X-bar and R control chart from a CSV (Python + matplotlib)

"""Plot an X-bar and R control chart from a CSV of subgroup measurements.

Each row is one subgroup; each column is one sample within it.
No header row. Example (n=5 samples per subgroup):
    20.02,19.98,20.01,20.00,19.99
    20.05,20.01,19.99,20.03,20.02
    ...

Usage:  python xbar_r_chart.py measurements.csv --out chart.png
"""

import argparse
import csv

import matplotlib.pyplot as plt

# Standard SPC constants for X-bar/R charts, subgroup size 2-10
# (A2 for X-bar limits, D3/D4 for R limits)
CONSTANTS = {
    2: (1.880, 0, 3.267),
    3: (1.023, 0, 2.575),
    4: (0.729, 0, 2.282),
    5: (0.577, 0, 2.114),
    6: (0.483, 0, 2.004),
    7: (0.419, 0.076, 1.924),
    8: (0.373, 0.136, 1.864),
    9: (0.337, 0.184, 1.816),
    10: (0.308, 0.223, 1.777),
}


def read_subgroups(path):
    with open(path, newline="") as fh:
        return [[float(v) for v in row if v.strip()] for row in csv.reader(fh) if row]


def main():
    ap = argparse.ArgumentParser(description=__doc__)
    ap.add_argument("csv_file", help="CSV of subgroup measurements, no header")
    ap.add_argument("--out", default="xbar_r_chart.png")
    args = ap.parse_args()

    subgroups = read_subgroups(args.csv_file)
    n = len(subgroups[0])
    if n not in CONSTANTS:
        raise SystemExit(f"No published A2/D3/D4 constants for subgroup size {n} "
                          f"(supported: {sorted(CONSTANTS)})")
    if any(len(g) != n for g in subgroups):
        raise SystemExit("Every subgroup must have the same number of samples")

    a2, d3, d4 = CONSTANTS[n]

    means = [sum(g) / n for g in subgroups]
    ranges = [max(g) - min(g) for g in subgroups]

    x_bar_bar = sum(means) / len(means)   # grand mean - the chart's centerline
    r_bar = sum(ranges) / len(ranges)     # average range - the R chart's centerline

    ucl_x = x_bar_bar + a2 * r_bar
    lcl_x = x_bar_bar - a2 * r_bar
    ucl_r = d4 * r_bar
    lcl_r = d3 * r_bar

    out_of_control = [i + 1 for i, m in enumerate(means) if m > ucl_x or m < lcl_x]

    fig, (ax1, ax2) = plt.subplots(2, 1, figsize=(9, 7), sharex=True)

    ax1.plot(range(1, len(means) + 1), means, "o-", color="#1d4ed8")
    ax1.axhline(x_bar_bar, color="black", linewidth=1)
    ax1.axhline(ucl_x, color="#dc2626", linestyle="--", linewidth=1)
    ax1.axhline(lcl_x, color="#dc2626", linestyle="--", linewidth=1)
    ax1.set_title(f"X-bar chart (n={n}, centerline={x_bar_bar:.4f})")
    ax1.set_ylabel("Subgroup mean")

    ax2.plot(range(1, len(ranges) + 1), ranges, "o-", color="#0891b2")
    ax2.axhline(r_bar, color="black", linewidth=1)
    ax2.axhline(ucl_r, color="#dc2626", linestyle="--", linewidth=1)
    if lcl_r > 0:
        ax2.axhline(lcl_r, color="#dc2626", linestyle="--", linewidth=1)
    ax2.set_title(f"R chart (centerline={r_bar:.4f})")
    ax2.set_xlabel("Subgroup")
    ax2.set_ylabel("Range")

    fig.tight_layout()
    fig.savefig(args.out, dpi=150)

    print(f"X-bar-bar={x_bar_bar:.4f}  UCL={ucl_x:.4f}  LCL={lcl_x:.4f}")
    print(f"R-bar={r_bar:.4f}  UCL_R={ucl_r:.4f}  LCL_R={lcl_r:.4f}")
    if out_of_control:
        print(f"Out-of-control subgroups: {out_of_control}")
    else:
        print("No subgroups outside the X-bar control limits.")
    print(f"Chart saved to {args.out}")


if __name__ == "__main__":
    main()