Monte Carlo Tolerance Stack-Up Python Script Generator

import math
import random
import statistics

random.seed(42)
N = 200000
SIGMA_DIV = 3
GAP_MIN = 0.10
GAP_MAX = 0.80

# (name, nominal, +/- tolerance, direction) ; direction +1 adds to the gap, -1 subtracts
DIMS = [
    ('housing_depth', 42.00, 0.10, 1),
    ('bearing_width', 12.00, 0.05, -1),
    ('shaft_shoulder', 28.00, 0.08, -1),
    ('spacer', 1.50, 0.02, -1),
]

nominal_gap = sum(d * nom for _, nom, _, d in DIMS)
worst_range = sum(tol for _, _, tol, _ in DIMS)
rss_range = math.sqrt(sum(tol ** 2 for _, _, tol, _ in DIMS))

gaps = []
for _ in range(N):
    gap = 0.0
    for _, nom, tol, d in DIMS:
        gap += d * random.gauss(nom, tol / SIGMA_DIV)
    gaps.append(gap)

out_low = sum(1 for g in gaps if g < GAP_MIN)
out_high = sum(1 for g in gaps if g > GAP_MAX)
ppm = (out_low + out_high) / N * 1e6

print('Nominal gap        : %.4f mm' % nominal_gap)
print('Worst case range   : %.4f to %.4f mm' % (nominal_gap - worst_range, nominal_gap + worst_range))
print('RSS range (+/-)    : %.4f to %.4f mm' % (nominal_gap - rss_range, nominal_gap + rss_range))
print('Simulated mean     : %.4f mm' % statistics.mean(gaps))
print('Simulated std dev  : %.4f mm' % statistics.pstdev(gaps))
print('Simulated min/max  : %.4f / %.4f mm' % (min(gaps), max(gaps)))
print('Below %.2f mm      : %d of %d' % (GAP_MIN, out_low, N))
print('Above %.2f mm      : %d of %d' % (GAP_MAX, out_high, N))
print('Out of limits      : %.0f PPM' % ppm)
print('Worst case fits?   :', nominal_gap - worst_range >= GAP_MIN and nominal_gap + worst_range <= GAP_MAX)