= Optimal allocation of detector repetitions across calibration blocks
<Optimal allocation of detector repetitions across calibration blocks> chooses block sizes using the dependence and acquisition-cost model, not just the desired number of stored traces. For fixed total $N$, number of independent blocks $K$, common success probability, and positive within-block correlation $\rho$, <effective repetition count across independent calibration blocks> gives
$$
N_{\rm eff}=\frac{N^2}{N+\rho(\sum_j n_j^2-N)}.
$$
Maximizing it is equivalent to minimizing $\sum_j n_j^2$. If two integer block sizes differ by at least two, transferring one repetition from the larger to the smaller decreases that sum by $2(n_i-n_j-1)>0$. Therefore the optimal integer sizes differ by at most one.
For an original fixed-count example, $N=23$ and $K=5$ give balanced sizes $(5,5,5,4,4)$. At $\rho=0.1$, their effective count is $529/31.4\approx16.85$. Sizes $(11,3,3,3,3)$ give only $529/36.4\approx14.53$ under the same assumptions.
More independent blocks can help, but preparing one may consume time. In a continuous planning model let each block cost setup time $h>0$, each repetition cost $\tau>0$, and each block contain $n$ repetitions. With total time $T$, the effective count becomes
$$
N_{\rm eff}=\frac{Tn}{(h+\tau n)(1-\rho+\rho n)}.
$$
For $0<\rho<1$, differentiation gives the interior choice $n_* =\sqrt{h(1-\rho)/(\tau\rho)}$. Integer block counts, minimum sizes, and hardware restrictions must subsequently be imposed.
For chosen $h=9\,\mathrm s$, $\tau=1\,\mathrm s$, $\rho=0.1$ and $T=180\,\mathrm s$, the continuous optimum $n_*=9$ is feasible with ten blocks and gives $N_{\rm eff}=50$. Single-repetition blocks give 18, while two blocks of 81 repetitions also give 18. These are model-based comparisons, not measured apparatus timings.
Unequal block noise or different drift correlations require <unequal-noise allocation across calibration blocks>. Independence between prepared blocks must also be justified by the reference and environmental model; NIST explicitly retains shared-input <covariance>.<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}
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