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.
""" anyplot.ai
histogram-capability: Process Capability Plot with Specification Limits
Library: plotly 6.8.0 | Python 3.13.14
Quality: 90/100 | Updated: 2026-06-20
"""
import os
import numpy as np
import plotly.graph_objects as go
from scipy import stats
# Theme tokens — Imprint palette (see prompts/default-style-guide.md)
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"
INK_MUTED = "#6B6A63" if THEME == "light" else "#A8A79F"
GRID = "rgba(26,26,23,0.15)" if THEME == "light" else "rgba(240,239,232,0.15)"
BRAND = "#009E73" # Imprint position 1 — histogram bars (first series)
LIMIT_COLOR = "#AE3030" # matte red — spec limit boundaries (semantic: bad/rejection)
TARGET_COLOR = "#DDCC77" # amber — target nominal reference line
# Data — shaft diameter measurements (mm), slightly off-center to contrast Cp vs Cpk
np.random.seed(42)
measurements = np.random.normal(loc=10.010, scale=0.012, size=200)
lsl = 9.95
usl = 10.05
target = 10.00
mean_val = np.mean(measurements)
sigma = np.std(measurements, ddof=1)
# Capability indices
cp = (usl - lsl) / (6 * sigma)
cpk = min((usl - mean_val) / (3 * sigma), (mean_val - lsl) / (3 * sigma))
# Normal distribution curve (fitted to sample mean and sigma)
x_min, x_max = 9.925, 10.075
x_curve = np.linspace(mean_val - 4 * sigma, mean_val + 4 * sigma, 300)
y_curve = stats.norm.pdf(x_curve, mean_val, sigma)
# Scale curve to match histogram area (count scale)
bin_width = (measurements.max() - measurements.min()) / 25
y_scaled = y_curve * len(measurements) * bin_width
# Plot
fig = go.Figure()
# Rejection zone shading via vrect — clearly visible background, below all traces
fig.add_vrect(x0=x_min, x1=lsl, fillcolor="rgba(174,48,48,0.10)", line_width=0, layer="below")
fig.add_vrect(x0=usl, x1=x_max, fillcolor="rgba(174,48,48,0.10)", line_width=0, layer="below")
# Histogram bars (Imprint brand green — first categorical series)
fig.add_trace(
go.Histogram(
x=measurements,
nbinsx=25,
marker={"color": "rgba(0,158,115,0.75)", "line": {"color": PAGE_BG, "width": 1.2}},
name="Measurements",
hovertemplate="Diameter: %{x:.4f} mm<br>Count: %{y}<extra></extra>",
)
)
# Normal distribution curve (INK — analytical/structural layer)
fig.add_trace(
go.Scatter(
x=x_curve,
y=y_scaled,
mode="lines",
line={"color": INK, "width": 3.0, "shape": "spline"},
name="Normal Fit",
hoverinfo="skip",
)
)
# LSL vertical line (matte red — rejection boundary)
fig.add_shape(
type="line", x0=lsl, x1=lsl, y0=0, y1=0.90, yref="paper", line={"color": LIMIT_COLOR, "width": 2.5, "dash": "dash"}
)
fig.add_annotation(
x=lsl,
y=0.93,
yref="paper",
text=f"<b>LSL</b><br>{lsl}",
showarrow=False,
font={"size": 11, "color": LIMIT_COLOR},
align="center",
)
# USL vertical line (matte red — rejection boundary)
fig.add_shape(
type="line", x0=usl, x1=usl, y0=0, y1=0.90, yref="paper", line={"color": LIMIT_COLOR, "width": 2.5, "dash": "dash"}
)
fig.add_annotation(
x=usl,
y=0.93,
yref="paper",
text=f"<b>USL</b><br>{usl}",
showarrow=False,
font={"size": 11, "color": LIMIT_COLOR},
align="center",
)
# Target line (amber — nominal reference point)
fig.add_shape(
type="line",
x0=target,
x1=target,
y0=0,
y1=0.90,
yref="paper",
line={"color": TARGET_COLOR, "width": 2.5, "dash": "dashdot"},
)
fig.add_annotation(
x=target,
y=0.93,
yref="paper",
text=f"<b>Target</b><br>{target:.2f}",
showarrow=False,
font={"size": 11, "color": TARGET_COLOR},
align="center",
)
# Capability status
cpk_status = "Capable" if cpk >= 1.33 else "Marginal" if cpk >= 1.0 else "Not Capable"
cpk_flag = "PASS" if cpk >= 1.33 else "WARN" if cpk >= 1.0 else "FAIL"
# Process capability annotation card
fig.add_annotation(
x=0.98,
y=0.86,
xref="paper",
yref="paper",
text=(
f"<b>Process Capability</b><br>"
f"Cp = {cp:.2f} Cpk = {cpk:.2f}<br>"
f"<br>"
f"μ = {mean_val:.4f} mm<br>"
f"σ = {sigma:.4f} mm<br>"
f"<br>"
f"<b>{cpk_status}</b> [{cpk_flag}]"
),
showarrow=False,
font={"size": 11, "color": INK},
align="left",
xanchor="right",
yanchor="top",
bgcolor=ELEVATED_BG,
bordercolor=INK_SOFT,
borderwidth=1.5,
borderpad=10,
)
# Layout
fig.update_layout(
autosize=False,
title={
"text": (
"<b>Shaft Diameter Process Capability</b>"
f"<br><span style='font-size:12px;color:{INK_MUTED}'>"
"histogram-capability · python · plotly · anyplot.ai</span>"
),
"font": {"size": 16, "color": INK},
"x": 0.5,
"xanchor": "center",
"y": 0.97,
"yanchor": "top",
},
xaxis={
"title": {"text": "Shaft Diameter (mm)", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": False,
"zeroline": False,
"showline": True,
"linecolor": INK_SOFT,
"linewidth": 1,
"range": [x_min, x_max],
"dtick": 0.01,
"tickformat": ".2f",
"gridcolor": GRID,
"zerolinecolor": INK_SOFT,
},
yaxis={
"title": {"text": "Frequency", "font": {"size": 12, "color": INK}},
"tickfont": {"size": 10, "color": INK_SOFT},
"showgrid": True,
"gridcolor": GRID,
"gridwidth": 0.5,
"zeroline": False,
"showline": False,
"rangemode": "tozero",
"linecolor": INK_SOFT,
"zerolinecolor": INK_SOFT,
},
template="plotly_white",
paper_bgcolor=PAGE_BG,
plot_bgcolor=PAGE_BG,
font={"color": INK},
bargap=0,
margin={"l": 80, "r": 50, "t": 80, "b": 60},
showlegend=True,
legend={
"font": {"size": 10, "color": INK_SOFT},
"x": 0.02,
"y": 0.78,
"bgcolor": ELEVATED_BG,
"bordercolor": INK_SOFT,
"borderwidth": 1,
},
)
# Save
fig.write_image(f"plot-{THEME}.png", width=800, height=450, scale=4)
fig.write_html(f"plot-{THEME}.html", include_plotlyjs="cdn")
Part of Process Capability Plot with Specification Limits on anyplot.ai.