Nelson and Western Electric rules in Python

The task: flag non-random patterns on a control chart, the way Nelson (Journal of Quality Technology, 1984) and the Western Electric handbook (1956) define them, and get the violations as data you can route, not just as red dots on a plot.

Usage

import shewhart as sw

r = sw.imr(df, value="torque", rules="nelson")           # rules 1-8
r = sw.imr(df, value="torque", rules="western_electric") # WE 1-4
r = sw.imr(df, value="torque", rules="none")             # limits only

for s in r.signals:
    print(s.rule, s.chart, s.points, s.note)

Signals are structured events. r.ok is False as soon as any rule fires, and r.to_dict()["signals"] is JSON, which makes routing to Slack, dashboards, or ticket systems a one-liner.

The rules

Alias	Pattern
nelson_1	1 point beyond 3 sigma
nelson_2	9 in a row on one side of the center line
nelson_3	6 in a row steadily increasing or decreasing
nelson_4	14 in a row alternating up and down
nelson_5	2 of 3 beyond 2 sigma, same side
nelson_6	4 of 5 beyond 1 sigma, same side
nelson_7	15 in a row within 1 sigma
nelson_8	8 in a row beyond 1 sigma, either side
we_1 to we_4	the Western Electric zone tests (1 beyond 3 sigma; 2 of 3 beyond 2; 4 of 5 beyond 1; 8 on one side)

Two details that hand-rolled implementations usually get wrong:

• Attribute charts use four tests, not eight. Zone tests assume symmetric normal zones around the center line; p/np/c/u data is not normal, so shewhart applies only the four pattern tests there and rejects zone rule sets with an explanatory error.
• EWMA gets no run rules at all. EWMA values are autocorrelated by construction, which invalidates run tests; the EWMA chart signals on limit violations only.

Semantics

Rules operate on the standardized distance from the center line using the within-process sigma, exactly as on the chart itself. Runs are reported as one signal covering the full run, not as eight separate flags, so downstream consumers can deduplicate trivially.