Manufacturing & Quality

Is either filling line drifting outside its normal range?

Whether a line is drifting is the daily quality question. This runs on the library's sample fill volumes for two lines.

The data. standard_control_charts_v2.csv, the published sample file for Control chart and process capability: 110 rows; columns batch_id, produced_at, fill_volume_ml, line. Sample data, not a customer's.

The calculation. Python, standard library only. This exact code ran against the file when this page was built, and printed the output below it.

import csv
rows = list(csv.DictReader(open("standard_control_charts_v2.csv")))
rows.sort(key=lambda r: r["produced_at"])
for line in sorted({r["line"] for r in rows}):
    x = [float(r["fill_volume_ml"]) for r in rows
         if r["line"] == line and r["fill_volume_ml"]]
    mr = [abs(b - a) for a, b in zip(x, x[1:])]  # moving ranges
    centre = sum(x) / len(x)
    sigma = sum(mr) / len(mr) / 1.128  # d2 constant for n = 2
    lo, hi = centre - 3 * sigma, centre + 3 * sigma
    out = [round(v, 2) for v in x if v < lo or v > hi]
    print(line, len(x), "batches, centre", round(centre, 2),
          "limits", round(lo, 2), "to", round(hi, 2), "outside:", out)

Line A 55 batches, centre 250.38 limits 245.71 to 255.04 outside: [245.56, 255.53]
Line B 55 batches, centre 250.51 limits 244.81 to 256.22 outside: []

What it says. Each line gets its own centre and limits three standard deviations either side, with the standard deviation estimated from the average jump between consecutive batches so that a slow drift does not widen its own limits. Points outside the limits are the batches worth investigating; the printout lists them by volume.

What it does not say. A point outside the limits is a signal to look, not proof of a fault, and a process can drift inside its limits. The library analysis adds run rules for those patterns and a capability index against the specification.

Run Control chart and process capability on this file or your own, or open its stored sample report.