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Laney p' charts in Python

The task: your p chart flags half the points as out of control, but the process is visibly fine. With large subgroups this is expected, not a process problem, and the Laney p' chart is the standard fix.

The problem: overdispersion

Classic p-chart limits shrink with 1/sqrt(n). With subgroups of tens of thousands (call-center days, e-commerce orders, high-volume lines), the limits collapse onto the center line, and the ordinary day-to-day drift of the true rate, which binomial theory does not model, makes nearly every point signal. The chart is not detecting special causes; it is measuring the failure of the binomial assumption.

The fix

Laney (Quality Engineering, 2002) standardizes the points, measures their short-term variation with a moving range (sigma_z), and widens the limits accordingly:

UCL_i = pbar + 3 * sigma_i * sigma_z

import shewhart as sw

r = sw.laney_p(df, defectives="rejects", size="inspected")
r.stats["sigma_z"]

Reading sigma_z:

  • around 1: no overdispersion; the classic sw.p_chart was fine, and the Laney chart reproduces it (sigma_z = 1 gives identical limits)
  • well above 1: overdispersion confirmed; the Laney limits are the honest ones

The test suite contains exactly this contrast: binomial data yields sigma_z near 1, while data with day-to-day rate variation yields a classic chart that signals everywhere and a Laney chart that correctly stays quiet.

Rate data

The same logic for defects per unit:

r = sw.laney_u(df, defects="flaws", size="units")

Both charts support the usual Phase I/II workflow (limits=), varying subgroup sizes with stair-step limits, and the four attribute-chart run rules.