= Repeatability floor from surface-area model discrepancy
A \b[repeatability floor from surface-area model discrepancy] is the remaining uncertainty when repeated measurements reduce input noise but reuse the same imperfect anatomical predictor. Repeating height and <mass> measurements does not independently redraw the relationship between those quantities and one person's actual <body surface area>.
An original local model writes prediction $X_i=S+D+\epsilon_i$, where $S$ is the true area, $D$ a shared model discrepancy and $\epsilon_i$ independent repeat noise. Represent uncertainty about $D$ by variance $\tau^2$ and repeat noise by variance $\sigma^2$, assuming independence between them. For the mean of $n$ repeats,
$$
\operatorname{Var}(\overline X)=\tau^2+\frac{\sigma^2}{n},\qquad
\operatorname{cov}(X_i,X_j)=\tau^2\quad(i\ne j).
$$
The correlation is a consequence of reusing the same discrepancy. The GUM requires significant common-input correlations to be included and permits additional model quantities for incomplete knowledge.<Guide to the expression of uncertainty in measurement by JCGM>[§§4.1.2 and 5.2.4]{ref}
For stipulated $\sigma=0.04\,\mathrm{m^2}$ and $\tau=0.08\,\mathrm{m^2}$, the mean's <standard uncertainty> is about $0.0894\,\mathrm{m^2}$ after one reading, $0.0825\,\mathrm{m^2}$ after four and $0.0801\,\mathrm{m^2}$ after one hundred. The lower limit is $0.08\,\mathrm{m^2}$ in this model, not zero. These values illustrate the distinction rather than report a measured error distribution for the <Mosteller formula>.
<Repeat-count targets under shared model error> make a useful planning calculation. Requiring the repeat-noise variance to be at most a fraction $\eta$ of the shared variance gives $n\ge\sigma^2/(\eta\tau^2)$. With the chosen values and $\eta=0.01$, 25 repeats suffice; further repetition changes the total uncertainty little while leaving the dominant model term intact.
The shared term need not fluctuate between actual readings. For a fixed person, an unknown prediction bias can remain fixed while repeatability looks excellent. Its distribution represents uncertainty or variation across the validation population, not a physical mechanism that changes body shape on each measurement.
A useful validation therefore combines repeat measurements with independent reference-area evidence across an appropriate range of individuals. Distinguish within-person repeatability, shared calibration effects and model residuals. If a systematic bias is established, correcting it is a separate step from describing residual uncertainty.
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