Process Capability Plot with Specification Limits — Seaborn

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 Seaborn

Python source (Seaborn)

""" anyplot.ai
histogram-capability: Process Capability Plot with Specification Limits
Library: seaborn 0.13.2 | Python 3.13.14
Quality: 90/100 | Updated: 2026-06-20
"""

import os

import matplotlib.pyplot as plt
import numpy as np
import seaborn as sns
from matplotlib.lines import Line2D
from scipy.stats import norm


# Theme tokens — Imprint palette
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"

BRAND = "#009E73"  # Imprint position 1 — histogram bars
BLUE = "#4467A3"  # Imprint position 3 — theoretical normal fit
CYAN = "#2ABCCD"  # Imprint position 6 — empirical KDE
RED = "#AE3030"  # Imprint position 5 — semantic: spec limits / out-of-spec
AMBER = "#DDCC77"  # Imprint semantic anchor — target / caution

sns.set_theme(
    style="ticks",
    rc={
        "figure.facecolor": PAGE_BG,
        "axes.facecolor": PAGE_BG,
        "axes.edgecolor": INK_SOFT,
        "axes.labelcolor": INK,
        "text.color": INK,
        "xtick.color": INK_SOFT,
        "ytick.color": INK_SOFT,
        "grid.color": INK,
        "grid.alpha": 0.15,
        "legend.facecolor": ELEVATED_BG,
        "legend.edgecolor": INK_SOFT,
    },
)

# Data — pharmaceutical tablet weight QC (target 500 mg, n=200)
np.random.seed(42)
weights = np.random.normal(loc=500.2, scale=2.8, size=200)
lsl = 490.0
usl = 510.0
target = 500.0

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

# Fitted normal distribution curve (scipy — not KDE)
x_fit = np.linspace(lsl - 4, usl + 4, 400)
y_fit = norm.pdf(x_fit, mean, sigma)

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

# Histogram bars
sns.histplot(weights, bins=25, stat="density", color=BRAND, edgecolor=PAGE_BG, linewidth=0.6, alpha=0.70, ax=ax)

# Fitted normal distribution (parametric — theoretical)
ax.plot(x_fit, y_fit, color=BLUE, linewidth=2.5, zorder=5)

# Empirical KDE (seaborn's non-parametric density estimation)
sns.kdeplot(weights, color=CYAN, linewidth=2.0, linestyle=":", ax=ax, zorder=6)

# Specification limit and target lines
ax.axvline(lsl, color=RED, linestyle="--", linewidth=2.0, zorder=4)
ax.axvline(usl, color=RED, linestyle="--", linewidth=2.0, zorder=4)
ax.axvline(target, color=AMBER, linestyle="-.", linewidth=2.0, zorder=4)

# Shaded capability zones
xlim = ax.get_xlim()
ax.axvspan(lsl, usl, alpha=0.05, color=BRAND, zorder=0)
ax.axvspan(xlim[0], lsl, alpha=0.07, color=RED, zorder=0)
ax.axvspan(usl, xlim[1], alpha=0.07, color=RED, zorder=0)

# Capability status color and label
status = "Capable" if cpk >= 1.33 else "Adequate" if cpk >= 1.0 else "Not Capable"
cp_color = BRAND if cpk >= 1.33 else AMBER if cpk >= 1.0 else RED

# Metrics annotation box — status integrated as 5th line
annotation_text = (
    f"Cp     = {cp:.2f}\nCpk   = {cpk:.2f}\nμ       = {mean:.2f} mg\nσ       = {sigma:.2f} mg\nStatus: {status}"
)
ax.text(
    0.975,
    0.96,
    annotation_text,
    transform=ax.transAxes,
    fontsize=8,
    verticalalignment="top",
    horizontalalignment="right",
    family="monospace",
    bbox={
        "boxstyle": "round,pad=0.4",
        "facecolor": ELEVATED_BG,
        "edgecolor": cp_color,
        "linewidth": 1.5,
        "alpha": 0.95,
    },
    color=INK,
)

# Style
title = "histogram-capability · python · seaborn · anyplot.ai"
ax.set_xlabel("Tablet Weight (mg)", fontsize=10, color=INK)
ax.set_ylabel("Density", fontsize=10, color=INK)
ax.set_title(title, fontsize=12, fontweight="medium", color=INK)
ax.tick_params(axis="both", labelsize=8, colors=INK_SOFT)
ax.spines["top"].set_visible(False)
ax.spines["right"].set_visible(False)
for s in ("left", "bottom"):
    ax.spines[s].set_color(INK_SOFT)
ax.yaxis.grid(True, alpha=0.15, linewidth=0.6, color=INK)

# Legend
legend_handles = [
    Line2D([0], [0], color=BLUE, linewidth=2.5, label="Parametric Fit (Normal)"),
    Line2D([0], [0], color=CYAN, linewidth=2.0, linestyle=":", label="Empirical KDE (seaborn)"),
    Line2D([0], [0], color=RED, linestyle="--", linewidth=2.0, label=f"LSL = {lsl:.0f} mg"),
    Line2D([0], [0], color=RED, linestyle="--", linewidth=2.0, label=f"USL = {usl:.0f} mg"),
    Line2D([0], [0], color=AMBER, linestyle="-.", linewidth=2.0, label=f"Target = {target:.0f} mg"),
]
ax.legend(handles=legend_handles, fontsize=8, loc="upper left", frameon=True, framealpha=0.95)

# Save
plt.savefig(f"plot-{THEME}.png", dpi=400, facecolor=PAGE_BG)
plt.close()

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

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