Process Capability Plot with Specification Limits — Matplotlib

A process capability plot displays a histogram of measured process data overlaid with a fitted normal distribution curve and vertical lines for specification limits (LSL, USL) and target value. Capability indices (Cp, Cpk) are annotated on the plot to quantify how well the process meets specifications. This is a standard tool in quality engineering and Six Sigma for assessing whether a manufacturing or production process is capable of consistently producing output within tolerance.

Process Capability Plot with Specification Limits rendered with Matplotlib

Python source (Matplotlib)

""" anyplot.ai
histogram-capability: Process Capability Plot with Specification Limits
Library: matplotlib 3.11.0 | Python 3.13.14
Quality: 92/100 | Updated: 2026-06-20
"""

import os

import matplotlib.patheffects as pe
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker
import numpy as np
from scipy import stats


# Theme tokens
THEME = os.getenv("ANYPLOT_THEME", "light")
PAGE_BG = "#FAF8F1" if THEME == "light" else "#1A1A17"
ELEVATED_BG = "#FFFDF6" if THEME == "light" else "#242420"
INK = "#1A1A17" if THEME == "light" else "#F0EFE8"
INK_SOFT = "#4A4A44" if THEME == "light" else "#B8B7B0"

# Imprint palette positions used in this chart
BRAND = "#009E73"  # position 1 — histogram bars (first categorical series)
BLUE = "#4467A3"  # position 3 — target line
OCHRE = "#BD8233"  # position 4 — mean line
RED = "#AE3030"  # position 5 — spec limits (semantic: reject / bad zone)

# Data — mean shifted from target to demonstrate Cp vs Cpk distinction
np.random.seed(42)
measurements = np.random.normal(loc=10.008, scale=0.014, size=200)
lsl = 9.95
usl = 10.05
target = 10.00

# Capability indices
mean = np.mean(measurements)
sigma = np.std(measurements, ddof=1)
cp = (usl - lsl) / (6 * sigma)
cpk = min((usl - mean) / (3 * sigma), (mean - lsl) / (3 * sigma))

# Plot
title = "histogram-capability · python · matplotlib · anyplot.ai"
title_fontsize = max(8, round(12 * 67 / len(title))) if len(title) > 67 else 12

fig, ax = plt.subplots(figsize=(8, 4.5), dpi=400, facecolor=PAGE_BG)
ax.set_facecolor(PAGE_BG)

# Histogram — brand green bars with page-background edges
ax.hist(measurements, bins=25, density=True, alpha=0.85, color=BRAND, edgecolor=PAGE_BG, linewidth=0.8, zorder=3)

# Fitted normal curve — theme-adaptive ink color with path effect depth
x_range = np.linspace(lsl - 0.012, usl + 0.012, 400)
y_curve = stats.norm.pdf(x_range, mean, sigma)
ax.plot(
    x_range,
    y_curve,
    color=INK,
    linewidth=2.5,
    zorder=4,
    path_effects=[pe.withStroke(linewidth=4.5, foreground=PAGE_BG, alpha=0.75)],
)

# Rejection regions shaded under curve tails beyond spec limits
ax.fill_between(x_range, y_curve, where=(x_range < lsl), color=RED, alpha=0.20, zorder=2)
ax.fill_between(x_range, y_curve, where=(x_range > usl), color=RED, alpha=0.20, zorder=2)

# Specification limits and reference lines
ax.axvline(lsl, color=RED, linestyle="--", linewidth=2.0, zorder=5, label=f"LSL = {lsl}")
ax.axvline(usl, color=RED, linestyle="--", linewidth=2.0, zorder=5, label=f"USL = {usl}")
ax.axvline(target, color=BLUE, linestyle="-.", linewidth=2.0, zorder=5, label=f"Target = {target:.2f}")
ax.axvline(mean, color=OCHRE, linestyle="-", linewidth=2.0, alpha=0.9, zorder=5, label=f"Mean = {mean:.4f}")

# Capability stats box
verdict = "CAPABLE" if cpk >= 1.0 else "NOT CAPABLE"
verdict_color = BRAND if cpk >= 1.0 else RED
stats_text = f"Cp   = {cp:.2f}\nCpk  = {cpk:.2f}\nσ    = {sigma:.4f}\nn    = {len(measurements)}"
ax.text(
    0.98,
    0.96,
    stats_text,
    transform=ax.transAxes,
    fontsize=8,
    verticalalignment="top",
    horizontalalignment="right",
    fontfamily="monospace",
    color=INK,
    bbox={"boxstyle": "round,pad=0.5", "facecolor": ELEVATED_BG, "edgecolor": INK_SOFT, "alpha": 0.93},
    zorder=6,
)
ax.text(
    0.98,
    0.70,
    verdict,
    transform=ax.transAxes,
    fontsize=9,
    fontweight="bold",
    verticalalignment="top",
    horizontalalignment="right",
    fontfamily="monospace",
    color=verdict_color,
    zorder=6,
)

# Style
ax.set_xlabel("Shaft Diameter (mm)", fontsize=10, color=INK, labelpad=6)
ax.set_ylabel("Density", fontsize=10, color=INK, labelpad=6)
ax.set_title(title, fontsize=title_fontsize, fontweight="medium", color=INK, pad=10)
ax.tick_params(axis="both", labelsize=8, colors=INK_SOFT, labelcolor=INK_SOFT)
ax.xaxis.set_major_formatter(ticker.FormatStrFormatter("%.3f"))
ax.yaxis.grid(True, alpha=0.12, linewidth=0.6, color=INK)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
ax.spines["left"].set_color(INK_SOFT)
ax.spines["bottom"].set_color(INK_SOFT)

# Legend
leg = ax.legend(fontsize=8, loc="upper left", framealpha=0.93)
if leg:
    leg.get_frame().set_facecolor(ELEVATED_BG)
    leg.get_frame().set_edgecolor(INK_SOFT)
    plt.setp(leg.get_texts(), color=INK_SOFT)

# Trim x-axis to bracket spec limits with a small margin — eliminates empty canvas edges
x_lo = min(lsl - 0.010, mean - 4.5 * sigma)
x_hi = max(usl + 0.010, mean + 4.5 * sigma)
ax.set_xlim(x_lo, x_hi)

# Save — no bbox_inches='tight' (would shave canvas pixels)
plt.tight_layout()
plt.savefig(f"plot-{THEME}.png", dpi=400, facecolor=PAGE_BG)

Part of Process Capability Plot with Specification Limits on anyplot.ai.

Process Capability Plot with Specification Limits — Matplotlib

Python source (Matplotlib)

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