Gage R&R Python Script Generator

# Gage R&R, average and range method. Standard library only.
# Input CSV columns: operator, part, trial, value
import csv
import math
from collections import defaultdict

CSV_PATH = 'grr_study.csv'
TOLERANCE = 0.050
UNIT = 'mm'

# 5.15-sigma (99 percent) constants from the AIAG MSA average and range method
K1 = {2: 4.56, 3: 3.05}
K2 = {2: 3.65, 3: 2.70}
K3 = {2: 3.65, 3: 2.70, 4: 2.30, 5: 2.08, 6: 1.93, 7: 1.82, 8: 1.74, 9: 1.67, 10: 1.62}

cells = defaultdict(list)
with open(CSV_PATH, newline='') as f:
    for row in csv.DictReader(f):
        cells[(row['operator'], row['part'])].append(float(row['value']))

operators = sorted({k[0] for k in cells})
parts = sorted({k[1] for k in cells})
trials = len(next(iter(cells.values())))
n, o, r = len(parts), len(operators), trials
if r not in K1 or o not in K2 or n not in K3:
    raise SystemExit('Layout not covered by the constants table: %d parts, %d operators, %d trials' % (n, o, r))

# Equipment variation (repeatability)
op_rbar = []
for op in operators:
    ranges = [max(cells[(op, p)]) - min(cells[(op, p)]) for p in parts]
    op_rbar.append(sum(ranges) / len(ranges))
rbar_bar = sum(op_rbar) / len(op_rbar)
ev = rbar_bar * K1[r]

# Appraiser variation (reproducibility)
op_mean = []
for op in operators:
    vals = [v for p in parts for v in cells[(op, p)]]
    op_mean.append(sum(vals) / len(vals))
x_diff = max(op_mean) - min(op_mean)
av_sq = (x_diff * K2[o]) ** 2 - (ev ** 2) / (n * r)
av = math.sqrt(av_sq) if av_sq > 0 else 0.0

grr = math.sqrt(ev ** 2 + av ** 2)

# Part variation
part_mean = []
for p in parts:
    vals = [v for op in operators for v in cells[(op, p)]]
    part_mean.append(sum(vals) / len(vals))
rp = max(part_mean) - min(part_mean)
pv = rp * K3[n]

tv = math.sqrt(grr ** 2 + pv ** 2)
ndc = int(1.41 * pv / grr) if grr > 0 else 0

print('Layout: %d parts, %d operators, %d trials' % (n, o, r))
print('EV  (repeatability)   : %.5f %s' % (ev, UNIT))
print('AV  (reproducibility) : %.5f %s' % (av, UNIT))
print('GRR                   : %.5f %s' % (grr, UNIT))
print('PV  (part variation)  : %.5f %s' % (pv, UNIT))
print('TV  (total variation) : %.5f %s' % (tv, UNIT))
print('%%GRR of total variation: %.1f %%' % (100 * grr / tv))
print('%%GRR of tolerance      : %.1f %%' % (100 * grr / TOLERANCE))
print('ndc                   : %d' % ndc)

operator,part,trial,value
A,1,1,0.652
A,1,2,0.648
A,2,1,0.701
A,2,2,0.705
B,1,1,0.650
B,1,2,0.655
B,2,1,0.698
B,2,2,0.703