Process Analytical Technology: SPC Control Chart & Feedback Correction (2D)

Setpoint & Disturbance

Target moisture setpoint 12.0%

Disturbance magnitude 1.0

Process & Control Chart

Process noise (σ_proc) 0.25

Control-limit width (L·σ) 3.0σ

Feedback gain (K_p) 0.40

Live Readout

Measured x

0.00%

True mean μ

0.00%

σ̂ (MR/1.128)

0.00

Status

In control

Out-of-control pts

Correction applied

0.000

How it works

A simulated in-line probe samples a quality attribute (moisture content, %) at a fixed interval. Each sample is plotted on an individuals (X) control chart. Sigma is estimated from the average moving range of consecutive points, the standard I-MR method:

MR_i = |x_i − x_(i−1)|
σ̂ = MR̄ / 1.128        (d2 constant, n=2)
UCL = μ0 + L·σ̂
LCL = μ0 − L·σ̂

Two real out-of-control rules run every sample:

Rule 1 (Western Electric / Nelson 1) — a single point beyond the L·σ control limits.
Rule 2 (Nelson 2) — 2 of the last 3 points beyond 2σ on the same side of center.

When either rule fires and closed-loop mode is active, a proportional controller nudges the process mean back toward the target each sample: μ += K_p·(target − μ), exactly the automated feed/temperature correction a real PAT loop performs, until the process is back inside the 1σ zone.

Sample (x) Centerline / target Out-of-control point