XmR Chart in Python

An XmR chart pairs an individuals chart (X — each measurement plotted in time order) with a moving-range chart (mR — the gap between consecutive measurements). It is the right chart whenever you have one measurement per period: weekly KPIs, daily yields, per-batch readings.

The 60-second version¶

import numpy as np
import pandas as pd
from processbehavior import ProcessBehavior

rng = np.random.default_rng(3)
df = pd.DataFrame({
    'on_time_pct': np.clip(rng.normal(92, 2.5, 24), 80, 100).round(1),
})

# No time column: the values are charted in the order received
study = ProcessBehavior(df).formulate(response='on_time_pct')
result = study.execute(chart='X', companion=True)

print(result.get_statistics('X'))
print(result.get_statistics('mR'))
result.plot()   # interactive plotly figure: X on top, mR below

Output:

{'N': 1, 'center': 91.883, 'lpl': 83.211, 'upl': 100.556}
{'N': 2, 'center': 3.261, 'lpl': 0.0, 'upl': 10.654}

With no time column the rows are numbered 1..N in an Observation column, in the order received. If your data carries its own order (a week column, a timestamp), name it and the points are charted in that order instead:

study = ProcessBehavior(df).formulate(response='on_time_pct', time='week')

Reading it¶

• center on the X chart is the process’s typical level; lpl/upl are the natural process limits, computed from the moving ranges (not from the overall standard deviation — that classic shortcut inflates the limits).

• The mR chart watches variation: a spike there with a level shift on X says “the level moved once”; a widening mR says the process got noisier.

• companion=True is what makes it an XmR chart — execute(chart='X') alone returns just the individuals chart.

Going further¶

• Signals beyond eyeballing: result.detect_signals(chart='X') applies the full set of Western Electric run and zone rules (all eight apply to X and mR charts).

• Guided version with a planted shift: Your First X/mR Chart.

• Multiple streams (one XmR per machine/lane): Stratified Analysis.