorname{Var}(\overline X)
=\frac{p(1-p)}{N^2}\sum_jn_j\{1+(n_j-1)\rho\}.
$$
Matching this to the <variance> of an average of independent indicators yields
$$
N_{\rm eff}=\frac{N^2}{N+\rho(\sum_jn_j^2-N)}.
$$
For $K$ equal blocks of size $m$, this reduces to $N_{\rm eff}=Km/[1+(m-1)\rho]$. 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 $N_{\rm eff}=120/6.95\approx17.27$. Six independent blocks of twenty give $N_{\rm eff}=120/1.95\approx61.54$. Six very uneven blocks of sizes $(100,4,4,4,4,4)$ instead give
$$
N_{\rm eff}=\frac{14400}{120+0.05(10080-120)}\approx23.30.
$$
All 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 $\sum_jn_j^2$ 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.<Guidelines for Evaluating and Expressing the Uncertainty of NIST Measurement Results by Barry N. Taylor and Chris E. Kuyatt>[Appendix A, equation A-3]{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.
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