Lilienfeld 1926 Reproducibility Across Specimens
# Establish Reproducibility Across Specimens: Shared Glass Sheets Correlate Fracture Quality the 1925 Geometry Never Had to Adjust For
A single device's full characterization (Steps 1 through 10) proves nothing about the construction method in general — it proves one specimen worked, or didn't. Step 11 repeats the entire construction and test sequence across a pre-fixed population of specimens, exactly as the 1925 series required at its own Step 24. But this construction has an independence hazard the 1925 flat-electrode geometry never faced: specimens cut and fractured from the same glass sheet share whatever internal stress pattern that sheet carries, so their fracture quality — and by extension, their Step 3 bond quality — is correlated in a way the 1925 specimens' flat, individually-prepared faces never were.
The correlation hazard begins at Step 2, not Step 1. Glass sheet selection (Step 1) sets material properties that are largely uniform across a sheet by specification. But the transverse fracture (Step 2) interacts with whatever residual internal stress exists in that specific sheet — stress introduced during the sheet's own manufacture, annealing, or storage. Two specimens fractured from the same sheet are more likely to show similar fracture-edge quality (flat vs. irregular, chip-free vs. chipped) than two specimens from different sheets, simply because they share the stress field the fracture propagated through.
This is structurally the same independence problem the 1925 series solved for foil lot and furnace run, applied to a new shared resource. The 1925 protocol required an independence-adjustment correction for specimens sharing a foil lot or sulfurization furnace run, because those shared resources could introduce correlated defects. This construction's equivalent shared resource is the glass sheet: specimens sharing a sheet are not statistically independent draws, and the population's effective sample size must be adjusted downward to reflect that, exactly as the 1925 correction did for its own shared-resource risks.
Population size is fixed before any specimen reaches Step 7, exactly as the 1925 rule required. No adaptive adjustment is permitted after specimens begin the baseline test — the number of specimens to attempt, and the number of glass sheets they will be drawn from, must be decided and recorded before Step 7 testing begins on the first specimen. This prevents a researcher from quietly adding specimens if early results look weak, or stopping early once a favorable pass rate appears.
| Step | Process operation | Input | Output | Specification | Constraint |
|---|---|---|---|---|---|
| 11.1 | Fix population size N and number of distinct glass sheets before first specimen reaches Step 7 | Construction plan | Locked population parameters | N and sheet count recorded in a pre-registered document, timestamped before Step 7 begins on specimen 1 | Adjusting N after seeing early results defeats the purpose of pre-registration |
| 11.2 | Assign specimens to glass sheets, recording which specimens share a sheet | Locked parameters from 11.1 | Specimen-to-sheet assignment table | Each specimen's sheet ID recorded alongside its specimen ID from Step 1 onward | Without this record, the independence correction in 11.6 cannot be computed |
| 11.3 | Carry each specimen through Steps 1-6 (construction) independently | Assignment table from 11.2 | Constructed specimen population | Each specimen's fracture quality (Step 2.5) and seal verification (Step 6.7) recorded individually | Skipping individual QC recording loses the data needed to detect sheet-level correlation later |
| 11.4 | Carry each specimen through Steps 7-10 (characterization) independently | Constructed population from 11.3 | Fully characterized specimen population | Same measurement discipline (four-wire, settling waits, pre-registered thresholds) applied uniformly | Inconsistent test procedure across specimens introduces a confound separate from genuine population variation |
| 11.5 | Tabulate pass/fail disposition per specimen against the Step 9 modulation criterion | Characterized population from 11.4 | Raw disposition table | Each specimen's pass/fail recorded with its sheet ID | This table is the direct input to both the naive and corrected pass-rate calculations |
| 11.6 | Compute independence-adjusted effective sample size based on sheet sharing | Disposition table from 11.5, assignment table from 11.2 | Effective N | Effective N ≤ nominal N, reduced according to the degree of sheet sharing observed | Using nominal N when specimens share sheets overstates the statistical power of the result |
| 11.7 | Compute pass-rate confidence interval using effective N | Effective N from 11.6, disposition table from 11.5 | Population pass-rate with interval | Wilson or Clopper-Pearson interval, consistent with 1925 Step 24 methodology | A naive interval computed on nominal N is narrower than justified and overstates confidence |
| 11.8 | Compare observed pass rate against the chance-rate reference derived from Step 8's blank/leakage-only data | Pass-rate interval from 11.7 | Final reproducibility verdict | Reference derived from this construction's own blank data, not an arbitrary external benchmark | Using a benchmark from a different construction (e.g., the 1925 specimens) does not account for this construction's own leakage and noise floor |
Step 11 is where "this device worked once" becomes "this construction method works, within a stated confidence interval, for a population that accounts for its own correlation structure." The sheet-level independence adjustment is not a generic statistical nicety borrowed from the 1925 protocol — it is a correction specifically required by this construction's reliance on transverse fracture (Step 2), a step the 1925 flat-electrode geometry never needed and therefore never had to statistically account for.