Python Script Generator for X-bar R Charts and Cpk

import csv
import statistics

CSV_PATH = "bore_diameter.csv"
COLUMN = "diameter_mm"
N = 5
USL = 25.05
LSL = 24.95
LABEL = "Bore diameter (mm)"

# Shewhart constants by subgroup size
A2 = {2: 1.880, 3: 1.023, 4: 0.729, 5: 0.577, 6: 0.483, 7: 0.419, 8: 0.373, 9: 0.337, 10: 0.308}
D3 = {2: 0.0, 3: 0.0, 4: 0.0, 5: 0.0, 6: 0.0, 7: 0.076, 8: 0.136, 9: 0.184, 10: 0.223}
D4 = {2: 3.267, 3: 2.574, 4: 2.282, 5: 2.114, 6: 2.004, 7: 1.924, 8: 1.864, 9: 1.816, 10: 1.777}
D2 = {2: 1.128, 3: 1.693, 4: 2.059, 5: 2.326, 6: 2.534, 7: 2.704, 8: 2.847, 9: 2.970, 10: 3.078}

values = []
with open(CSV_PATH, newline="") as f:
    for row in csv.DictReader(f):
        if row[COLUMN].strip() != "":
            values.append(float(row[COLUMN]))

groups = [values[i:i + N] for i in range(0, len(values) - N + 1, N)]
if len(groups) < 20:
    print("Warning: only", len(groups), "subgroups; use 20 to 25 or more for stable limits")

xbars = [sum(g) / N for g in groups]
ranges = [max(g) - min(g) for g in groups]
xbarbar = sum(xbars) / len(xbars)
rbar = sum(ranges) / len(ranges)

ucl_x = xbarbar + A2[N] * rbar
lcl_x = xbarbar - A2[N] * rbar
ucl_r = D4[N] * rbar
lcl_r = D3[N] * rbar

sigma_within = rbar / D2[N]
mean_all = statistics.mean(values)
sigma_overall = statistics.stdev(values)

cp = (USL - LSL) / (6 * sigma_within)
cpk = min(USL - xbarbar, xbarbar - LSL) / (3 * sigma_within)
pp = (USL - LSL) / (6 * sigma_overall)
ppk = min(USL - mean_all, mean_all - LSL) / (3 * sigma_overall)

print(LABEL)
print("Subgroups:", len(groups), "Readings used:", len(groups) * N)
print("X-bar chart: LCL %.4f  CL %.4f  UCL %.4f" % (lcl_x, xbarbar, ucl_x))
print("R chart:     LCL %.4f  CL %.4f  UCL %.4f" % (lcl_r, rbar, ucl_r))
print("Sigma within %.5f  Sigma overall %.5f" % (sigma_within, sigma_overall))
print("Cp %.3f  Cpk %.3f  Pp %.3f  Ppk %.3f" % (cp, cpk, pp, ppk))

for i, (xb, r) in enumerate(zip(xbars, ranges), start=1):
    flags = []
    if xb > ucl_x or xb < lcl_x:
        flags.append("X-bar beyond limits")
    if r > ucl_r or r < lcl_r:
        flags.append("R beyond limits")
    if flags:
        print("Subgroup", i, "->", ", ".join(flags))