Mesa Production 1958 Statistical Process Control Chart

# Establish In-Line Statistical Process Control: Watching the Process, Not Just the Part

## 1. Why Waiting for a Bad Device Is Too Slow to Catch a Drifting Process

This step installs regular, charted measurements — junction depth, sheet resistance, oxide thickness — at fixed points along the production line, and plots each measurement against control limits derived from the process's own historical variation, rather than against the device specification alone. A device specification only tells an operator whether a finished part passed or failed; it says nothing about whether the *process* that made it is still behaving the way it did last week. By the time enough finished devices fail to make a drift visible in yield, the furnace or the etch bath may have been drifting for days, and every wafer made during that drift is already built. The statistical tool this step borrows is the control chart, built on a simple but powerful idea: a process in control produces measurements that vary randomly around a stable mean, within predictable bounds —

$$UCL,\, LCL = \bar{x} \pm 3\,\frac{\sigma}{\sqrt{n}}$$

where $\bar{x}$ is the long-run process mean, $\sigma$ its standard deviation, and $n$ the sample size per check. A measurement that falls outside these bounds is not, by itself, proof of a bad device — it is evidence that something about the *process* has shifted, and it is evidence available days or weeks before that shift would otherwise show up as a yield problem at Step 16's wafer probe.

A Process Can Drift Long Before a Device Fails a control chart catches the drift; the device specification only catches the failure CONTROL CHART, JUNCTION DEPTH OVER TIME production time → UCL x̄ LCL out of control, here yield drop appears here, days later UCL, LCL = x̄ ± 3σ/√n — three measurements outside these bounds precede the yield drop they explain the chart is a warning; the finished-device failure is the same event, arriving too late to prevent

## 2. Real Diagram: A Measurement Station at Every Checkpoint This Series Has Already Built

The control points this step establishes are not new measurement techniques — they reuse the oxide-thickness check from Step 2 of the 1957 series, the resist-pattern inspection from Step 9, and the critical-dimension audit from Step 12. What is new is charting each of them continuously against the process's own history, rather than treating each measurement as a one-off pass or fail.

Existing Checkpoints, Now Charted Instead of Just Checked the same measurement stations this project already documented, reused as a continuous record OXIDE THICKNESS from 1957 step 2 RESIST PATTERN from 1957 step 9 CRITICAL DIMENSION from 1957 step 12 CHART one continuous time series per station, not isolated pass/fail events nothing about the measurement changes; what the measurement is compared against does

## 3. Why Neither Earlier Series Treated a Measurement as a Time Series

Every inspection step this project has documented before this one — Step 2's oxide check, Step 9's resist inspection, Step 12's critical-dimension audit, all from 1957 — asked the same question each time it was performed: does this one measurement, on this one wafer, meet specification right now. None of them asked whether the measurement itself, considered across many wafers over time, was behaving consistently with its own history. That second question only becomes meaningful once a line produces enough wafers, frequently enough, for a history to exist — which 1956 and 1957's single-wafer-at-a-time narration never quite had. This step does not add a new inspection; it adds the discipline of remembering every past inspection and asking whether today's measurement still belongs to the same distribution they came from.

Step 4 does not catch a single bad device; it catches the process drifting toward making bad devices, often before the first one has actually been made.

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