Classify and Mark

# Classify and Mark: Subdividing the Region Final Test Only Accepted or Rejected

Final test drew a single boundary around the acceptance region — everything inside passes, everything outside is scrapped. This step does something final test never attempted: it subdivides the inside of that region into graded tiers, because devices that all pass the same specification still don't land at the same point within it. A batch of devices that all cleared step thirty-six's combined gain, breakdown, and leakage thresholds will still show real, continuous variation in exactly where each one landed inside the acceptance region — some closer to the high-gain edge, some comfortably mid-range, some near the margin. Classification converts that continuous spread into discrete grade codes a customer can actually select against, rather than treating every passing device as electrically identical.

## 1. Grading Partitions the Same Acceptance Region Into Priced Tiers

$$\text{Grade A: } \alpha \ge \alpha_A; \quad \text{Grade B: } \alpha_{\min} \le \alpha < \alpha_A; \quad \ldots$$

Each grade boundary is itself just another threshold drawn inside the larger region step thirty-six already established as acceptable — the device still has to be inside the full acceptance region to be graded at all, but grading adds finer internal structure on top of that outer boundary. This matters economically as well as technically: a device landing well above the minimum gain requirement can serve applications a marginal-but-passing device can't, and treating both identically would either underprice the better device or misrepresent the marginal one, rather than letting the market find a price for each tier the natural distribution of outcomes actually produced.

## 2. Real Diagram: The Same Acceptance Region, Now Subdivided

Grading Adds Internal Structure Final Test Didn't Need step thirty-six only drew the outer boundary — this step draws the lines inside it breakdown voltage → current gain, α Grade A threshold, α_A Grade A Grade B all three devices passed final test — only this step distinguishes between them

## 3. Marking Has to Be as Reliable as the Measurement It Records

$$\text{grade code on device} = \text{grade}(\alpha_{\text{measured}}) \;\text{permanently}$$

Once marked, a device's grade code travels with it indefinitely — there is no later step in this process, or realistically in the device's service life, where the grading decision gets revisited. This gives the marking operation itself a quiet but real importance: an error here doesn't just mis-grade a device, it permanently attaches an incorrect claim to a part that already passed every electrical test correctly, which is why the marking step is treated as a distinct, auditable operation rather than folded silently into the test step that produced the underlying measurement.

Gain Distribution of the Passing Population, Graded the same accepted bars, sorted into priced tiers rather than treated as one group measured α → number of devices Grade B Grade A α_A threshold every device shown already passed step thirty-six

## Classify and Mark's Place in the Process Lineage

Classifying and marking is step thirty-seven of the 1951 grown-junction transistor's full manufacturing sequence — immediately after final electrical tests have confirmed the device sits inside the overall acceptance region, and before conforming units are released. It is the step that subdivides that single accept/reject boundary into graded tiers based on where each surviving device actually landed within it, and permanently records that distinction on the device itself.

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